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NATIONAL UNIVERSITY OF ENGINEERING

COLLEGE OF ENVIRONMENTAL ENGINEERING

SANITARY ENGINEERING PROGRAM

MA113 – MATHEMATICS I

I. GENERAL INFORMATION CODE : AA211 Mathematics I SEMESTER : 1 CREDITS : 4 HOURS PER WEEK : 6 (Theory – Practice) CONDITION : Compulsory II. COURSE DESCRIPTION The course prepares students in the understanding and application of one-dimensional calculus for analyzing and solving engineering problems. The concepts of limits, continuity of real functions, derivatives of real functions and their applications in function approximation and drawing, computation of change rates, and solution of optimization problems are analyzed. The course focus on both, clear understanding of concepts and correct application of methods for solving engineering problems. III. COURSE OUTCOMES

1. Identify the scientific character of Mathematics and appraise the rigor and objectivity of the discipline.

2. Recognize the fundamental theorems of Mathematics and apply them into specific and real problematic situations thoroughly.

3. Understand the concept of limit of a function as well as the concept of a continuity and apply them to analyze diverse problems.

4. Understand the concept of derivative as a basic tool in the study of Mathematics and its engineering applications.

5. Model optimization problems and solve them to find he optimal solution and analyze its characteristics and properties.

6. Draw functions of a real variable analyzing their behavior in different ranges.

IV. COURSE CONTENTS

1. FUNCTIONS Functions / Domain and range / Properties / Functions drawing / Special functions / Algebra of real functions / Composition of functions / Surjective, injective and bijective functions / Inverse functions.

2. LIMITS AND CONTINUITY OF REAL FUNCTIONS Limits of real functions: properties / Calculus of algebraic and trigonometric limits / Lateral limits / Limits involving the infinity: theorems / Indefinite limits and limits at infinity / The

number e as a limit / Asymptotes / Continuity of functions: in a point, in an interval / Properties / Bounded function / Extreme value theorem / Zero theorem.

3. DERIVATIVE OF REAL FUNCTIONS Derivative: geometric interpretation of the derivative / Tangent and normal line / Derivative rules / Rule of the chain: derivative of trigonometric functions / Derivatives of the exponential and logarithmical functions / Derivative of higher order / Implicit derivative / Increasing and decreasing functions / Local maximums and minimums: the second derivative test for extreme values calculus / Concavity and inflection points / Graphical representations of functions / Maximum and minimum problems. 4. APPLICATIONS OF DERIVATIVES Derivative as an instantaneous change rate / Instantaneous velocity and acceleration / De Rolle Theorem and Mean Value Theorem / Criteria of first and second derivatives for relative extreme values / Concave functions and inflexion points / Application of maximum and minimum / L’Hospital rule. 5. FINITE DIFFERENCES Definition / Table of differences / Interpolation / Differences of elemental functions / Polynomials generating n-order differences

V. METHODOLOGY The course takes place in theory and practice sessions. In theory sessions, the instructor presents the concepts, theorems and applications. In practice sessions, different kinds of problems are solved and the solutions are analyzed. Active participation of students is encouraged in all sessions. VI. GRADING SYSTEM The Final Grade (PF) is calculated with the following formula:

PF = (EP + EF + PP) / 3

ME: Mid-term exam EF: Final Exam PP: Average of quizzes

VII. BIBLIOGRAPHY

1. LARSON – HOSTETLER Differential and Integral Calculus Mc Graw Hill, Ed., 2012, Mexico

2. ROSS L. FINNERY Single Variable Calculus Prentice - Hall, Ed., 2012, Mexico




AA221 – MATHEMATICS II

I. GENERAL INFORMATION CODE : AA221 Mathematics II SEMESTER : 2 CREDITS : 4 HOURS PER WEEK : 6 (Theory – Practice) PREREQUISITES : A211 Mathematics I CONDITION : Compulsory II. COURSE DESCRIPTION The course prepares students in the understanding and application of one-dimensional calculus for analyzing and solving engineering problems. Students understand the concepts of anti-derivative, indefinite and definite integrals and their applications for computing areas and volumes. Students also analyze the polar representation of real functions and use them to solve diverse problems. The course focus on both, clear understanding of concepts and correct application of methods for solving engineering problems. III. COURSE OUTCOMES


2. Recognize the fundamental theorems of Mathematics and apply them into specific and real problematic situations thoroughly.

3. Interpret the concept of indefinite and definite integrals and apply integrations methods to calculate areas and volumes.

4. Apply proper integration methods to compute the integral of a function. 5. Apply the integral concepts into Physics: Work / Inertia moments / Center of mass / Gravity

center. 6. Define and apply the polar coordinates into the graphical representations of functions and

into the calculus of surface areas. 7. Calculate integral using numeric methods.

IV. COURSE CONTENTS

1. INDEFINITE INTEGRAL. METHODS OF INTEGRATION Anti-derivative / Indefinite integrals / Immediate integrals / Integration by algebraic substitution / Integration by parts / Integrals of trigonometric functions / Integration by trigonometric substitution / Real function integrations by decomposition into simpler fractions / Integration of rational expressions of trigonometric functions.

2. DEFINITE INTEGRALS

Summations and their properties / Definite integrals: properties / First and second fundamental theorems of calculus / Improper integrals / Improper integrals with non-negative integrands: convergence criteria / Areas of flat surfaces / Volume of a solid of revolution: disc, ring and cylindrical shell methods. 3. TRASCENDENTAL FUNCTIONS Exponential, logarithm and hyperbolic functions / Logarithms and exponentials in different bases / Derivatives and integrals / Integration of trigonometric functions and their inverses / 4. INTEGRATION TECHNIQUES Integration of powers series of trigonometric functions / Integration of rational functions by partial fractions / Integration of sine and cosine rational functions / Integration of non-rational functions / Integration of binomial differentials / Integration by substitution. 5. NON-PROPER INTEGRALS Non-proper integrals of first and second type / Convergence and divergence criteria of non-proper integrals / Gamma function / Beta function / Introduction to first order differential equations / Formulation of problems with differential equations / Separable variables differential equations.

6. APPLICATION OF DEFINITE INTEGRAL Arc length in rectangular coordinates / Work / Inertia moments / Center of mass / Center of gravity / Quadratic surfaces / Polar coordinates / Graphical representations in polar coordinates / Areas in polar coordinates. 7. NUMERIC INTEGRATION Approximation of integrals / Trapeze method / Prism method / Simpson method / Power series: Taylor series, McLaurin series / Approximation of integrals through power series.

V. METHODOLOGY The course takes place in theory and practice sessions. In theory sessions, the instructor presents the concepts, theorems and applications. In practice sessions, different kinds of problems are solved and the solutions are analyzed. Active participation of students is encouraged in all sessions. VI. GRADING SYSTEM The Final Grade (PF) is calculated with the following formula:

PF = (EP + EF + PP) / 3


VII. BIBLIOGRAPHY

1. LARSON – HOSTETLER Differential and Integral Calculus Mc Graw Hill, Ed., 2012, Mexico

2. ROSS L. FINNERY Single Variable Calculus Prentice - Hall, Ed., 2012, Mexico




AA231 – MATHEMATICS III

I. GENERAL INFORMATION CODE : AA231 Mathematics III SEMESTER : 3 CREDITS : 4 HOURS PER WEEK : 6 (Theory – Practice) PREREQUISITES : MA221 Mathematics II CONDITION : Compulsory II. COURSE DESCRIPTION The course prepares students in the understanding and application of multi-dimensional calculus for analyzing and solving engineering problems with application of Physics, Geometry and Optimization. The concepts and methods of vector functions, spatial curves, function of several variables, gradients, directional and partial derivatives, double and triple integrals, line and surface integrals, Gauss and Stokes theorems, and vector fields, are analyzed and applied to model and solve diverse problems. The course focus on both, clear understanding of concepts and correct application of methods for solving engineering problems. III. COURSE OUTCOMES


2. Interpret the concept of vector function and apply it to calculate limits, derivatives and integrals, and appraise its importance in the solution of engineering problems.

3. Understand the concept of real functions or several variables and apply it to calculate limits, partial derivatives, and double and triple integrals.

4. Define and calculate line, rotational integral and apply Green theorem thoroughly. 5. Define and analyze rotational, divergence, surface area, Stokes and Gauss theorems, and

appraise its importance in the solution of engineering problems. IV. COURSE CONTENTS

1. VECTOR FUNCTIONS Vector functions: limit, continuity, derivative, integral, arc length / Fundamental vectors: tangent, normal, binormal / Fundamental planes: oscillator, normal / Curvature and torsion.

2. FUNTIONS OF SEVERAL VARIABLES Real functions of several variables: limit, continuity / Partial derivative / Directional derivative, gradient, tangent plane / Chain rule / Implicit derivative / Second derivative criteria / Maximums

and minimums / Lagrange multipliers for well-conditioned problems / Transformations: polar, cylindrical and spherical coordinates / Double integrals: definition and properties.

3. MULTIPLE INTEGRALS: DOUBLE AND TRIPLE Iterated double integrals, calculus of double integrals over general regions / Change of variable in double integrals / Double integrals in polar coordinates / Applications: area of plane regions, center of mass, moments of inertia / Triple integrals, geometric interpretation, volume / Change of variables in triple integrals / Triple integrals in cylindrical and spherical coordinates.

4. LINE INTEGRALS, STOKES AND GAUSS THEOREM Line integrals: definition and properties / Line integrals independent of paths / Work / Green’s theorem in the plane / Area of the surface / Integral of the surface / Vector fields: rotation and divergence / The flow of vector fields / Stokes’ and Gauss theorems and applications.

V. METHODOLOGY The course takes place in theory and practice sessions. In theory sessions, the instructor presents the concepts, theorems and applications. In practice sessions, different kinds of problems are modeled and solved and their solutions are analyzed. Active participation of students is encouraged in all sessions. VI. GRADING SYSTEM The Final Grade (PF) is calculated with the following formula:

PF = (EP + EF + PP) / 3


VII. BIBLIOGRAPHY

1. STEWART, James Multivariable Calculus I.T.E. Editions, 2014

2. APÓSTOL, Tom Calculus, Vol. II Reverte Ed., 2010




AA212 – BASIC MATHEMATICS I

I. GENERAL INFORMATION CODE : AA212 Basic Mathematics I. SEMESTER : 1 CREDITS : 3 HOURS PER WEEK : 5 (Theory–Practice) PREREQUISITES : --

CONDITION : Compulsory

II. COURSE DESCRIPTION The course prepares students for the analysis and calculation of matrices and their application to solve systems of linear equations. Students analyze and solve problems of analytic geometry including lines and planes in two and three dimensions, as well as conic sections such as circumferences, ellipses, parabolas and hyperbolas. The course provides students with the principles of matrices and analytic geometry to be applied to solve engineering problems. III. COURSE OUTCOMES At the end of the course, students:

1. Analyze the properties of matrices and complete matrix operations including determinant and inverse.

2. Build mathematical models of matrices and system of linear equations to solve practical mining engineering problems.

3. Understand and apply analytic geometry in two and three dimensions 4. Analyze and solve problems of lines in two and three dimensions. 5. Analyze and solve problems in three dimensions. 6. Analyze and apply coordinate transformations (translation and rotation).

IV. LEARNING UNITS

1. MATRICES, DETERMINANTS AND LINEAR EQUATIONS Matrix. Elements. Rows and columns / Order / Types of matrices. Square, null, triangular, diagonal, identity, nilpotent and periodic matrices / Equality of matrices / Operations with matrices. Addition, Multiplication of a scalar by a matrix. Product of matrices / Transpose of a matrix / Symmetric and antisymmetric matrices / Properties of determinants / Non-singular matrix / Inverse matrix / Minors and cofactors of a matrix / Adjoint matrix / Inverse matrix by the method of the adjoint / Determination of the cofactors of a matrix of order 4 / Generalization to matrices of order n / Step matrix / Calculation of the range of a matrix / Calculation of the inverse of a matrix by sequential basic operations / Solution of linear equation systems by matrix methods: Cramer's law, elementary operations.

2. ANALYTIC GEOMETRY IN 2 DIMENSIONS R2: Coordinate system in two dimensions / Distance between two points / Midpoint / Vector space in two dimensions / Radius vector and vector in R2 / Coordinates and representation of vector as oriented segment / Components of vectors in the plane / Equality of vectors, addition and multiplication of a scalar by a vector / Properties of vector operations / Cancellation between two vectors / Dot product / Properties of the dot product / Parallel vectors, geometric interpretation / Orthogonal vectors / Canonical vectors, angles and cosines / Orthogonal projection and component / Applications of vectors.

3. ANALYTIC GEOMETRY IN 3 DIMENSIONS

R3: Coordinate system in three dimensions / Distance between two points / Midpoint. / Vector space in three dimensions / Radio vector and vector in R3 / Coordinates and representation of the vector as oriented segment / Components of vectors in the space / Equality of vectors, addition and multiplication of a scalar by a vector / Operations with vectors / Angle between two vectors / Dot product / Parallel vectors, geometric interpretation / Orthogonal vectors / Canonical vector / Orthogonal projection and components / Vector product / Properties / Geometric interpretation / Applications / Triple dot product / Triple vector product.

4. LINES IN TWO AND THREE DIMENSIONS. PLANES The line in R2. / Tilt and slope / Relationship between slope and directional vector / General equation. Vector equation. Parametric equation / Symmetric equation (Intersection point with the 2 axis) / Angle between lines / Parallelism and orthogonality between lines / Normal equation of a straight line / Area of a triangle / Distance from a point to a line / Distance between parallel lines / Barycenter of a triangle / Lines in the space / Equation / Vector, parametric and symmetrical / Angle between two lines / Planes / Equation of the plane: Vector, parametric, normal, general and symmetric / Intersection point of the 3 axis / Distance from a point to a plane / Distance between parallel planes / Angle between planes / Intersection of planes / Angle between line and plane / Intersection of a straight line with a plane / Distance between two lines.

5. TRANSFORMATIONS R² transformations / Translation and rotation of coordinate axis / Transformation of coordinates of a point and a vector in R² / Transformations in R³ / Translation and rotation of coordinate axis. / Transformation of coordinates of a point in R³. / Determination of the cartesian equation of a geometrical locus from given conditions / Conics / General definition / Determination of the cartesian equation of a geometrical locus from given conditions / The circumference: Definition and elements / General, cartesian and vector equation of the circumference / Tangent and normal lines to a circumference

6. CIRCUMFERENCE AND CONIC SECTIONS The parabola: focus, focal axis, vertex, focal cord, straight side and vector radius / Eccentricity. / Cartesian, general, and vector equations / Tangent and normal lines to a parabola / Polar and vector forms / Applications / The ellipse: focus, focal axis, vertex, focal cord and straight side / Eccentricity / Cartesian, general and vector equations / Tangent and normal lines to an ellipse / Polar and vector representations / Applications / Hyperbola: focus, focal axis, vertex, focal cord and straight side / Eccentricity / Cartesian, general and vector equations / Tangent and normal lines to a hyperbola / Polar and vector representations.

V. PRACTICAL EXPERIENCES:

1. Session 1: Matrices and linear equation systems. 2. Session 2: Analytic geometry in R2 and R3. 3. Session 3: Lines in R2 and R3. 4. Session 4: Transformations, and circumference and conic sections.

VI. METHODOLOGY

The course takes place in theory and practice sessions. In theory sessions, faculty presents the concepts, methods and principles. In practice sessions, students, under the guidance of faculty, solve diverse problems on matrices, analytic geometry, conics and so on. Student active participation is promoted.

VII. GRADING FORMULA

The Final Grade PF is calculated as follow: PF = (EP + EF + PP) / 3

EP: Mid-Term Exam EF: Final Exam PP: Average of 4 Practical Works

VIII. BIBLIOGRAPHY

1. KOLMAN, BERNARD. Linear Algebra, Pearson Ed.

2. GORDON FULLER, DALTON TARWATER. Analytic Geometry, Pearson Ed.




AA222 – BASIC MATHEMATICS II

I. GENERAL INFORMATION CODE : AA222 Basic Mathematics II SEMESTER : 2 CREDITS : 3 HOURS PER WEEK : 5 (Theory–Practice) PREREQUISITES : AA212 Basic Mathematics I


II. COURSE DESCRIPTION The course prepares students for the analysis sequences and series and determining their properties and convergence. Students also complete operations with complex numbers and find the real and complex roots of a given polynomial, compute and interpret the eigenvalues and eigenvector of matrices, and construct the quadratic form of real functions. The course provides students with the principles of series, complex number and matrix transformations to be applied to solve engineering problems. III. COURSE OUTCOMES At the end of the course, students:

1. Analyze the properties of sequences and series determining their convergence and properties.

2. Carry put operations with complex numbers in different representations. 3. Find the roots of a polynomial using exact or numeric methods. 4. Calculate and interpret the eigenvalues and eigenvectors of a matrix. 5. Construct matrix representation of functions.

IV. LEARNING UNITS

1. SEQUENCES IN R Real sequences / Limit of a sequence / Notable limits / Convergence theorems / Divergent sequences / Increasing and decreasing sequences / Bounded sequences.

2. SERIES IN R Real series / Convergence and divergence of series / Notable series. Geometric series / Series properties / Addition of series / Convergence criteria / Absolut convergence / Power series / Convergence (divergence) of power series / Convergence radius / Differentiation and integration of series.

3. COMPLEX NUMBER AND POLYNOMIAL ROOTS System of complex numbers / Real part and imaginary part / Magnitude and angle of complex numbers / Polar form / Exponential form / Operation with complex numbers / Moivre formula / Roots of a complex numbers / Root of grade 3 polynomials / Roots of a polynomial / Algebra fundamental theorem / Solution of polynomial equations / Synthetic division method / Numeric method: Newton method bisection method / Interpolation / Lagrange formula.

4. EIGENVALUES AND EIGENVECTORS

Linear transformations / Translation. Rotation. Dilation. Contraction / Nonsingular transformations / Characteristic polynomial of a matrix / Eigenvalues of a matrix / Eigenvectors of a matrix / Matrix diagonalization. Necessary conditions / Orthogonal matrix / Gram Schmidt process.

5. QUADRATIC FORMS Matrix representation of a quadratic form / Diagonalization of quadratic forms / Identification of conic sections / Identification of quadratic surfaces.

6. VECTOR SPACES Vector spaces / Core / Image / Matrix representation of linear transformations.

V. PRACTICAL EXPERIENCES Session 1: Sequences and series Session 2: Complex numbers and polynomial roots Session 3: Eigenvalues and eigenvectors Session 4: Quadratic forms Session 5: Vector spaces

VI. METHODOLOGY The course takes place in theory and practice sessions. In theory sessions, faculty presents the concepts, methods and principles. In practice sessions, students, under the guidance of faculty, solve diverse problems on series, complex numbers, eigenvalues and eigenvector, quadratic forms. Student active participation is promoted.

VII. GRADING FORMULA The Final Grade PF is calculated as follow:

PF = (EP + EF + PP) / 3

EP: Mid-Term Exam EF: Final Exam PP: Average of 4 Practical Works

VIII. BIBLIOGRAPHY

1. KOLMAN, BERNARD. Linear Algebra, Pearson Ed.

2. GORDON FULLER, DALTON TARWATER. Analytic Geometry, Pearson Ed.

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AA213 – CHEMISTRY I

I. GENERAL INFORMATION CODE : AA213 Chemistry I SEMESTER : 1 CREDITS : 3 HOURS PER WEEK : 5 (Theory – Practice - Laboratory) CONDITION : Compulsory II. COURSE DESCRIPTION The course provides students the knowledge of the fundamental concepts and principles of chemistry for the analysis of the composition, structure, properties and physical and chemical changes of matter. It includes the study of atoms, how they form chemical bonds to create chemical compounds, as well as the interactions between substances through chemical reactions to form different substances. Students also carry out stoicheometry calculations, analyze electrochemical reactions and the chemical equilibrium in compounds and substances. Laboratories experiences are carried out to verify the validity and applicability of chemistry laws and principles. Chemistry problems with engineering applications are analyzed and solved. III. COURSE OUTCOMES

1. Identify the scientific character of Chemistry and appraise the objectivity of the discipline. 2. Work with basic mathematical tools in the study of chemistry. 3. Analyze and interpret chemical transformations. 4. Develop the abilities to model, pose and solve problems related to chemical reactions

and transformations. 5. Analyze, interpret and perform stoichiometric calculations and basic math tools such as:

exponential, logarithmic, Etc. 6. Understand electrochemical processes and the generation of electricity through chemical reactions.

IV. COURSE CONTENTS 1. MATTER AND ATOMIC STRUCTURE Matter / Physical and Chemical Properties / States, changes of state / Classification: mixtures and pure substances / Introduction to the structure of the atom / Electromagnetic Radiation / Planck’s Quantum Theory / Photoelectric effect / Bohr Model / Louis De Broglie Equation / Spectrum of H2 / Quantum mechanics, energy levels / Orbital / Electronic configuration of the atom. 2. PERIODIC TABLE AND CHEMICAL BOND Periodic Table and classification / Periodic Properties: atomic radius, ionization energy, electron affinity / Chemical Bond / Lewis Structure / Octet Rule / Parameters of chemical bonds, energy, length, bond angle / Bond types: ionic, covalent, metallic / Solid State / Amorphous solids, crystalline solids / Classification: ionic, covalent metal / Properties: conductors, semiconductors, insulators. 3. FUNCTIONS AND CHEMICAL REACTIONS

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Valence / Oxidation number / Chemical features: oxides, hydroxides, acids, salts / Inorganic nomenclature / Chemical reactions and types of chemical reactions / Balance of redox reactions by changes in oxidation number. 4. STOICHIOMETRY Key concepts / Gram-atom / Atomic weight / Formula weight / Mole / Avogadro’s number / Equivalent weight / Molar volume / Proximate composition / Stoichiometric ratios: weight-weight, mole-mole, weight-volume / Purity / Percentage yield / Limiting reagent. 5. ELECTROCHEMISTRY AND SOLUTIONS Definition / Electrochemical processes / Galvanic cells / Standard hydrogen potential / Table of potential / potential of cells / Primary and secondary batteries / Electrolysis / Electrolytic cells / Faraday laws / Electrochemical corrosion / Nature of Solutions / Components / Types of solutions / Concentration units: physical and chemical / Dilution / Arrehnius acids and bases / Neutralization. 6. CHEMICAL EQUILIBRIUM AND CHEMICAL ELEMENTS Reversible reactions / reaction speed / Guldberg and Waage and the law of mass action / Chemical Balance / Kc / Ionization of water pH and pOH / Strong electrolytes / Chemical elements: aluminum, carbon, silicon, germanium and copper / Collection / Physical and chemical properties / Alloys / Applications. V. LABORATORY OF CHEMISTRY I

Laboratory 1: Mixture and combination Laboratory 2: Study of flame Laboratory 3: Periodic table Laboratory 4: Chemical bonds and chemical reactions Laboratory 5: Redox reactions Laboratory 6: Stoichiometry Laboratory 7: Electrochemistry

VI. METHODOLOGY The course consists of theory, practice and laboratory sessions. The instructor presents the concepts and chemistry laws and principles using applets and videos. Problems related to engineering are solved with active student participation. Laboratory experiences are carried out using specialized equipment and software simulation. For every experience, students work in group and present a report summarizing main results, analysis and conclusions. Student active participation is promoted. VII. GRADING SYSTEM The Final Grade (FG) is calculated with the following formula:

FG = (EP + EF + PP) / 3

EP: Mid-term exam EF: Final exam PP: Average of quizzes and laboratories VIII. BIBLIOGRAPHY

1. BROWN THEODORE- LEMAY EUGENE. Chemistry: The Central Science Prentice Hall Editorial, 2014

2. CHANG RAYMOND Chemistry McGraw-Hill Editorial, 2012

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AA223 – CHEMISTRY II

I. GENERAL INFORMATION CODE : AA223 Chemistry II SEMESTER : 2 CREDITS : 3 HOURS PER WEEK : 5 (Theory – Practice - Laboratory) PREREQUISTE : AA213 Chemistry I CONDITION : Compulsory II. COURSE DESCRIPTION The course provides students the knowledge of the fundamental concepts and principles of chemical thermodynamics including the first, second and third law of thermodynamics, chemical equilibrium and chemical kinetics for analyzing the speed of chemical reactions. Students also analyze the ionic equilibrium in ionic solutions, and electrochemistry and corrosion processes. III. COURSE OUTCOMES

1. Identify the scientific character of Chemistry and appraise the objectivity of the discipline. 2. Work with basic mathematical tools in the study of chemistry. 3. Analyze and interpret chemical transformations. 4. Develop the abilities to model, pose and solve problems related to chemical

thermodynamics and chemical kinetics. 5. Analyze, interpret and apply the concept of chemical equilibrium and ionic equilibrium. 6. Understand and analyze electrochemistry and corrosion processes.

IV. COURSE CONTENTS

1. CHEMICAL THERMODYNAMICS First thermodynamics law. Thermal chemistry. Hess law. Second thermodynamics law. Third thermodynamics law.

2. CHEMICAL KINETICS Speed of chemical reactions. Gulber and Waage law. Factor affecting speed of reactions. Reaction order. Activation energy and catalyzers.

3. CHEMICAL EQUILIBRIUM Equilibrium and stability. Physical equilibrium and chemical equilibrium. Determination of equilibrium constant. Influence of temperature. Chemical reactions. Le Chatelier principle.

4. IONIC EQUILIBRIUM IN IONIC SOLUTIONS Acids and bases. Theories of Arrhenius, Bronsted-Lowry and Lewis. Strong and weak electrolytes. Ionic equilibrium constant. Ionization degree. Water ionic product. Hydrogen potential pH scale. pOH, pKa, pKb, pKw. Common ion. Salt hydrolysis. Buffer solutions. Solubility. Kps. Acid, base indexes. Titration.

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5. ELECTROCHEMISTRY AND CORROSION REDOX normal potentials. REDOX strength. Galvan cells. Potential of Galvan cells. Nernst equation. Concentration cells. Fuel cells. Corrosion. Corrosion speed. Electrolytic cells. Faraday law.

V. LABORATORY AND PRACTICE

Laboratory 1: Speed of chemical reactions Laboratory 2: Application of LeChatelier principle Laboratory 3: Ionic equilibrium Laboratory 4: REDOX potentials Laboratory 5: Faraday law

VI. METHODOLOGY The course consists of theory, practice and laboratory sessions. The instructor presents the concepts and chemistry laws and principles using applets and videos. Problems related to engineering are solved with active student participation. Laboratory experiences are carried out using specialized equipment and software simulation. For every experience, students work in group and present a report summarizing main results, analysis and conclusions. Student active participation is promoted. VII. GRADING SYSTEM The Final Grade (FG) is calculated with the following formula:

FG = (EP + EF + PP) / 3


1. BROWN THEODORE- LEMAY EUGENE. Chemistry: The Central Science Prentice Hall Editorial, 20102

2. CHANG RAYMOND Chemistry McGraw-Hill Editorial, 2012




AA224 – PHYSICS I

I. GENERAL INFORMATION CODE : AA224 Physics I SEMESTER : 2 CREDITS : 4 HOURS PER WEEK : 6 (Theory – Practice - Laboratory) CONDITION : Compulsory II. COURSE DESCRIPTION The course prepares students in the understanding and application of the fundamentals laws of classis mechanics that models the surrounding physical world. Students apply Newton Laws for analyzing the motion of a particle and a system of particles, as well as the related work and energy and their mechanical transformations. Linear and rotational motions are analyzed and diverse problems related to engineering are solved. Laboratories experiences are carried out to verify the validity and applicability of physics laws. III. COURSE OUTCOMES

1. Analyze the concepts of vector algebra applied to mechanics. 2. Design static equilibrium and apply to specific cases. 3. Specify the equations of motion to specific cases of particles using the differential and integral

calculus. 4. Model the motion of particles relating it to the laws of dynamics. 5. Analyze the concepts of work – energy and energy conservation into conservative and non

conservative areas to specific cases. 6. Select the concepts of kinematics and dynamics applied to a particle system related to the

conservation of the linear momentum and kinetic energy. 7. Specify Newton’s laws and conservation laws of energy applied to rotation and translation of

rigid bodies. IV. COURSE CONTENTS

1. VECTOR ANALYSIS Course general description / Scalar and vector magnitudes / Coordinate System and unit vectors, addition and vector difference / Graphic and analytical methods / Scalar and vector product / Examples.

2. STATIC EQUILIBRIUM Concepts of force / Concurrent force systems / Equilibrium of a particle / Non-concurrent force systems / Torque or moment of force: applications / Center of gravity / Equilibrium of a rigid body / Concepts of static friction: applications.

3. PARTICLE KINEMATICS Differentiation and integrals / Rectilinear and curvilinear motion of a particle: average and instantaneous velocity / Average and instantaneous acceleration / Rectilinear uniform motion / Uniformly varied motion / Varied motion: applications / Projectile motion / Free fall and parabolic motion / Trajectory equation: applications / Circular motion: angular velocity and angular acceleration / Uniform circular motion / Uniformly varied circular motion / Tangential and normal components of acceleration: applications.

4. PARTICLE DYNAMICS Concepts of force / Friction force / Coefficient of friction: static and dynamic / Applications / Newton's laws / Internal and external forces / Inertial mass / Force and linear momentum: applications.

5. WORK AND ENERGY Concept of work / Work of constant and variables forces / Kinetic energy / Theorem of work and kinetic energy / Potential energy: applications / Conservative forces / Elastic and gravitational force / Gravitational and elastic potential energy / Mechanical energy / Power: applications / Principle of energy conservation / Conservative and non-conservative systems / Particle system and its relation to the case of a particle: applications.

6. PARTICLE SYSTEMS Dynamics of a particle system / Center of mass (CM) / CM movement / Velocity and acceleration / Linear momentum of a particle system: applications / Conservation of the linear momentum / Kinetic and potential energy of a particle system / Elastic and inelastic collisions / One-dimensional and two-dimensional collision: applications.

7. ROTATIONAL DYNAMICS OF SOLID Rotational motion of a particle system / Conservation of angular momentum / Moment of inertia of a particle system and a rigid body / Torque and angular momentum / Torque and moment of inertia: applications / Kinetic energy of a rigid body / Kinetic energy of rotation and translation / Energy conservation / Kinetic energy and moment of inertia / Mechanical energy of a rigid body: applications.

V. PRACTICE AND LABORATORY EXPERIENCES

Laboratory 1: Measurements and curve fitting Laboratory 2: Instantaneous velocity and acceleration Laboratory 3: Relative motion Laboratory 4: Two dimensional motion and collision Laboratory 5: Work and energy Laboratory 6: Gravitational and elastic potential energy

VI. METHODOLOGY The course consists of theory, practice and laboratory sessions. The instructor presents the concepts and physical laws using applets, videos and formulating equations using differential and integral expressions. Problems related to engineering are solved with active student participation. Laboratory experiences are carried out using specialized equipment and software simulation. For every experience, students work in group and present a report summarizing main results, analysis and conclusions. VII. GRADING SYSTEM The Final Grade (FG) is calculated with the following formula:

FG = (EP + EF + PP) / 3

EP: Mid-term exam EF: Final exam PP: Average of quizzes and laboratories

VIII. BIBLIOGRAPHY

1. Sears-Zemansky-Young-Freedman University Physics Vol. 1, 2010, 12th Ed. Pearson Education.

2. Resnick-Halliday-Krane Physics, Vol. 1. 2011, 5th Ed. CECSA.




AA234 – PHYSICS II

I. GENERAL INFORMATION CODE : AA234 Physics II SEMESTER : 3 CREDITS : 4 HOURS PER WEEK : 6 (Theory – Practice - Laboratory) PREREQUISITES : AA224 Physics I CONDITION : Compulsory II. COURSE DESCRIPTION The course prepares students in the understanding and explaining the physical phenomena related to periodic motion, oscillatory motion, fluid mechanics and thermodynamics. Student applies thermodynamic laws to analyze heat transfer and energy transformation in thermodynamic processes. Laboratories experiences are carried out to verify the validity and applicability of physics laws. Physics problems with engineering applications are analyzed and solved. III. COURSE OUTCOMES

1. Describe the basic mechanical deformations of solids. 2. Analyze, describe and depict the oscillatory motion, according with kinematic, dynamic and

energetic theory. 3. Describe and depict transverse, longitudinal and travelling waves. 4. Formulate, interpret and apply the basic principles and laws governing fluid statistics and

dynamics. 5. Describe and apply the concepts of temperature and heat in order to understand the

thermal properties of matter. 6. Distinguish, depict and apply microscopic and macroscopic models of gases and apply its

laws into thermodynamics. 7. Formulate and interpret thermodynamic laws governing heat, work and energy

transformations in thermal processes. IV. COURSE CONTENTS

1. ELASTICITY Elasticity of materials / Stress and deformation / Hooke’s law / Elastic modulus / Elastic energy.

2. OSCILLATIONS Simple harmonic motion (SHM) / Kinematics of SHM / Dynamics of SHM / Simple harmonic oscillator energy / Damped harmonic motion / Forced oscillations and resonance / Combinations of SHM.

3. MECHANICAL WAVES Wave concept / Characteristics of waves / Types of wave / Mathematical description of one-dimensional waves propagation / Sinusoid or harmonic wave / Velocity of wave propagation / Oscillation velocity / One-dimensional wave equation / Wave power and intensity / Superposition principle / Harmonic wave interference / Standing and harmonic waves / Sound waves / Characteristics / Sound waves power and intensity / Vibrations and sound origin / Doppler effect.

4. FLUIDS Fluids statistics / Density / Specific weight and pressure / Variation in a fluid with depth / Pascal and Archimedes principle / Fluids dynamics / Motion characteristics / Ideal fluid / Fluid lines / Fluid tube / Continuity and Bernoulli equation / Real fluids and viscosity / Poiseuille equation.

5. HEAT AND TEMPERATURE Temperature / Macroscopic and microscopic description of a system / Temperature concept / Thermal equilibrium / Temperature measurement and temperature scales / Thermal expansion / Heat concept / Internal and Thermal energy / Heat capacity / Specific heat / Mechanical equivalent of heat / Changes of state / Heat transfer / conduction, convection and radiation.

6. GASES Ideal gas / Macroscopic description / Equation of state / Microscopic description of an ideal gas / Kinetic theory / Molecular model of an ideal gas / Pressure Kinetic calculus / kinetic interpretation of temperature / Internal energy / Theorem of Energy Equipartition / Heat capacity of ideal gases / Real gases.

7. HEAT AND THE FIRST LAW OF THERMODYNAMICS Heat and work / Internal energy / Heat capacity and specific heat / Internal energy of an ideal gas / Phase changes / Latent heat of melting and vaporization / First thermodynamics law / Heat and work in thermodynamic processes / Application of first law of thermodynamics / Heat transfer: conduction, convection and radiation.

8. THERMAL MACHINES, ENTROPY AND SECOND LAW OF THERMODYNAMICS Thermal machines / Second thermodynamics law / Reversible and non-reversible processes / Carnot machine / Coolers and freezers / Entropy / Changes of entropy in non-reversible processes.

V. LABORATORY EXPERIENCES

Laboratory 1: Elasticity and Hooke law Laboratory 2: Simple Harmonic motion Laboratory 3: Vibrating waves Laboratory 4: Density and surface tension Laboratory 5: Linear dilation Laboratory 6: Specific heat of solids

VI. METHODOLOGY The course consists of theory, practice and laboratory sessions. The instructor presents the concepts and physical laws using applets, videos and formulating equations using differential and integral expressions. Problems related to engineering are solved with active student participation. Laboratory experiences are carried out using specialized equipment and software simulation. For every experience, students work in group and present a report summarizing main results, analysis and conclusions. VII. GRADING SYSTEM The Final Grade (FG) is calculated with the following formula:

FG = (EP + EF + PP) / 3


1. R. A. Serway Physics, Vol I, Mc Graw-Hill Interamerica, 2005





FI403 – PHYSICS III

I. GENERAL INFORMATION CODE : FI403 Physics III SEMESTER : 4 CREDITS : 5 HOURS PER WEEK : 7 (Theory – Practice - Laboratory) PREREQUISITES : AA234 Physics II CONDITION : Compulsory II. COURSE DESCRIPTION The course prepares students in the understanding and explaining the physical phenomena related to electricity and magnetism and their interactions. Students analyze the principles of electrostatics and magnetism, electric and magnetic fields, electromagnetism and their application in mechanical-electrical energy transformations. Direct current and alternating current circuits with diverse configurations are solved. The concept of impedance is applied for analyzing resonance and power factor in alternating current circuits. Laboratories experiences are carried out to verify the validity and applicability of physics laws and principles. Physics problems with engineering applications are analyzed and solved. III. COURSE OUTCOMES

1. Apply the fundamental principles of Electrostatics, Electricity and Magnetism. 2. Identify the parameters related to Electrostatics, Electricity and Magnetism. 3. Understand the static manifestation and the dynamics of electric charges. 4. Understand the magnetic effects under the electric charges and conduct wires. 5. Understand the mechanical-electrical transformations in changing electromagnetic fields. 6. Analyze and solve direct current circuits with diverse configurations. 7. Analyze and solve alternating current circuits, transient responses, phasor representation

and power factor. IV. COURSE CONTENTS

1. ELECTROSTATICS Charge and Coulomb’s law / Electric charge and matter / Electrization phenomena /

Conductors and insulators / Coulomb’s law / Definition / Electric field lines / Electric field of a punctual and continuous charges / Gauss’s law / Electric field of an infinite line and uniform charged-plane / Punctual charges motion in a constant electric field / Applications: Cathode ray tubes / Electric power / Electric potential energy / Potential difference / Electric potential / Potential calculus: punctual and continuous charges / Relation between field and potential / Equipotential curve / Electrostatic properties of conductors / Electric dipole / Capacitor and dielectric / Capacitance / Parallel plate capacitor / Series and parallel capacitor / Energy stored / Dielectric capacitor.

2. CONTINUOUS CURRENT CIRCUITS Electric current / Introduction / Electric current intensity / Current density / Ohm’s law,

conductivity, resistivity and resistance / Power / Joule effect / Continuous current circuits /

Resistance in series and parallel / Continuous current circuits / Electromotive force / Ammeter, voltmeter, ohmmeter / Kirchhoff’s laws / RC circuit / Charge and discharge of a capacitor graph / Current and voltage relation with time.

3. ELECTROMAGNETISM Magnetic field / Introduction / Magnetic induction, definition / Field lines / Force on a charge in

motion / Force on a conductor wire / Magnetic momentum / Application: DC motor / Currents as sources of magnetic fields / Bio–Savart and Ampere’s law / Field produced by straight cables and circular loops / Filed inside a coil / Magnetism / Experimental study on magnetic induction / Magnetic force on charges in motion / Magnetic force on a conductor with current / electromagnetic induction / Magnetic flux / Electromotive force and inductive current / Faraday and Lenz law / Transformer.

4. ALTERNATING CURRENT CIRCUITS Alternating current (AC) / Introduction / Parameters of a sinusoidal current: amplitude,

frequency, period, phase angle / Effective values / Dephase / Series RLC circuit / Parallel RLC circuit / Wave representations / Phasor representations / Impedances, reactances and inductances / Dephase of signals / Resonance / AC circuit / Analysis of alternating current circuits / Phasorial calculus of impedances, voltages and currents / Power factor.

5. MAXWELL EQUATIONS

Ampere-Maxwell law / Differential form / Electromagnetic waves / Maxwell equations.

V. LABORATORY AND PRACTICE Laboratory 1: Electrostatics Laboratory 2: Equipotential curves Laboratory 3: Electric field Laboratory 4: Magnetic field Laboratory 5: Charge and discharge of a capacitor. Use of oscilloscope Laboratory 6: Alternating current circuits VI. METHODOLOGY The course consists of theory, practice and laboratory sessions. The instructor presents the concepts and physical laws using applets, videos and formulating equations using differential and integral expressions. Problems related to engineering are solved with active student participation. Laboratory experiences are carried out using specialized equipment and software simulation. For every experience, students work in group and present a report summarizing main results, analysis and conclusions. Student active participation is promoted. VII. GRADING SYSTEM The Final Grade (FG) is calculated with the following formula:

FG = (EP + EF + PP) / 3


1. R. A. Serway Physics, Vol. 2, Mc Graw-Hill Interamerican, 2012





AA233 – PHYSICAL CHEMISTRY I

I. GENERAL INFORMATION CODE : AA233 Physical Chemistry SEMESTER : 3 CREDITS : 3 HOURS PER WEEK : 5 (Theory, Practice, Laboratory) PREREQUISITES : AA223 Chemistry II, AA221 Mathematics II


II. COURSE DESCRIPTION The course prepares students in the application of physics and chemistry laws for analyzing processes involving physical and chemical transformations. Physical-chemical calculations methods are applied to optimize the behavior and outcomes physical-chemical processes including one-component and multi-component systems, homogeneous and heterogeneous systems, as well as electrolytic and non-electrolytic solutions. Students carry out laboratory experiences to verify theoretic developments.

III. COURSE OUTCOMES At the end of the course, students:

1. Resolve problems applying the laws of physics and chemistry to different physical-chemical processes and verify them in the laboratory.

2. Complete kinetic and thermodynamic calculations to predict the spontaneity and speed of physical-chemical processes in order to optimize their efficiency.

3. Analyze phase diagrams to separate and purify with effectiveness the mixtures that are found in different aggregation stages.

IV. LEARNING UNITS

1. INTRODUCTION The nature of physical-chemical sciences / The place of physical chemistry in the science system and its importance in the study of environment and industrial development / Physical-chemistry and mining / Review of thermodynamic laws.

2. PHASE EQUILIBRIUM IN ONE-COMPONENT SYSTEMS Thermodynamics of phase transformations / Clausius-Clapeyron equation / Phase diagrams of one-component systems: water, carbon dioxide, sulfur and phosphorus.

3. HOMOGENEOUS MULTICOMPONENT SYSTEMS. NON-ELECTROLYTIC SOLUTIONS Definition and classification of solutions / Vapor pressure of solutions / Units of multicomponent systems concentration / Chemical potential / Partial molar quantities / Criterion for phase equilibrium / Gibbs-Duhem equation / Mixture of ideal gases / Mixture of real gases / Ideal liquid solutions / Law of Raoult / Composition, vapor pressure diagrams / Positive and negative deviations of Raoult law / Henry's law / Colligative properties / Vapor pressure decrease / Boiling point increase / Freezing point decrease / Osmosis / Osmotic pressure / Non-ideal solutions / Activity and activity coefficient.

4. PHASE EQUILIBRIUM IN MULTICOMPONENT SYSTEMS Gibbs’s phase law / Vapor-liquid equilibrium in two component systems / Temperature-composition diagrams / Distillation / Azeotropes / Fractional distillation / Distillation of immiscible liquids / Distillation of partially miscible liquids / Liquid-liquid equilibrium in two component systems / Critical temperature of solubility / Solid-liquid equilibrium in two-component systems / Thermal analysis / Crystallization curves / Simple eutectic phase diagrams / Formation of compounds with congruent melting point / Formation of compounds with incongruent melting point / Partial miscibility in solid stage with eutectic. / Partial miscibility in solid state with peritectic / Three component systems.

5. ELECTROLYTE SOLUTIONS Definition and classification of electrolytes / Colligative properties of electrolytes / Van´t Hoff factor / Arrhenius electrolytic dissociation theory / Law of dilution of Ostwald / Chemical potentials in electrolyte solutions / Debye-Hückel theory / Ionic strength / Activity and electrolyte activity coefficients / Electric conductivity of electrolyte solutions / Molar conductivity / Equivalent conductivity / Independent ion migration / Kohlrausch law / Ionic mobility / Transport numbers / Experimental methods of determination of transport numbers / Electrochemical cell / Standard electrode potentials / Thermodynamics of electrochemical cells / Nernst equation / Classification of electrochemical cells / Applications of EMF determinations / Electrolysis. / Faraday laws in electrolysis.

6. CHEMICAL KINETICS Classification of kinetic reactions / Homogeneous reactions / Heterogeneous reactions / Order and molecularity of reactions / Speed constant / Analysis of kinetic results / Method of integration / Chemical average life / Differential method / Types and kinetics of compound reactions / Opposite reactions / Influence of temperature in reaction speed / Arrhenius equation / Activation energy / Pre-potential factor.

V. LABORATORY AND PRACTICAL EXPERIENCES

Laboratory 1. Phase equilibrium in one-component system Laboratory 2. Non-electrolytic solutions Laboratory 3. Phase equilibrium in multi-component systems Laboratory 4. Electrolyte solutions Laboratory 5. Chemical kinetics

VI. METHODOLOGY The course takes place in theory, practice and laboratory sessions. In theory sessions, faculty presents concepts, laws and applications. In practice sessions, various problems are solved and their solution analyzed. In laboratory sessions students carry out experiments to verify physical-chemistry theory. At the end of each laboratory experience, students present report summarizing main findings, results and conclusions. Student’s active participation is promoted throughout the course.


PF = (EP + EF + PL) / 3

EP: Mid-term Exam. EF: Final Exam. PL: Average of Laboratory and Practice Works.

VIII. BIBLIOGRAPHY

1. ADAMSON ARTHUR W. Physical Chemistry, Reverte Editorial, Barcelona, Spain.

2. ADAMSON ARTHUR W. Physical Chemistry - Problems and Applications, Reverte Editorial, Barcelona, Spain.

3. CASTELLAN GILBERT W. Physical Chemistry – Pearson Education, Spain.

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AA232 – BIOSTATISTICS

I. GENERAL INFORMATION CODE : AA232 Biostatistics SEMESTER : 3 CREDITS : 4 HOURS PER WEEK : 6 (Theory – Practice – Labs) PREREQUISITES : AA221 Mathematics II CONDITION : Compulsory II. COURSE DESCRIPTION This course prepares students in the application of concepts, methods and techniques of the differential and descriptive statistics to describe and analyze data and variable sets. Concepts of probability and random variables are introduced and applied to predict expected future values. Regression techniques are applied to build models relating a data and variable set. Problems of engineering application are solved and specialized software is used too. III. COURSE OUTCOMES

1. Organize data for their adequate analysis and interpretation and calculate and interpret their fundamental statistical properties (Average value y variance).

2. Explain and determine the random probability of events and variables, as well as their probability density function.

3. Understand and apply random vectors and determine their function of joint probability density. 4. Interpret the concept of sampling distribution and apply it to calculate the probability of an event

or variable. 5. Build models of linear regression to represent the relationship between the representative

parameters of a data set. 6. Apply chi-square tests to check the probability density function of a data set, as well as the

dependence or independence of two variables.

IV. LEARNING UNITS 1. DATA ORGANIZATION AND MAIN STATISTICAL PARAMETERS / 8 HOURS Statistics / Population, sample and variable / Classification of variables / Methods for organizing and presenting data / Qualitative data / Frequency distribution table / Graphic representations / Measures of central tendency: mean, median, weighted mean / Dispersion methods: variance, standard deviation, coefficient of variation / Measures of quartile, decile and percentile positions / Box plots. 2. PROBABILITY / 8 HOURS Count methods / Addition and multiplication rules / Permutations and combinations / Probability / Random experiments, sampling space and events / Operations with events / Conditional probability / Total probability / Bayes’ theorem / Tree chart / Independent events. 3. RANDON VARIABLES AND PROBABILITY DISTRIBUTION / 12 HOURS Random variable: Types, expected value and standard deviation / Distribution of probability of a discrete variable: binomial, Poisson and hyper-geometric / Distribution of probability of a continuous variable: uniform, normal, gamma and exponential.

2

4. RANDOM VECTORS / 4 HOURS Joint probability density function / Marginal distribution / Expected vector, variance and covariance / expected value of two random functions / Covariance of two random variables. 5. SAMPLING DISTRIBUTION / 4 HOURS Sampling / Sampling techniques / Probability sampling / Sampling distribution of average value, the variance / Central limit theorem. 6. ESTIMATION AND HYPOTHESIS TESTING / 12 HOURS Punctual estimation of a random sampling / Punctual estimators: mean, mean proportional, difference of means, variance / Hypothesis testing / Interval estimation. Confidence intervals: mean, mean proportional and variance / Hypothesis testing / Types of error / Correlation coefficient / Prediction intervals / Hypothesis testing on regression coefficients. 7. REGRESSION AND CORRELATION ANALYSIS / 8 HOURS Simple regression / Scatter plot / Parameter estimation / Total variance decomposition / Determination coefficient / Estimation errors / Correlation coefficient / prediction intervals / Hypothesis testing on regression coefficients. 8. CHI-SQUARE TESTS / 8 HOURS Setting tests for uniform, binomial and Poisson’s distributions / Contingency tables / Independence tests, V. LABORATORIES AND PRACTICAL EXPERIENCES Lab 1: Generation of random signals. Lab 2: Determination and graphs of the probability density function. Lab 3: Linear and quadratic regression. VI. METHODOLOGY This course is carried out in theory, practical and lab sessions. In theory sessions, the instructor introduces concepts, theorems and applications. In practical sessions, several problems are solved and their solution is analyzed. In lab sessions, Minitab simulation software is used to solve problems and analyze their solutions. At the end of the course, students should hand in and expose an integrating paper and project. In all sessions, students’ active participation is encouraged. VII. EVALUATION FORMULA The average grade PF is calculated as follows: PF = 0.25 EP + 0.25 EF + 0.10 P1 + 0.10 P2 + 0.07 L1 + 0.07 L2 + 0.07 L3 + 0.09 TF

EP: Mid-Term Exam EF: Final Exam TF: Final paper P#: Quizzes L#: Final paper

VIII. BIBLIOGRAPHY

1. MENDENHALL, WILLIAM Statistics and probability for engineering (Spanish) Prentice Hall Editorial (2012)

2. ALVAREZ, JOSÉ AND TORRES LUIS Probability and Statistics (Spanish) Alfa Omega Editorial (2012)

3. MONTGOMERY, DOUGLAS AND RUNGER GEORGE Probability and Statistics Applied to Engineering (Spanish) McGraw Hill Editorial (2010)

1




AA216 - COMPUTER PROGRAMMING I

I. GENERAL INFORMATION CODE : AA216 Computer Programming I SEMESTER : 1 CREDITS : 2 HOURS PER WEEK : 4 (Theory – Practice) PREREQUISITES : None CONDITION : Compulsory II. COURSE DESCRIPTION

The purpose of this course is to train students in the use of programming languages so they can be applied in later courses and professional career. This course deals with subjects such as: algorithms, standard functions, decision, repetition, selection and control instructions, array, functions and pointers. Students develop computer programs applied to diverse engineering problems. III. COURSE OUTCOMES

1. Understand the steps for solving computer programming problems. 2. Analyze and design algorithms for solving a specific problem. 3. Develop programs using a programming language in the solution of problems of practical

cases applied to engineering projects. 4. Understand step by step the developing of computer programs. 5. Properly use programming languages for the scientific and technological research.

IV. LEARNING UNITS

1. PROGRAMMING FUNDAMENTALS / 8 HOURS Introduction / Definition of problems and casuistries / Concept of program and instructions /Programming languages and source code / programming steps / Concepts and characteristics of algorithms / Decision, repetition and control algorithms / Flow diagrams and their symbols / Diagramming and pseudocodes / Diagrams with decisions and repetitions.

2. INPUT/OUTPUT INSTRUCTIONS AND OPERATIONS / 8 HOURS Structure of a program, types and methods / Programming rules and its libraries / data, constant and variables concept / Types of data / variable declaration: int, float, char, long, double/ Input instructions Console()/ output instructions Console.Write()/ Arithmetic operators and their rules / mathematical operations, priorities and use of parenthesis / Assignment statement and its rules / Type conversions / Math functions: / Multiple assignments and include operator / Operators: ++.

3. REPETITION AND DECISION INSTRUCTIONS / 8 HOURS Logic operators: ==, !=, >, <, >=, <= / Logic operators: !, &&. || / Rules / Logics. Algorithms and diagrams with decisions. / Logics / Instruction “if-else”, syntax and rules / Instruction “only If”, “if-else” with bocks, “If within if” / Algorithms and programs with “if-else” / Instruction “while”, syntax and rules / Instructions “while” with an instruction and with a block of instructions / Instructions do-while, syntax and rules / Algorithms and programs with do-while.

4. SELECTION AND CONTROL INSTRUCTIONS / 8 HOURS

2

Instruction “for”, start expression. Assessment and preparation / Control, syntax and rules / Instruction “for” with one instruction and with a block of instructions / “For” nested instructions, “internal” for and “external” for / Algorithms and programs with “for” and “nested for”, “nesting” / Until instruction “for” / Switch-case instruction, syntax and rules / Break instruction, syntax and rules / Use of “break” within switch-case / “Continue” instructions.

5. ARRAYS / 8 HOURS Concept of array, declaration, subscript. Syntax and rules / reading and writing of arrays of one dimension / Sorting and deleting of the elements of an array / Operations with one-dimensional arrays / String arrays, string reading and writing / Comparisons and initializations of strings / String internal functions / Two-dimensional arrays, syntax and rules / Subscripts, addresses and declarations of two-dimensional arrays / Reading, writing and operations with two-dimensional arrays / Multidimensional arrays, syntax, rules and uses / Matrix operations.

6. FUNCTIONS / 8 HOURS Concept of function, syntax and rules / Definition of a function, arguments and parameters / Local and global variables / Call of a function and transfer values / Typical variables of a function, repeated execution of a function / Return instruction / One-function algorithms and programs / Programs with several function and their iterative function / Concept of recursion / programs with function recursion / Functions with scripts / Reading and writing functions.

7. POINTERS / 8 HOURS Concept of pointer and pointer assignment / Values exchange among arguments and parameters / Declaration, rules, syntax and pointers / Pointers to arrays / Pointers to scripts / Algorithms and programs with pointers / Concept of pointer array, syntax and rules / Pointer array addressing / Algorithms and programs with pointer array / Algorithms and programs with pointer’s pointer.

V. LABORATORY EXPERIENCES

Lab 1: Decision instructions. Lab 2: Repetitive instructions. Lab 3: Array and selection sentences. Lab 4: Functions and pointers. VI. METHODOLOGY

Sessions will be carried out stimulating students’ active participation, through practical cases programming. Students will form groups for researching and exchanging learning and work experiences. The instructor’s expositions will guide every programming work and they will also advised be individually and in groups using real applications. Lab practical sessions will complement knowledge and develop students’ skills and abilities in problem solving through programming language techniques. Papers’ originality and creativity will be motivated encouraging a constant research. VII. EVALUATION FORMULA

The average grade PF is calculated as follows: PF = 0.25 EP + 0.50 EF + 0.15 PP + 0.10 PL

EP: Mid-Term Exam EF: Final Exam PP: Average of five quizzes PL: Average of four laboratory reports

VIII. BIBLIOGRAPHY

1. JOYANES, LUIS C# Programming Mc Graw – Hill, 2011

2. SCHILDT, Herbert Turbo C Programming Osborne/McGraw-Hill, 2012




AA236 – COMPUTER PROGRAMMING II

I. GENERAL INFORMATION CODE : AA236 Computer Programming II SEMESTER : 3 CREDITS : 2 HOURS PER WEEK : 4 (Theory – Practice) PREREQUISITES : AA216 Computer Programming I CONDITION : Compulsory II. COURSE DESCRIPTION At the end of this course, students will be able to solve medium-complexity problems through computer programs. This course is made up of six subject units: classification and encapsulation; arrays, Inheritance, interfaces, polymorphism, multimedia, images, and application project. III. COURSE OUTCOMES

1. Apply programming characteristics with classes and objects in the programs development. 2. Use the concept of heritance and polymorphism for the code reuse. 3. Implement methods for solving problems using arrays (vectors and matrices). 4. Carry out auto-documented and sorted programs development works. 5. Carry out research on Object-oriented Programming topics.

IV. LEARNING UNITS 1. CLASSIFICATION AND ENCAPSULATION / 18 HOURS Classification / Classes and objects / Methods / Encapsulation / Access modifier / The reference “this” / Methods overloading / Instance member / Class members (Static).

2. ARRAYS, STRINGS / 36 HOURS 1-level array: vectors / Definition of vectors / Solution to vector problems: sorting, search and other problems / 2-level array: matrices / Definition of matrices /Solution to matrices problems / Objects array / Solution of problems involving object vectors and matrices / Strings / Solution to problems involving strings / Use of predefined library for the string work. 3. HERITANCE AND INTERFACES / 27 HOURS Heritance: Concepts and application / Superclasses / Subclasses, hierarchy of classes / Heritance: Types / Simple heritance / Interfaces: Introduction to interfaces / Interfaces applications / Interface hierarchies.

4. POLYMORPHISM / 18 HOURS Static polymorphism: Methods overloading, conductor overloading, methods superimposition / Dynamic polymorphism from methods superimposition / Interfaces and polymorphism.

5. MULTIMEDIA AND IMAGES / 18 HOURS Multimedia: basic concepts / Image file formats / Multimedia: produced images creation and show / Images file show / use of images. 6. INTERMEDIATE-COMPLEXITY APPLICATION PROJECT / 9 HOURS Execution and introduction of an intermediate-complexity application (team work). V. LABORATORIES AND PRACTICAL EXPERIENCES: Lab 1: Classification and encapsulation. Lab 2: Arrays. Lab 3: Heritance and interfaces. Lab 4: Polymorphism. Lab 5: Multimedia: Images. VI. METHODOLOGY The course is carried out in theory, lab and workshop sessions; there is one computer available for each student, and the instructor has a projector and a computer too. In theory sessions, the instructor introduces concepts and explains how lab guide problems should be solved. In lab and workshop sessions, Java Netbeans programming language is used for encoding the proposed solutions in theory sessions. Lab guides and offprints are published in the virtual campus. At the end of the course, students must hand in and expose a group application paper of intermediate complexity. In all sessions, feedback is required: answer to questions and constant reinforcements, encouraging students’ active participation. VII. EVALUATION FORMULA The average grade PF is calculated as follows: PF = 0.1*PA + 0.04*(G1 + G2 + G3 + G4 + G5) + 0.2*TA + 0.25*EP + 0.25*EF

EP: Mid-Term Exam EF: Final Exam TA: Application paper PA: Active participation G#: Course guides

VIII. BIBLIOGRAPHY

1. BOBADILLA, JESÚS Java Through Examples (Spanish) Ra-Ma Editorial, 2006

2. CEBALLOS, FRANCISCO JAVIER Java 2: Programming Course Alfaomega Editorial, 2005

3. DEITEL, HARVEY Programming in Java Pearson Education, 2005




AA215 – GEOLOGY

I. GENERAL INFORMATION CODE : AA215 Geology SEMESTER : 1 CREDITS : 3 HOURS PER WEEK : 4 (Theory – Practice) PREREQUISITES : None CONDITION : Compulsory II. COURSE DESCRIPTION Identify soils and rocks upon which mining engineering works are built, and have a vast knowledge about several geological phenomena related to diverse types of engineering problems and constructions. Every single class students carry out workshop. Students will be provided knowledge about minerals, soils and rocks, tectonics, valleys, groundwater, geological planes, photogeology, the rock as construction material, tunnels, coastal defense, sedimentation, constructions, bridges, pavement, airports, dams, soil removal, channels, external geodynamics and internal geodynamics. III. COURSE OUTCOMES

1. Students should be able to describe and analyze several geological processes that occur on Earth.

2. Students will be able to identify and describe the geological context in the application to several civil engineering works.

IV. LEARNING UNITS

1. ROCKS AND TECTONICS / 4 HOURS Classification of rocks: igneous rock and its minerals / sedimentary rock and its minerals / metamorphic rocks and its minerals / Rock engineering properties. Structural geology: fractures and faults / Form of folds

2. SOILS, VALLEYS AND GOUNWATERS / 4 HOURS Geological study of soil: Soil parts / Types of soil. Types of valleys: river valley / Glacial valley. Development of a river: juvenile sector, maturity, old age. Groundwater research: Groundwater parts / Determination of the groundwater trajectory direction, its velocity, its gradient, its water level and its permeability coefficient.

3. UNDERGROUND RESEARCH / 4 HOURS Soil sampling: How to carry out soil sampling / Drilling: Types of drilling and its registers / Geophysical research / Types of geophysical research: Seismic geophysical research / electric geophysical research / Magnetometric geophysical research / gravimetric geophysical research.

4. GEOLOGICAL PLANES AND PHOGEOLOGY / 4 HOURS Geological cartography: Steps in the geological surveying / Scales / Conventional signals / Photogeology; its importance / Scales, interpretation / Geological sketch surveying with aerial photographs.

5. ROCK AS CONSTRUCTION MATERIAL / 4 HOURS Research of construction materials: Their application / Quarry / Exploitation / rock material crushing: dangers / Gravel and sand study / Aggregate / Aggregate for roads and railroads.

6. COASTAL DEFENSE AND SEDIMENTATION / 4 HOURS Geological study of coastal defense: coasts and beaches, tides, ocean soil subdivisions / Sandspit, ports location, airports location according to wind. Sedimentation engineering elements / Reservoir life by sedimentation effect.

7. CONSTRUCTIONS / 4 HOURS Foundation: types of foundation / Piers / Foundation according to soil type / Foundation in residential, commercial and industrial buildings.

8. SOIL REMOVAL / 8 HOURS Geological aspects in the soil removal: terminology / Soil removal equipment / Soil quarry / Embankment foundations / Embankment density, Compaction trial / Soil mechanics study of soil embankments. Soil dams: Generalized definitions of soil dams / Side protection of soil dams / Channels formation, how to avoid those channels, Soil dam rupture / Geotechnical research in the soil removal.

V. PRACTICAL EXPERIENCES Two field practices are carried where students, under the guidance of instructors, analyze the geological characteristics of different regions of Lima or other nearby cities. Students should present a report. VI. METHODOLOGY Exposition of the learning units using multimedia projection. Discussion about every single subject with all the class, questions on that regard to students and answers to questions posed by students. Presentation and discussion on geological cases in Peru. VII. EVALUATION FORMULA The average grade PF is calculated as follows: PF = 0.3 EP + 0.3 EF + 0.2 PP + 0.2 PC

EP: Mid-Term Exam EF: Final Exam PP: Average of four quizzes PC: Two report of in-field practice

VIII. BIBLIOGRAPHY

1. KRYNINE. D. JUDDD, W Principles of Geology and Geotechnics for Engineers Omega Editions, Mexico, 2012

2. LEGGET, R. KARROW, P Geology Applied to Civil Engineering Mc. Graw-Hill, 2012




AA227 – TECHNICAL DRAWING

I. GENERAL INFORMATION CODE : AA227 Technical Drawing SEMESTER : 2 CREDITS : 2 HOURS PER WEEK : 4 (Theory - Practice - Laboratory) PREREQUISITES : None CONDITION : Compulsory II. COURSE DESCRIPTION This course is theoretical and practical and is based on creativity. Its aim is to provide students with the practical and conceptual framework of the main aspects related to projection of objects placed in the outer space and represented in a plane based on the drawing. It also encompasses the following: 1) Point, Straight line, Plane, Planes and Straight lines: Distances, angles, parallelism and perpendicularity and intersections. 2) Polyhedron intersections and surfaces of revolution. 3) Volumes formation. III. COURSE OUTCOMES

1. Understand and apply the principles of projection in one plane and the concepts of descriptive geometry.

2. Understand and apply the concepts of geometric constructive drawings. 3. Allow the conceptual and practical development of the main aspects as the projection of objects as

rational and creative framework for other courses. 4. Organize the imagination to express through creativity two-dimensional and three-dimensional

technical objects. 5. Determine the constructive drawing regarding the necessary size conveniently using the scale and

establishing the need. 6. Apply national and international standards in the representation of engineering drawings..

IV. LEARNING UNITS 1. POINT, STRAIGHT LINE, PLANE, PLANES AND STRAIGHT LINES: DISTANCES, ANGLES, PARALLELISM AND PERPENDICULARITY AND INTERSECTIONS / 42 HOURS The point / Definition / Application of the orthogonal projection principles to the descriptive geometry / Plan view of a point / Drawing of a point using coordinates / Relative positions of 2 points / Consecutive position of a point or geometric solids in space / Visibility rule / The straight line / Positions: particular and particulars of straight lines, cases: oblique, horizontal, in profile, normal and vertical / relative positions of two straight lines in space: concurrent parallel, crossing and perpendicular / Distance from a point to a straight line / Straight line: real length, orientation and slope / The oblique line and its consecutive views: Auxiliary views or direct method and the contour differences method / The plane / representation of a plane surface. For two concurrent straight lines, for two parallel straight lines, for a straight line and a external point and for 3 noncollinear points / Particular positions of a plane: Horizontal plane, frontal plane, profile plane, normal plane and vertical plane. Plan view of an oblique plane / Notable lines in a plane / Inclination

angle of a plane / Oblique plane / Orientation of any plane / Edged projection of a plane / Slope and real magnitude of any plane / Lines and planes distances: Shortest distance between two crossing points and their technical characteristics / Angles: straight, plane and dihedral / Lines and planes: Parallelism and perpendicularity conditions / For an external point to a given plane, stroke a line or plane parallel to it / Bisector plane / For an external point to a given plane, stroke a line or plane perpendicular to it / Lines and planes: Intersections and visibility / line-plane intersection. Methods: Edged view and sectioning plane / Planes intersection. Cases: Limited and unlimited planes. Methods. Edged plane and sectioning planes.

2. POLYHEDRONS INTERSECTION AND SURFACES OF REVOLUTION / 24 HOURS Polyhedrons, their representation / Points I the face of a polyhedron / Intersection and visibility of a line and a polyhedron. Cases: Prisms and pyramids / Sectioning plane and edged plane methods / Polyhedrons intersection and visibility: Intersection in particular positions and numeral systems / Surfaces of revolution and their representation / Points in the surface of revolution / Visibility / Intersection of a line and a surface of revolution, cases. With cylinder and sphere / Sectioning plane method. Application in engineering / Intersection of surfaces of revolution / Types of intersections in particular positions / Cones intersection, cylinders intersection and intersection between a cone and a cylinder. Method: Sectioning plane / Application in civil engineering. 3. VOLUMES FORMATION / 18 HOURS Formations: Definition / Methods: triangulation and others / Oblique and right prism formation / Oblique and right pyramid formation / Oblique and right cone formation / Application in designing and formation of a civil engineering container or module and its multiple use / Formation of the intersection of two polyhedrons / Formation of the intersection of two surfaces of revolution / Application in designing and formation of a civil engineering container or module and its multiple use / Conference: Modern structures (filmic projection, in the classroom). Cases: Buildings and bridges. Speaker: Instructor of the course. V. LABORATORY EXPERIENCES Lab. 1. Software for graphic representation. Lab. 5. Revolution surfaces. Lab. 2. Point and line. Lab. 6. Angles and rotations. Lab. 3. Plane. Intersections. Lab. 7. Distances and tangent surfaces. Lab. 4. Polyhedrons. Lab. 8. Final project. VI. METHODOLOGY The course is carried out in theory and practice sessions. In theory sessions, the instructor introduces and explains concepts and definition of the subjects. In practice sessions, the instructor applies concepts and definitions of the subjects studied in theory sessions. Likewise, these practical works are exercises and the others are graded using drawing engineering materials. There will also be five quizzes and the lowest grade will be eliminated, all quizzes worth the same. VII. EVALUATION FORMULA The average grade PF is calculated as follows: PF = 0.25 EP + 0.50 EF + 0.25 PP + 0.25 TE

EP: Mid-Term Exam EF: Final Exam PP: Average of three quizzes TE: Average of three projects

VIII. BIBLIOGRAPHY

1. DESKREP, C.L. Descriptive Geometry University Library Editions, 2011

2. MINOR CLYDE HAWK

Descriptive Geometry Mc Graw – Hill Editorial, Mexico, 2002




AA235 - TOPOGRAPHY

I. GENERAL INFORMATION CODE : AA235 Topography SEMESTER : 3 CREDITS : 4 HOURS PER WEEK : 6 (Theory – Practice) PREREQUISITES : AA227 Technical Drawing, AA215 Geology CONDITION : Compulsory II. COURSE DESCRIPTION This course prepares students for the understanding and application of topography methods for the study, representation and analysis of the shape and features of the surface of the Earth. The course deals with subjects such as: Horizontal control using triangulation and trilateration methods. Determination of the relative and total error. Figure compensation methodologies, figure resistance theory, coordinates calculation, off-center station, supplementary horizontal control using direct and inverse intersection (Pothenot problem), volume calculation: methods and considerations, introduction to road theory, applications to mining engineering. III. COURSE OUTCOMES

1. Carry out topographical surveys of large and medium expanse controlled with triangulation and apply them to engineering works.

2. Propose several work systems that allow them to represent a stretch of land and take decisions.

3. Students will have the possibility to fit in with criteria and requirements of a certain and specific civil work, so their work meet the needs required.

4. The mastery and practice of this conceptual subject matter will allow students to perform in the technical-professional field of topography, and will also provide students with conceptual basis for their later courses.

IV. LEARNING UNITS 1. CONCEPTS AND PRELIMINARY WORKS / 8 HOURS Topogrphical triangulation / Planimetric control / Clasification / Common figures / Stages / Work planning / propagation of error / geodesic triangulation / Spherical excess. Terrain reconnaissance / Hub location / Monumentation and hub signaling / Daytime and evening observation / Base measurement / Classification and precisions. 2. ANGULAR MEASUREMENTS / 15 HOURS Base measurements with steel tape and invar bar / electronic instruments / Base orientation with sight and gyro / GPS. Precision theodolites / Measurement of horizontal angles / for reiteration / Precautions / measurement of vertical angles / trigonometric leveling / Off-center station. 3. ANGULAR MEASUREMENTS II / 12 HOURS Figure compensation / Method used / Equations of condition. Error theory method / Successive-approximations method / Least squares method. Figure resistance / Side calculation / UTM coordinates calculation / Dimension lines calculation.

4. TACHOMETRY WITH TOTAL STATION AND THEODOLITE / 8 HOURS Tachymetry / Horizontal and inclined sights / Formulas / Optical and electrical instruments / Total station / Curve diagram tachymeter / Errors and precautions. Elaboration of contour lines / Field and lab research methods / Interpolation / Methods / Verifications / Errors and precautions. 5. SUPPLEMENTARY HORIZONTAL CONTROL / 16 HOURS Applications for contour lines / Gradient stroke / Construction of sections / Volume calculation / Supplementary horizontal control / Simple intersection / inverse intersection (Pothenot) / Analytical development / Common cases / trilateration with electric instruments. Triangulation application for bridges and tunnels / Triangulation networks for basic and cadastral plans / Supplementary control in photogrammetry. Calculation of areas / Surveying / Planimeter / Coordinates / Decomposition into simple figures / Precisions / calculation of volumes / Topographic laser scanner. 6. USE OF TOPOGRAPHICAL TECHNIQUES / 4 HOURS Boundary rectification / Gradient line / Circular curves / Bathymetric survey / Budges / test of topographic instruments.

V. LABORATORY AND PRACTICAL EXPERIENCES Terrain reconnaissance using preliminary works. Measurement with theodolites. Equations of condition. Topographical survey. Measurement with total station. Stroke of contour lines. Triangulation scope and uses. Calculation of areas. VI. METHODOLOGY The course is carried out in theory and practice sessions. In theory sessions, the instructor introduces concepts, theorems and applications. In practice sessions, several problems are solved, and their solutions are analyzed using topographic equipment (topographical level, theodolite, total station, GSP). At the end of the course, students must hand in and expose a paper. In all sessions student’s active participation is encouraged. VII. EVALUATION FORMULA The average grade PF is calculated as follows: PF = EP + 2EF + PP PP = PC1 + PC2 4 2

EP: Mid-Term Exam EF: Final Exam PC1, PC2: Quizzes

VIII. BIBLIOGRAPHY

1. BANNISTER A., RAYMOND S., BAKER R. Modern Techniques in Topography Alfa Omega Editions, 2011

2. DOMINGUEZ GARCIA, Francisco General and Applied Topography Dossat Editions, 2009

3. DAVIS, Raymond Treatise on Topography Mc. Graw Hill Editorial, 2012




EC115 – RIGID BODY MECHANICS

I. GENERAL INFORMATION CODE : EC115 Rigid Body Mechanics SEMESTER : 4 CREDITS : 4 HOURS PER WEEK : 5 (Theory, Practice) PREREQUISITES : AA234 Physics II, AA221 Mathematics II CONDITION : Compulsory II. COURSE DESCRIPTION This course introduces the main principles of Mechanics and its applications. Its general objective is the grasp of concepts such as force, torque, force system reduction, equilibrium applied to iso-static structures (lattices or reinforcements, casing and others), distributed forces. Centers of gravity. Moments and products of inertia in flat areas. Beams and its internal actions due to loads, axial and shear forces diagram, bending moment. Cables and friction. III. COURSE OUTCOMES

1. Identify load systems interacting on a particle and a rigid body. 2. Reduce any load system to the simplest resultant acting on a particle or rigid body. 3. Determine the geometric and resistance characteristics of the structural element. 4. Apply methods for the calculation of internal forces for framework, frame and cable elements. 5. Make diagrams of axial force, shear force and bending moment in a beam statically determined. 6. Handle main principles of statics and apply them in the solution to problems of isostatic systems

equilibrium. 7. Create models representing the dynamics of moving particles and bodies (longitudinal and rotational

motion).

IV. LEARNING UNITS

1. FORCE AND REDUCTION OF FORCE SYSTEMS / 18 HOURS General comments about Forces / Characteristics. Moment of a force regarding a point and an axis / pair of Forces / translation of a force / Equivalence of a system of forces / resultant of force systems: collinear, concurrent, parallel, coplanar and spatial / Torsion characteristics / Force systems distributed on a line / Force systems distributed on a surface (center of pressure) and a volume (Center of gravity).

2. EQUILIBRIUM OF A PARTICLE AND A RIGID BODY / 24 HOURS Equilibrium / Reactions associated to support or end types / Equilibrium principles for a particle in the plane and in the space / Equilibrium principles in the plane and in the space for a rigid body / free body diagram / Reinforcements / Main elements / Shaping / reinforcement analysis / Node equilibrium method / Section method / Casing and frame / Force analysis in casings / Simple mechanisms.

3. CENTROIDS. INERTIA MOMENTS AND PRODUCTS Centroids of lines and areas and compound and simple volumes / Pappus’ Theorems / Center of gravity / Inertia moments and products of inertia in flat areas / Inertia moments and products in compound areas / Radiuses of gyration / Parallel Axes Theorem (Steiner) / Inertia moments and products regarding inclines axes / Main inertia axes and moments / Determination of maximum and minimum inertia products axes / Mohr’s circumference.

4. BEAMS AND INTERNAL ACTIONS IN THEM. CABLES. FRICTION

Beams / classification according to the type of support / Definition of the internal actions in a section: Axial stress, shear stress and bending moment / Diagram of variation of these internal actions throughout the beam axis, under different load conditions / Relationships against load intensity, shear stress and bending moment / calculation of the maximum and minimum of these internal actions / flexible cables: cables with concentrated loads / Cables with distributed loads: parabolic and overhead power cables / Maximum and minimum cable stress / Cable length / friction. Types of friction: dynamic and static / Friction coefficient / Angle of repose / Roll angle.

5. PARTICLE KINEMATICS. RELATIVE MOTION Framework of reference. Position. Trajectory parametrical equations. Velocity and acceleration. Velocity and acceleration in Cartesian coordinate system. Intrinsic components of acceleration. Applications. Particle movement in other coordinate systems. Coordinate systems that revolve with respect to a fixed coordinate system. General equation for the particle movement with respect to the moving coordinate system. Applications.

6. KINEMATICS OF A RIGID BODY General equation for the movement of a rigid body. Translational motion. Rotation movement around a fixed axis. Main properties of the rigid body movement. Instantaneous axis of rotation and slipping. Movement in one plane of a rigid body. Instantaneous center of rotation. Rigid body movement with respect to a moving coordinate system. Rigid body movement with a fixed point. Euler angles. Euler velocities. General movement of a solid. Applications.

7. WORK AND ENERGY Differential equations for movement in various coordinate systems. Impulse and momentum. Conservation of momentum. Momentum and impulse theorem. Work and energy. Work-energy theorem and kinetic energy. Fields of conservative forces. Potential energy. Mechanical energy conservation. Center of mass movement. Total kinetic energy of a system of particles. Work and energy equation. Impulse and momentum. Angular momentum. Application. V. METHODOLOGY An active method in the learning-teaching process is used in this course. Students participate in this method every class either individually or in work groups. The instructor exposes and gives examples to complement the students’ activity, using the available audiovisual aids and afterward the virtual campus. The classroom work is complemented with quizzes and homework uploaded to the virtual that students do periodically and/or weekly. VI. EVALUATION FORMULA The average grade PF is calculated as follows:

PF = 0.25 EP + 0.25 PP + 0.50 EF

EP: Mid-Term Exam EF: Final Exam PP: Average of six quizzes

VIII. BIBLIOGRAPHY

1. HIBBELER, R. C. Mechanical Engineering: Statics Prentice Hall Editorial, 10th Edition, 2008

2. BEER, FERDINAND AND JOHNSTON JR. RUSSELL Vectorial Mechanics for Engineering Mc. Graw Hill Editorial, 7th Edition, 2007

3. PYTEL, ANDREW AND JAAN, KIUSALAS Mechanical Engineering International Thomson Edition, 2nd Edition, 2000




EC121 – STRENGTH OF MATERIALS I

I. GENERAL INFORMATION CODE : EC121 Strength of Materials I SEMESTER : 5 CREDITS : 5 HOURS PER WEEK : 6 (Theory, Practice) PREREQUISITES : EC115 Rigid Body Mechanics CONDITION : Compulsory II. COURSE DESCRIPTION This course provides students with basic concepts of the elastic body behavior. Concepts of stress, strain and displacement as response to several types of solicitation (isolated or combined), and the application of these provide the foundations for the development of the structure area courses. This course is made up of topics such as axial solicitation, shear stress bending, bending moment, torsional moment and responses in terms of stress and strain. In all the theory exposed, application problems are solved. III. COURSE OUTCOMES

1. Identify the characteristics of deformable elastic bodies and interpret their properties. 2. Apply knowledge and skills in science and mathematics to solve problems. 3. Understand the behavior of an elastic body subject to external solicitations: Axial, shear, bending

and torsional. 4. Understand the proper use of materials, taking into consideration their characteristics of strength

and deformability. 5. Interpret the rigor and the objectivity of the theories exposed in the course and their applications. 6. Apply the knowledge given in class to the solution of related problems.

IV. LEARNING UNITS 1. AXIAL SOLICITATIONS / 18 HOURS Elasticity / Traction and compression axial solicitations / Compression and tensile axial strain / Axial strain / Normal stress / Hooke’s law / Stress-strain curve / Allowable stress / Transverse strain: Poisson’s ratio / Nodes Displacement in structures / Isostatics / Stress and strain due to the own weight and to temperature variations / Stresses and strains due to inertial forces / Analysis of statically indeterminate structures subject to axial solicitation / Connections: Shear stress and shear strain unit / Stress in inclined planes. 2. STRESSES IN AN ELASTIC BODY POINT / 9 HOURS Components of the stress in an elastic body point: / Stress tensor / Components of the strain in an elastic body point: strain tensor / Generalized Hooke’s Law / The state of pure shear: Relationship between shear stress and shear strain unit / Volumetric variation: Compressibility or expansion module.

3. STRESS AND STRAIN PLANE STATE / 9 HOURS Plane stress state / Plane strain state / Stress calculation in a point of stress or strain plane state: Main planes and stresses / Mohr’s stress circle / Strain calculation in a strain plane state point: Planes of main unit strain / Mohr’s circle for strains. 4. TRIAXIAL STATE OF STRESS / 6 HOURS Stress variation in an elastic body point / Normal stress variation / Stress ellipsoid / Determination of the main stresses / Determination of the maximum and minimum shear stress planes / Strains in a elastic body point / Main unit strains. 5. TORSION / 6 HOURS Circular shafts torsion: fundamental hypotheses / Stresses and strains / Design of circular section / Power transmission / Coupling of shafts subject to torsion by bolted flanges / Hyperstatic problems. 6. BENDING / 12 HOURS Simple bending of prismatic bars / Fundamental hypotheses / Normal and shear stress / Stress and strain distribution in the cross section / Design and testing of beams for bending and shear. 7. STRAIN IN BEAMS / 8 HOURS Elastic shaft equation / Angular and linear displacement of a section / Strains and displacements in isostatic beams / Double integration method. 8. REDUCED MOMENT-AREA METHOD / 8 HOURS First and second theorem / Sign convention / Bending moment diagram by parts. 9. CONJUGATE BEAM METHOD / 8 HOURS First and second proposition / Displacements in isostatic beams. V. METHODOLOGY This course is carried out in theory and practical sessions. In theory sessions, the instructor introduces concepts of the theory in the teaching-learning process, in which students participate either individually or in work groups. The instructor exposes and gives examples to complement students’ activities. Classroom work is complemented with homework. The instructor provides students with theory and problem offprints. VI. EVALUATION FORMULA The average grade PF is calculated as follows:

PF= 0.25 EP + 0.50 EF + 0.25 PP


VII. BIBLIOGRAPHY 1. GERE, J.M. AND TIMOSHENKO, S.P.

Mechanics of Materials Thomson Ed., 2012

2. BEER & JOHNSTON Mechanics of Materials

Editorial McGrawHill, 2010




EC122 – STRENGTH OF MATERIALS II

I. GENERAL INFORMATION CODE : EC122 – Strength of Materials II SEMESTER : 6 CREDITS : 5 HOURS PER WEEK : 6 (Theory–Practice) PREREQUISITES : EC121 – Strength of Materials I CONDITION : Compulsory

II. COURSE DESCRIPTION The course prepares students in the application of strength of materials methods for the design and mechanical verification of machine elements, considering static and dynamic solicitations. Students analyze different failure criteria, fatigue stress, deformation in beams with variable section, curved beams, flat plates, and cylinders and tubes. Students complete the mechanical design and verification of machine parts and components.

III. COURSE OUTCOMES At the end of the course, students: 1. Understand and apply failure criteria, as well as safety factor for designing mechanical

components and parts. 2. Understand the nature of fatigue phenomena in materials, and take it into account for

mechanical design. 3. Model and calculate deformations of beams with complicated shapes and loads (graphical

integration) and apply them for mechanical design. 4. Calculate stress, strain and deformation in curved beams. 5. Understand the nature of bending in flat plates. 6. Understand the calculation of stress and strain on cylinders and tubes with internal uniform

pressure.

IV. LEARNING UNITS

1. FAILURE CRITERIA Introduction / Maximum normal stress criteria / Maximum shear stress criteria / Maximum deformation criteria / Maximum energy of deformation criteria / Maximum energy of distortion criteria / Coulomb-Mohr criteria / Fault in ductile and brittle materials under static loads / Application problems.

2. FATIGUE STRESS Introduction / Tests to determinate fatigue resistance. / Fatigue limit and restricted fatigue limit. / Wohler diagram. / Modifying factors of the fatigue limit. / Theoretical stress concentration factor. / Fatigue stress concentration factor. / Sensitivity to kerf. / Fluctuating stresses. / Test of material with fluctuating stresses. / Goodman criteria. / Soderberg criteria. / Safety factors. / Transmission of mechanical power (axis). / Application problems.

3. BEAMS WITH VARIABLE SECTION General considerations / Method of graphic integration / Bending equations in beams / Application problems: different types of beams.

4. CURVED ELEMENTS General considerations / Stress general equation / Location of neutral axis in beams / Formula of Winkler-Bach / Application examples / Deformation in curved, thin and thick elements / Methods of elastic energy / Loads distributed on curved beams / Application problems.

5. FLAT PLATES Introduction / Pure bending / Generalization of pure bending in plates / Flex with crossed loads (shears) / Equations of bending in flat plates / Circular plates symmetrically charged / Solution of particular cases / Use of formulas for flat plates / Application problems.

6. CYLINDERS AND TUBES Introduction / Equations of Lame / Cylinders of thin wall / Resistance of cylinders / Complex cylinders / Deformation in cylinders / Assembly of a solid shaft in a cylinder: shaft-hole / Application to machine elements / Application problems.

V. PRACTICAL EXPERIENCE Practice 1: Failure criteria and review of Strength of Materials I. Practice 2: Fatigue stress. Practice 3: Deformation in beams with variable section (AutoCAD). Practice 4: Curved beams. Practice 5: Flat plates. Practice 6: Cylinders and tubes.

VI. METHODOLOGY The course takes place in theory and practice sessions. In theory sessions faculty presents the theory, concepts and methods. In practice sessions, students apply theory to solve diverse problems related to material failure criteria, fatigue stress, deformation in beams with variable section, curved beams, flat plates, and cylinders and tubes. At the end of the course, students submit and defend a final report. Student active participation is promoted throughout the course.


PF = (EP + 2*EF + PP) / 4

EP: Mid-term Exam EF: Final Exam PP: Average of practice grades.

VIII. BIBLIOGRAPHY

1. TIMOSHENKO Strength of Materials. Volume II. Espasa Ed. Spain, 2012.

2. DEUTSCHMANN Machine Design Theory and Practice. Mac Millan Ed., USA, 2012.

3. ROARK Formulas for Stress and Strain.




EC211 - STRUCTURAL ANALYSIS I

I. GENERAL INFORMATION CODE : EC211 SEMESTER : 7 CREDITS : 5 HOURS PER WEEK : 6 (Theory – Practice) PREREQUISITES : EC122 Strength of Materials II CONDITION : Compulsory II. COURSE DESCRIPTION This course trains students on the principles of the relationship between structures analysis and design, the analysis of displacements of several types of structures as a response to several solicitation applying energy methods for the solution to isostatic and hyperstatic structures. It deals with topics such as axial solicitations of bending shear force and torsion in structures, and responses in terms of stress and strain. During the course, students become aware of the importance of learning the structures action and the loads function in structures and its analysis through the force method, Castigliano’s second theorem and iterative method. III. COURSE OUTCOMES

1. Identify the characteristics of several types of structures and value the rigor and the objectivity of the theories exposed in the course.

2. Apply the knowledge and skills in science and mathematics to solve problems. 3. Understand that the structures’ analysis and design must go together in the activity of the civil

engineer. 4. Analyze the adequate use of the fundamentals and relate different procedures of the structural

analysis with the principles of the applied mechanics. 5. Adequately use materials, taking into consideration their characteristics of resistance and

deformability. 6. Apply energy methods in the solution to problems of isostatic and hyperstatic structures,

related to a certain type of solicitation or solicitations.

IV. LEARNING UNITS 1. STRUCTURES DETERMINATION AND STABILITY – STRAIN ENERGY Stability: External, internal and general stability / Structures determination: External, internal and general for several types of structures / Structural Isostatic change: Forms of Isostatic change / Strain energy: Clapeyron’s law / Strain energy for every concept: Application to several types of structures. 2. ENERGY METHODS FOR CALCULATING LINEAR AND ANGULAR DISPLACEMENTS Castigliano’s first theorem: Linear and angular displacements in structures due to normal force, shear force, bending and torsion / No-load point displacement / Unit load method: Displacements in arc, bar, composite and continuous structures / Applications to find linear and angular displacements / Betti’s theorem and Maxwell’s theorem.

3. FORCE METHOD (FLEXIBILITY METHOD) Undetermined structures analysis / Force method: Method Expression / Applications in continuous, reticular and arc structures / Applications in arc, articulated, composite and continuous structures. 4. CASTIGLIANO’S SECOND THEOREM Castigliano’s second theorem: Explanation of the theorem / Application sin undetermined structures: arc, articulated, composite and continuous. 5. CONTINUOUS STRUCTURES ANALYSIS Main definitions / Angular deformation method: explanation and main equations: Fundamental hypotheses / Application to structures with mobile and revolving nodes / Symmetrical continuous structures. 6. MOMENT DISTRIBUTION METHOD Moment distribution method / Applications to rigidly framed structures with mobile and revolving nodes / Applications to continuous structures with intermediate ball and socket joint. 7. KANI’S METHOD Kani’s method: fundamental equations for mobile and revolving nodes / Applications to continuous rigidly framed structures: Shear force and bending moment diagrams / Continuous structures with articulated elements / Analysis of continuous structures of various heights with bars embedment and articulation / Applications to continuous rigidly framed structures with lateral loads. 8. TAKABEYA’S METHOD Fundamental equations / Applications / Scalar focus of the stiffness and flexibility methods. VI. METHODOLOGY The course is carried out in theory and practice sessions. In theory sessions, the instructor introduces the analysis and the deduction of various theories in the learning process where students participate either individually or in work groups to solve problems. The instructor exposes and gives examples to complement students’ activity. Students’ learning is complemented with papers and problems given by the instructor in the classroom. The instructor provides offprints about theory and the solutions to several formulated problems. VII. EVALUATION FORMULA

The average grade PF is calculated as follows: PF = 0.3 EP + 0.4 EF + 0.3 PP


VIII. BIBLIOGRAPHY

1. HIBBELER R.C. Structural Analysis Prentice Hall Ed., 2003

2. KENNEETH M. LEET AND CHIA MING VANG Structural Analysis Mc. Graw Hill Ed., 2006

1




EC612 – CONCRETE TECHNOLOGY

I. GENERAL INFORMATION CODE : EC612 SEMESTER : 8-10 CREDITS : 4 HOURS PER WEEK : 5 (Theory – Practice) PREREQUISITES : EC611 Materials Technology CONDITION : Elective II. COURSE DESCRIPTION This course is theoretical and practical and provides students with the knowledge to assess the quality of materials used in a design of mortars, as well as aspects regarding the concrete which will be the base for the development of courses of the area. The course deals with: Concrete. Concrete resistance. Physical characteristics of aggregates. Concrete admixture. Properties of green and hardened concretes. Admixture design of normal and high-performance concrete. Quality control. Statistic assessment of resistance results. Ready mixed concrete batching and mixing plant. Concrete mixing, pumping and compaction equipment. III. COURSE OUTCOMES

1. Identify characteristics of materials making up the base for admixture designs. 2. Put forward cause – effect relationships in green and hardened concrete properties. 3. Interpret and apply methods of admixture dosage for normal weight and medium compress

resistance concrete. 4. Assess criteria for handling concrete in works. 5. Analyze concrete quality.

IV. LEARNING UNITS 1. MATERIALS / 15 HOURS Concrete as structural material / History of concrete components / Types of concrete. Properties of green concrete and hardened concrete / importance of the technical training / Cement / Definition / Classification / Composition / Structure / Gel / Capillary pore / Water for its preparation and curing / Aggregates / Physical characteristics / Classification / General specifications. Specific gravity / Volumetric gravity / Humidity condition / Granulometric design / Absolute and apparent volume of aggregates / Method of aggregate combination for a required granulometry / Specific surface area / Concrete admixtures / Classification / Reducer admixture of water retarding as modifiers of green concrete properties / Air incorporating admixtures / Waterproofing admixtures / Cutting-edge admixtures. 2. PROPERTIES OF CONCRETE / 25 HOURS Concrete permeability / Concrete temperature problems / Freezing and thaw processes in the concrete, weathering influences and causes / Concrete resistance / Compression resistance / Tensile strength due to diametrical compression / Flexural strength / Concrete resistance nature / Water-cement relation / Design water / Design water / Effective water / Factors modifying resistance.

2

3. DESIGN OF CONCRETE MORTARS / 15 HOURS Basic considerations in mortar design / Description. Factors having influence / Essential requirements and ratio expressions. Types of concrete mortars. Steps for designing a mortar. Criteria in the selection of design values / Design of concrete mortars: ACI methods, aggregate fineness modulus, Fuller’s curve / Procedures and applications. 4. CONCRETE QUALITY CONTROL / 15 HOURS Average resistance / general criteria / Statistic fundamentals / Results interpretations / Characteristic resistance / Destructive and nondestructive testing in the hardener concrete / Acceptance and rejection green and hardened concrete / Elasticity and plastic flow / Strain and crazing / Cracking interpretation. 5. EQUIPMENT / 15 HOURS Equipment / Concrete mixer / types / Mixing time / Transport / Concrete placing and finishing / Concrete compaction equipment / Concrete pumping equipment. V. LABORATORY EXPERIENCES Lab. 1: Granulometry / Unitary weight / Mesh 200 Lab. 2: Specific gravity / Humidity content / Percentage of absorption Lab 3: Abrassion resistance / Durability / Organic impurities Lab. 4: Mix design Lab. 5: Fresh concrete testing: settling, exudation, unitary weight, air content Lab. 6: Hardened concrete testing: compression tension, flexion, elasticity VI. METHODOLOGY This course applies an active method in the learning-teaching process in which students participate every class. The instructor exposes using the available audiovisual aids. An analysis is carried out in order to find out the interaction of the different materials within the mortar design. In class, there will be cases, debates, examples, demonstrations that allow students to understand performing and practicing in the training and handling of lab equipment and tools, as well as the achievement of feedback. VII. EVALUATION FORMULA The average grade PF is calculated as follows: PF = 0.25 EP + 0.25 EF + 0.25 PP + 0.25 PL

EP: Mid-Term Exam EF: Final Exam PP: Quizzes average PL: Labs average

VIII. BIBLIOGRAPHY

1. RIVVA LÓPEZ, ENRIQUE Recommendation for the process of planting concrete structures (Spanish) Sosfisa Editorial, lima - Peru (1988)

2. NEVILLE A.M. AND BROOKS J.J.

Concrete Technology (Spanish) Trillas Editorial, Mexico (1998)

3. KUMAR MEHTA, P. AND MONTEIRO, PAULO

Concrete, structure, materials and properties (Spanish) Mexican Institute of Cement and Concrete (1998)

1




EC61 – MATERIALS TECHNOLOGY

I. GENERAL INFORMATION CODE : EC611 Materials Technology SEMESTER : 7 CREDITS : 4 HOURS PER WEEK : 6 (Theory – Practice – Labs) PREREQUISITES : EC121 Strength of Materials I CONDITION : Compulsory II. COURSE DESCRIPTION This course trains students in the application of basic principles of science and technology of materials in engineering, with emphasis in the criteria for their elaboration and behavior in service based on their class, properties and applications. Ferrous and non-ferrous alloys are classified and studied, and non-metallic materials derived from the processing of natural raw materials and artificial and synthetic materials. In all cases, problems based on the integration of previous knowledge of physics, chemistry, mathematics and graphic expression are solved, using, specialized software and descriptive and analytical methods. III. COURSE OUTCOMES

1. Apply fundamental concepts and criteria for an adequate selection of materials for a certain use, based on the knowledge of its physical, chemical and technological properties, and considering the environment and the conditions in which it will be exposed during its behavior in service.

2. Recognize, recommend and participate in the implementation of different types of techniques of conformation for engineering materials.

3. Apply fundamental knowledge of simulation of the future behavior of new materials, applying quantitative methods and laws ruling the theory of manufacturing metallic and non-metallic materials, applying the related knowledge, programming software.

4. Adequately communicate the results of the assessment of possible materials to be used, to be employed in the decision making if an industrial plant.

IV. LEARNING UNITS 1. FUNDAMENTALS OF MATERIALS ENGINNERING AND SCIENCE / 20 HOURS Raw material and materials / Materials classification / Physical, chemical and technological properties / Auxiliary materials / Fundamentals of the procurement of iron and steel / General studies of flow charts / The solid state. Crystal structures / Typos of unit cells and metal crystal lattices / Principles of physical metallurgy / Principles of the processes of materials conformation in the industry / Principles of conformation by plastic deformation in cold and hot. Forge, lamination, embossing, drawing, etc. / Fundamentals about shear conformation with blowpipe and welded joint, dust metallurgy, machining and casting / Contractions of metals and alloys. 2. FUNDAMENTALS ABOUT MATERIAL TESTINGS / 10 HOURS Fundamentals about mechanical tests on materials. Materials hardness, tension, flexion and compaction. Standard tests. Stress- strain curves. Problems / Elasticity of materials. Elasticity module and its application. Tests of metallic materials fatigue and impact. Standardization. Problems / Non-destructive material test / Tests with penetrating liquids, video tape recording, industrial radiography and ultrasound. NDT and industrial quality. 3. STUDY OF FERROUS AND BINARY ALLOYS / 20 HOURS Fusion and solidification of a pure metal and metal alloys. Curves / Ways in which stages of alloys are presented: Solid solution, free element and inter-metallic compound / Diagrams of stages of binary metal alloys. Fundamental laws. Equilibrium diagrams of typical phases. Deduction of the lever law / Phase transformations in binary alloys: eutectics transformation, eutectoid transformation and peritectic transformation. Problems and analysis of solidification.

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4. FERROUS ALLOYS / 10 HOURS Ferrous alloys. Classification / Cast iron and common or carbon steel, cast iron and special steels, iron-carbon diagrams / Cast iron and steel structures / Influence of the different alloy element on cast iron and common and special steel / Problems about alloy laws applied to ferrous alloys, solidification analysis and determination of micro-structures / Elaboration of standard ferrous alloys. Melting furnace and load calculation / Problems about load calculation and cast iron and steel standardization / Solution to problems about elaboration of ferrous alloys. 5. NON-FERROUS ALLOYS / 15 HOURS Non-ferrous alloys. Classification of non-ferrous metals and their alloys. Standardization and name (Nomenclature) / Fusion and forge alloys / Copper alloys / Bronze and common and special brass / Load calculation for their elaboration / Light alloys. Aluminum. Properties and applications / Aluminum alloys. Classification, properties and applications / Aluminum-copper alloys. Classification, properties and applications. Special study of duralumin. Ultralight alloys. Magnesium and its alloys / Physical, chemical and technological properties of pure magnesium. Uses / Alloys of magnesium. Classification, properties and applications. Standardization / Other alloys of non-ferrous metals / Titanium and its alloys. 6. CERAMIC MATERIALS / 8 HOURS Concept, classification, procurement, uses, properties and applications / Ceramics derived from clay. Elaboration, classification, properties and applications / determination of properties of ceramic materials. Apparent and real porosity, apparent and real density, mechanical resistance and durability / Total porosity – mechanical resistance ratio. Problems / Special ceramics. Glasses, carbides, cement and refractory materials / Refractory materials. Concept, classification, elaboration, properties and applications / Silica-alumina diagram and other equilibrium diagrams for the study of refractory systems. 7. POLYMERIC MATERIALS / 8 HOURS Fundamentals, concepts and origin of polymers / Importance in modern life / Thermoplastic and thermostable polymers / Mechanism of formation of a polymer / Degree of polymerization / Distribution of molecular weight / properties and applications / Problems. 8. COMPOUND MATERIALS / 8 HOURS Compound materials (Composites) / Concept. Types of joint, classification, properties and application of compound materials / Compound hardened by fine particles dispersion, compound reinforced by real particles, cemented carbides, electrical contacts, special molds and conductors in synthetic sand for cast and other compound materials / Compounds reinforced by fibers / Special composites. Polymers and their compound materials. V. LABORATORIES AND PRACTICAL EXPERIENCES Lab 1: Determination of crystal structures of metals. Lab 2: Methods of conformation and mechanical tests. Lab 3: Microstructure of ferrous and non-ferrous materials. Lab 4: Determination of properties of ceramic materials. VI. METHODOLOGY The course is carried out in theory, practical and lab sessions. In theory sessions, the instructor introduces concepts, theoretical deduction and applications. In practical sessions, several problems are solved and their solutions are analyzed. In lab sessions, the available equipment and material is used, complementing with videos and prototypes that students elaborate in group works. At the end of the course, students must hand in and expose a paper or an integrating project. In all sessions, students’ active participation is encouraged. VII. EVALUATION FORMULA The average grade PF is calculated as follows: PF = 0.25 EP+ 0.25 EF + 0.25 [(P1 + P2 + P3 + P4)] /4 + 0.25 [(L1 + L2 + L3)] /3 EP: Mid-Term Exam EF: Final Exam P#: Quizzes L#: Labs

VIII. BIBLIOGRAPHY

1. ZBIEGNIEW D. JASTRZEBSKI Material Engineering (Spanish)

2. DONALD ASKELAND Materials Science and Engineering (Spanish)




HH223 – FLUID MECHANICS I

I. GENERAL INFORMATION CODE : HH223 Fluid Mechanics I SEMESTER : 5 CREDITS : 4 HOURS PER WEEK : 6 (Theory – Practice) PREREQUISITES : AA231 Mathematics III, EC115 Rigid Body Mechanics CONDITION : Compulsory II. COURSE DESCRIPTION This course is theoretical and practical and provides students with the main fundamentals and concepts of the characteristics of the behavior of fluids at rest and in motion under given conditions and considerations. Its general objective is to describe and explain phenomena related to fluid mechanics and their corresponding applications and to provide the basis for the development of the specialty courses. III. COURSE OUTCOMES

1. Identify the scientific experimental nature of the fluid mechanics and appreciate the rigor and objectivity of the discipline.

2. Work with equations, basic mathematical tools in the study of fluid mechanics. 3. Analyze fundamental laws fluid mechanics and apply them in problematic and specific situation with

thoroughness.

IV. LEARNING UNITS 1. FLUID PROPERTIES AND FLUID STATICS / 21 HOURS Preliminary concepts / Concept of fluid / Dimensions and unities / Physical and thermodynamic properties of fluids / Surface tension / Capillarity / Viscosity / Euler equation / Forces acting on a fluid / Manometrics / Hydrostatic forces acting on plane and curve surfaces / Examples of application / Points about laboratories.

2. FLUID KINEMATICS / 7 HOURS Stability and flotation / Motion equilibrium / Fluid kinematics / Flow fields / Acceleration curl and velocity vector fields. 3. FLUID DYNAMICS / 70 HOURS Classification of flows and methods to describe them / Conservation of momentum / Energy equation / Energy loss / Interpretation of Bernoulli’s equation / Holes and gates / General equations and loss coefficients / Pitot tube, venture tube and current meter / Dimensional analysis and similarity / Viscous flow in ducts / Flow and duct types / Pipe friction head loss / Flow in ducts / Pressure and underpressure criteria / general aspects of channel flow.

V. LABORATORY EXPERIENCES Lab 1: Fluid properties: viscosity. Lab 2: Fluid properties: surface tension. Lab 3: Manometrics. Lab 4: Reynolds experience. Lab 5: Guided technical visit. Lab 6: Capacity hole discharge. Lab 7: Outlet discharge. Lab 8: Outlet calibration using the gravimetric method. VI. METHODOLOGY The course is carried out in computing lab, theory and practice sessions. In theory sessions, the instructor introduces concepts, analysis, descriptions and applications. In practice sessions, several problems are solved, and their solutions are analyzed. In lab sessions, debate group research and analysis of solutions are carried out. The handing over of the lab reports will be held before the following session start. In all sessions student’s active participation is encouraged. VII. EVALUATION FORMULA The average grade PF is calculated as follows: PF = (EP+EF+((P1+P2+P3+P4)/3+(L1+L2+L3+L4+L5+L6+L7+L8)/8)/2)/3

EP: Mid-Term Exam EF: Final Exam P#: Quizzes L#: Labs

VIII. BIBLIOGRAPHY

1. FOX, ROBERT Introduction to Fluid Mechanics (Spanish) Mc Graw – Hill. 4th edition (2012)

2. POTTER, MERLE Fluid mechanics (Spanish) Prentice Editorial – May 2nd Edition (2008)

3. SHAMES, IRVING Fluid mechanics (Spanish) Mc. Graw Hill Editorial, 3rd Edition, (2009)

4. WHITE, FRANK Fluid Mechanics (Spanish) Mc. Graw – Hill Editorial, 1st edition (2011)

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HH113 – GENERAL HYDROLOGY

I. GENERAL INFORMATION

CODE : HH113 SEMESTER : 6 CREDITS : 3 HOURS PER WEEK : 4 (Theory – Practice) PREREQUISITES : AA232 Biostatistics, HH223 Fluid Mechanics I, AA215 Geology CONDITION : Compulsory II. COURSE DESCRIPTION This course is theoretical and practical and provides students with the main fundamentals and concepts of the characteristics of water resources behavior present in hydraulic projects. Its main purpose is to build professionals with knowledge in hydrology and watershed management. This course uses base elements and methods to be employed for carrying out a rational exploitation of hydraulic and hydrologic resources. Contents of subjects such as application of statistics and hydraulics are given for designing civil works destined to Peruvian hydraulic projects.

This course will facilitate the study of hydrographic watersheds and their potentialities, analyzing through inductive and deductive methods, likewise, quantitative, qualitative and explanatory methods also will be applied for the explanation of hydrologic and watershed phenomena. III. COURSE OUTCOMES

1. Identify the scientific-experimental nature of hydrology and hydraulics. 2. Assess with equations and basic mathematical tools the study of hydraulics and hydrology. 3. Organize data for their adequate analysis and interpretation and calculate and interpret its

fundamental statistics properties (average value and variance). 4. Analyze the fundamental fluid laws and apply them to certain situations in watersheds. 5. Interpret the concept of distributions and apply it to calculate the probability of an event or

variable. 6. Built linear regression models to represent the relationship between the representative

parameters of a set of data in hydrologic watersheds. IV. LEARNING UNITS

1. APPLIED STATISTICS / 16 HOURS Introduction / Basic statistics application / Population, sample and variable / variable classification /Methods for presenting and organizing data / Qualitative data / Quantitative data / Frequency distribution tables / Graphic representations /Central tendency measures: average, medium average weighted / Dispersion measures: variance, standard deviation, variation coefficient / Hydrologic cycle / Hydrology objectives / hydrology in Peru / Hydro-meteorological information / Time series / Characteristics curves / Hydrometrical methods / Statistics in applied to hydrology / Basic considerations / Statistic analysis / Empirical distributions / Theoretical distributions / Assessment methods / Normal density function / Logarithmic normal density function / Extreme events function / Maximal events / Gumbel’s method / Pearson’s method / Minimal events / Gumbel’s method / Pearson’s method / Application to the hydrographic watershed.

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2. WATERSHED HYDROGRAPHIC MORPHOLOGY / 28 HOURS Introduction / Basic Information / Activities planning / Basic information gathering / Consistency analysis / Graphic analysis / Double mass analysis / Statistic analysis / Computer program elaboration / Analysis of falls in the average / Identification / Assessment / Interpretation / Application / Analysis of falls in the standard deviation / / Identification / Assessment / Interpretation / Application / Analysis of tendencies / Properties / Analysis procedure / Tendency in average / Identification / Assessment / Interpretation / Application / Tendency in standard deviation / Identification / Assessment / Interpretation / Application / Meteorology and hydrology / Meteorological elements / Relative humidity / Total evaporation / Winds / Precipitation / Discharges. 3. APPLICATIONS TO HYDROLOGICAL WATEERSHEDS, PROJEECTS / 12 HOURS Group work: HYDROLOGICAL SURVEY / Cartography / Thematic maps / Hydrographic plan / Roadway plan / Basic information gathering / topographic plan / Geologic plan / Mining plan / Soil plan / Season plan / Statistic analysis / Basic Information gathering / Soil classification plan / Irrigation infrastructure plan / Ecology plan / Precipitation analysis / Average precipitations / Assessment methods / Elaboration of Isohyets plan / Mass curve / Histogram / Storm Analysis / Frequency-intensity-duration survey / hydrometrics / Concepts / Assessment methods / RIPPL diagram / Reservoir characteristic curves / Gagging methods / Domestic projects. V. METHODOLOGY

The course is carried out in computing lab, theory and practice sessions. In theory sessions, the instructor introduces concepts, theorems and applications. In practice sessions, several problems are solved, and their solutions are analyzed. In lab sessions, Hydrology application software is used to solve problems and analyze their solution. At the end of the course, students must hand over and expose a paper or project on watersheds. In all sessions student’s active participation is encouraged. Software HEC-HMS is used. VI. EVALUATION FORMULA

The average grade PF is calculated as follows:

PF = 0,33 EP + 0,33 EF + 0,34 PC

EP: Mid-Term Exam EF: Final Exam PC: Average of Quizzes and Project

VII. BIBLIOGRAPHY

1. GUIDE TO HYDROLOGYCAL PRACTICE N° 168 . OMM, 2012

2. RAY LINSLEY – MAX KOHLER – JOSEPH PAULUS

Hydrology For Engineers Mc Graw – Hill Book Company Inc., 2010

3. VEN TE CHOW – DAVIS MAIDMENT – LARRY W. MAYS Applied hydrology Mc Graw – Hill Science Ed. 2010.

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SA515 – WATER AND SEWAGE INTERIOR INSTALLATIONS

I. GENERAL INFORMATION CODE : SA513 Water and Sewage Interior Installations SEMESTER : 10 CREDITS : 4 HOURS PER WEEK : 6 (Theory – Practice) PREREQUISITES : HH224 Fluid Mechanics II CONDITION : Mandatory

II. COURSE DESCRIPTION This theoretical and practical course is elective and its objective is to provide students with knowledge about hydraulics methodology and techniques applied to the design, construction, operation and maintenance of water and drainage sanitary installations in buildings. This course explains theories such as: Integral conception of indoor installations, types of installations, construction materials, and economic - technical aspects; all of them under current National Building Regulations and the Standard 200. The domain of this conceptual and practical subject matter will allow students to develop a basic knowledge about materials, such as pipes, accessories, equipment and sanitary equipment to design, build and operate a technical – economic sanitary installation system in a building. Students complete an indoor sanitary installation project. III. COURSE OUTCOMES

1. Formulate with precision the problem for certain practical case proposed, identifying required data and information.

2. Assess the quality of materials and equipment to be used in a sanitary installation. 3. Learn the operation and use of the systems and their equipment. 4. Determine quantities of elements and accessories and estimate the cost of the installation. 5. Develop planes and complete the design of an indoor sanitary installation project.

IV. LEARNING UNITS 1. INTRODUCTION Pressure units, pressures under sanitary equipment operation. Availabilities. Application of NBR (National Building Regulations), standard 200.

2. HOT AND COLD WATER SYSTEM TYPOLOGY Water supply urban systems and indoor water systems in buildings, linear and non linear components. Pressure planes in public utilities.

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3. DIRECT SYSTEM Direct system elements / Design parameters / Units cost for public and private use / Pressure drop / Cold and hot water network calculation. 4. INDIRECT SYSTEM Linear and non linear components / Cold and hot water network design in sanitary atmospheres / Design and calculation of an indirect system – Electric pump / Materials: piping, cold and hot water accessories, sanitary equipment, equipment, drainage accessories and ventilation. 5. HYDRO PNEUMATIC SYSTEM Elements of the hydro pneumatic system / Storage and equipping / Description of every non linear element. 6. DRAINAGE AND VENTILATION Elements of drainage systems / Ventilation system / Types of ventilation / design. 7. DESIGN PROJECT Students complete the design of an indoor sanitary installation for a building from the initial formulation of the problem to planes and diagrams representing the proper solution. V. METHODOLOGY The methodology of the course is directed at encouraging the students’ active participation. It is made up of a number of quizzes and domiciliary designs (individual exposition) and visits to works, from which the lowest grade will be eliminated. Unlike those above mentioned, the elaboration of design and calculation of the final project about indoor sanitary installations receive advice from the instructor of the course so there is no replacement of these grades. The exposed methodology will make it possible for students to develop knowledge, aptitudes and skills. VI. EVALUATION FORMULA The average grade PF is calculated as follows: PF = 0.2 EP + 0.2 EF + 0.2 PP + 0.4 TF

EP: Mid-Term Exam EF: Final Exam PP: Average of four quizzes TF: Final design project report

VII. BIBLIOGRAPHY

1. PERU’S NATIONAL BUILDING REGULATIONS

2. INSTALLATIONS IN BUILDINGS Barcelona, Spain, Gustavo Gill Editorial Group, 2012

3. ENGINEER’S HANDBOOK Academia Hutte. Barcelona, Spain. Gustavo Gill Editorial Mc. Graw – Hill Editorial, 2015

4. AZEVEDO NETTO, JOSÉ MARÍA. Hydraulics Handbook Technical Editorial, Mexico, 2014.




EE342 – INTERIOR ELECTRICAL INSTALLATIONS

I. GENERAL INFORMATION CODE : EE342 Interior Electrical Installations SEMESTER : 9 CREDITS : 3 HOURS PER WEEK : 5 (Theory – Practice) PREREQUISITES : FI403 Physics III CONDITION : Compulsory II. COURSE DESCRIPTION The course aims to provide students with basics of electricity for the design of indoor and outdoor electrical wiring in buildings. It encompasses direct current circuits, single-phase and three-phase alternating current circuits, housing and building electrical wiring, primary and secondary electrical networks, lighting, electrical sub-stations, vertical transport, diesel generator, electric power station. III. COURSE OUTCOMES

1. Learn electric power applications in buildings and industrial facilities. Analyze and calculate direct current circuits.

2. Analyze and calculate single-phase and three-phase alternating current circuits. 3. Design indoor electrical wiring for housing and buildings. 4. Apply current design rules and regulations. 5. Identify and learn the application of several types of light fixtures. 6. Identify several types of electrical substation. 7. Select diesel generators for power supply in works as emergency diesel generator. 8. Learn electric power station operation principles.

IV. LEARNING UNITS 1. IMPORTANCE OF THE ELECTRICITY / 5 HOURS Importance of the electricity. Generation, transmission and distribution / National Interconnected System / Electricity charges / Peruvian energy situation.

2. DIRECT CURRENT CIRCUITS / 10 HOURS Fixed and variable circuit parameters / Ohm’s law / Kirchhoff’s laws / Series and parallel circuits / Direct current circuits’ analysis / Solution to application problems. 3. SINGLE-PHASE, THREE-PHASE AND ALTERNATING CURRENT CIRCUITS / 12 HOURS Alternating current single-phase circuits / Active power, apparent power, idle power and power factor / Star connection and delta connection / Three-phase circuit power / Examples, application problems.

4. HOME ELECTRICAL WIRING / 15 HOURS Primary and secondary electrical networks, aerial and underground wiring / Electrical transformation substation in buildings, schemes of principle, building sizing, equipment disposal / Loads and people vertical transportation, main components, basic sizing. Operation condition, civil works. 5. ELECTRIC POWER GENERATION / 10 HOURS Diesel generators, types, premise sizing. Equipment assembly. Ventilation. Equipment disposal / Hydroelectric power station. Types of turbines. Equipment disposal. Design conditions. Civil works / Thermal power station, steam turbines, gas turbine. Equipment disposal. Civil works.

V. METHODOLOGY This course is carried out in theoretical and practical sessions. In theoretical sessions, the instructor introduces concepts, theorems and applications, complementing with available audiovisual aids and encouraging the active participation of the students. In practical sessions, problems are solved and their solutions are analyzed with the participation of the students, likewise students are given individual homework. VI. EVALUATION FORMULA The average grade PF is calculated as follows: PF = 0.3 EP + 0.3 EF + 0.2 PP + 0.2 TE

EP: Mid-Term Exam EF: Final Exam PP: Average of three quizzes TE: Average of two design projects

VII. BIBLIOGRAPHY

1. NATIONAL ELECTRICITY CODE VOLUME I, IV, V. National Direction of Electricity. Energy and Mining Department, 2014

2. RICHART C, DORF Electric circuits, Introduction to Analysis and Design Alfa Omega Editorial, 2015

3. KERCHNER AND CORCORAN Alternating Current Circuits CESCA Editorial, 2012




AA217 – LANGUAGE AND COMMUNICATION

I. GENERAL INFORMATION CODE : AA217 Language and Communication SEMESTER : 1 CREDITS : 2 HOURS PER WEEK : 4 (Theory - Practice) CONDITION : Compulsory PREREQUISTES : None II. COURSE DESCRIPTION The course prepares students in the understanding of the characteristics and rules of oral and written communication. Through intensive practical work, students understand and apply strategies for reading comprehension and proper use of Spanish language. Writing and grammar rules are emphasized for a correct use of punctuation signs, lexical precision, and a proper use of prepositions, logical-textual connectors, as well as the elaboration of cohesive and coherent texts. III. COURSE OUTCOMES

1. Properly use the Spanish language in its different aspects: orthography, morphology, syntax, semantics and textual.

2. Use oral and written language with coherence, clarity, order, precision and correctly applying grammar rules.

3. Understand and apply the methods and techniques for writing academic-scientific texts.

IV. COURSE CONTENTS

1. READING COMPREHENSION Methodological strategies for reading comprehension / Underline method / Conceptual maps / Abstracts / Inferences.

2. COMMUNICATION STRUCTURE Interest audience / Objective audience / Types of communications / Types of documents / Oral presentations / General rules.

3. ACCENT MARK – GENERAL RULES Diphthong / Tripthong / Gaps / Examples / Text analysis / Themes for monographic work.

4. ACCENT MARK – SPECIAL RULES Accent mark in mono-syllabic words / Examples / Text analysis.

5. EXPRESIVE READING Intonation of phonic groups / Recognition of phonic groups / Punctuation marks in writing / Examples / Text analysis.

6. PERIOD, COMMA AND SEMICOLON Use of period, comma and semicolon / Final point / Two points / Examples / Text analysis.

7. WRITING BASIC STRUCTURE Basic structure of a grammar sentence / Structure of subject and predicate / Loism, laism and leism / Strategies for syntax expansion in writing / Examples / Text analysis.

8. COMPOUND SENTENCE IN WRITING Use of compound sentences in writing / Co-ordinate and sub-ordinate compound sentence / Queism / Writing strategies / Examples / Text analysis.

9. PREPOSITIONS AND LOCUTION Use of prepositions and prepositive locutions on writing / Correct use of adverbs / Grammar coherence / Examples / text analysis.

10. LOGICAL-TEXTUAL CONNECTOR Use of logic-textual connectors in writing / Examples / Text analysis.

11. WRITING Paragraphs / Paragraph formal structure / Main thematic sentence in a paragraph / Main ideas and secondary ideas in a paragraph / Examples / Text analysis.

12. TEXT AND ITS PROPERTIES Text coherence / Text properties / Cohesion and cohesive elements in writing / Repetitions / Substitutions / Ellipsis / Examples / Text analysis.

13. WRITING STEPS Writing steps: planning, textualization and revision / Examples / Presentation of monographic work.

V. METHODOLOGY The course takes place in theory and practice sessions. In theory sessions, the instructor presents the concepts, methods, grammar rules and applications. In practice sessions, different types of texts are analyzed, as well as student elaborate texts and complete monographic works. Active participation of students is encouraged in all sessions. VI. GRADING SYSTEM The Final Grade (PF) is calculated with the following formula:

PF = (EP + EF + PP) / 3


VII. BIBLIOGRAPHY

1. EFE AGENCY Spanish Manual Madrid Editions, 2012.

2. RAUL AVILA Language and Speakers Trillas Editions, Mexico, 2008

3. MANUEL CARNEIRO Advanced Writing Manual San Marcos Editions, Lima, 2010

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AA226 – ECONOMIC THEORY

I. GENERAL INFORMATION CODE : AA226 Economic Theory SEMESTER : 2 CREDITS : 4 HOURS PER WEEK : 6 (Theory – Practice) PREREQUISITES : AA211 Mathematics I CONDITION : Compulsory II. COURSE DESCRIPTION This practical and theoretical course encompasses microeconomic and macroeconomic theories. In this course, students will analyze the conceptual framework, theories of consumer behavior, production theories, production cost theories, perfect and imperfect competition market theories, and fundamental equilibrium. In the macro context, it deals with, aggregates of an economy such as, aggregate supply, aggregate demand and external sector in the dynamics of globalization and government policies such as the fiscal, monetary, foreign exchange and commercial ones, and plus economic growth and development subjects. The above mentioned content trains students in the analysis and solution to contextualized entrepreneurial problems, as well as the understanding of economic facts and phenomena in every single agent within the country and the world. III. COURSE OUTCOMES

1. Analyze and synthesize concepts related to microeconomic theory and principally differentiate it from the macroeconomic theory.

2. Explain and learn concepts related to the structure of an economy perfectly competitive according to the law of supply and demand.

3. Understand and apply the knowledge about consumer behavior to production and logistics strategies.

4. Analyze and solve problems about optimization of productions, costs, profits, investments in competition conditions.

5. Identify different types of imperfect markets to formulate their competition strategies. 6. Use basic concepts of macroeconomics, developing analysis and synthesis skills to understand

effects of global changes and make opportune and appropriate entrepreneurial decisions. 7. Interpret changes in the aggregate demand, aggregate supply, monetary system, financial

system and macroeconomic policies to obtain an accurate and successful economic and financial decision making at national and international level.

IV. LEARNING UNITS 1. GENERAL IDEAS AND CLASSIFICATION OF THE ECONOMY / 8 HOURS The sphere of economy / Methods and problems of economic theory / Classification of the economic science / Variables and indicators for the economic analysis / Introduction to microeconomics / Theory of demand / Demand conditioning factors / Income elasticity, cross elasticity and price elasticity of demand / Application cases and problems. 2. THEORIES OF CONSUMER BEHAVIOR / 8 HOURS Cardinal approach to the theory of consumer behavior / Total utility / Average utility / Marginal utility / Ordinal theory of consumer / Consumer budget / Equilibrium / Substitution effect / Income effect / Changes in consumer equilibrium / Application cases and problems. 3. MARKET EQUILIBRIUM AND SUPPLY THEORIES / 12 HOURS Supply curve / Conditioning factors / Changes in supply / Elasticity of supply / Market equilibrium / Changes in equilibrium / Shortage / Overproduction / IZO Production account / IZO

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curve / Producer costs / Short-term production / Long-term production / Producer equilibrium / Production surplus. 4. PRODUCTION COSTS THEORY / 5 HOURS Total cost of production / Fixed costs / Variable costs / Average cost / Average fixed cost / Average variable cost / Marginal cost / Cost functions / Entrepreneurial cases and problems. 5. THEORY OF THE MARKET ORGANIZATION / 5 HOURS Theory of the market organization / Perfect competition / Monopoly / Oligopoly / Monopolistic competition / Oligopsony / Monopsony / Business equilibrium and price determination in competitive and non competitive markets / Application problems. 6. INTRODUCTION TO MACROECONOMICS / 10 HOURS Basic concepts of macroeconomics / Global economic system / Globalization / Economic theory and policy / National accounts / Macroeconomic aggregates / Input-output model / Aggregate demand and supply / Consumption-saving-investment / Macroeconomic equilibrium / Two, three, and four economic sector models / Theory of the multiplier. 7. SECTORS OF AN ECONOMIC SYSTEM / 8 HOURS Real sectors / Fiscal sector, government budget / Macroeconomic aggregates / GDP and its measurement / Public sector / Arbitrary taxation / Public expenditure / Public investment / External sector. Balance of payments / International reserves / Inflation / Economic growth / Economic development. 8. MACROECONOMIC POLICY / 8 HOURS Monetary sector / National financial system / Central Reserve Bank of Peru / Monetary supply and demand / IS/LM model / Monetary policy / Fiscal policy / Foreign exchange policy / Commercial policy / Economic cycles / Exchange rate models / Free trade agreement / International financial and economic crisis.

V. PAPERS OF RESEARCH ON ECONOMY 1: Research on Primary Economic Activity. 2: Research on Secondary Economic Activity. 3: Research on Service Activities. 4: Research on the external sector and International Trade Agreements VI. METHODOLOGY This course is carried out in theory and practical sessions, research papers and conferences. In theory sessions, the instructor introduces the graph theoretical and mathematical analysis of concepts, principles, theories and applications. In practical sessions, different problems are solved and their contextualized solutions are analyzed. Research papers on several economic sectors are controlled throughout the semester allowing interaction with the real world. At the end of the course, students must hand over, expose and support executively dressed. In all sessions, students’ active participation is encouraged and graded. VII. EVALUATION FORMULA The average grade PF is calculated as follows: PF = 0.25 EP + 0.25 EF + 0.10 P1 + 0.10 P2 + 0.10 P3 + 0.20 TF

EP: Mid-Term Exam EF: Final Exam P#: Quizzes TF: Final Paper

VIII. BIBLIOGRAPHY

1. ROBERT S. PINDYCK, DANIEL L. RUBINDENFEL Microeconomics (Spanish) 7th edition (2012)

2. MICHAEL PARKING, GERARDO ESQUIVEL Macroeconomics (Spanish) 7th edition (2014)

3. JUAN FERNANDEZ CH., ENRIQUE ROMERO G. Basic Economy for Business Management (Spanish) 2008 Edition




AHD65 – CONSTITUTION AND HUMAN RIGHTS

I. GENERAL INFORMATION CODE : AHD65 Constitution and Human Rights SEMESTER : 7 CREDITS : 2 HOURS PER WEEK : 2 (Theory) PREREQUISITES : None CONDITION : Compulsory

II. COURSE DESCRIPTION The course prepares students for understanding the principles, contents and scope of the 1993 Peruvian constitution. Issues such as people rights and duties, the State, the territory, the three state powers (executive, legislative and judiciary) are analyzed for establishing the concept of nation and Peruvian identity. Students also analyze the structure of the government with its different estates, secretaries, and offices, and the public function they fulfill. III. COURSE OUTCOMES At the end of the course, students:

1. Knows the principles and components of 1993 Peruvian constitution 2. Knows and analyze the fundamental right of the person. 3. Knows and analyze the social, economic and political rights of people and groups. 4. Understand and analyze the principles of the state, nation and territory. 5. Knows and analyze the principles of the three state powers: executive power, legislative

power and judiciary power. 6. Understand Peruvian taxation system.

IV. LEARNING UNITS

1. INTRODUCTION Constitution: origin, evolution, importance / Peruvian constitution evolution / 1993 Constitution.

2. PERSON FUNDAMENTAL RIGHTS Fundamental rights / Classification and analysis / Exception regimens.

3. SOCIAL AND ECONOMIC RIGHTS The family: importance / Father and mother responsibilities / De facto home / Sons and daughters equality / Right to health / Right to social security / Right to safety / Right to education: primary and secondary education / University education / Job and work / Workers rights and protection / Working day.

4. POLITICAL RIGHTS AND DUTIES Citizenship / Citizen rights and duties / Civil capacity / Civil incapacity / Legal representatives / Suspension of citizen rights.

5. PUBLIC FUNCTION

Public servants: rights and duties / Public administrative career / Occupational groups and levels.

6. STATE, NATION AND TERRITORY State: concept, elements / Nation / Judiciary organization / Laws and law hierarchy / Territory / Ground, sea and air domain / national defense / Country symbols / Official languages / State and religion.

7. EXCUTIVE POWER Organization / Functions / President and vice-presidents / Functions / Requirements / Impediments / Vacancy, Suspension / Prime minister / State secretaries.

8. LEGISLATIVE POWER Organization / Functions / Attributions / Laws: generation, approval, validity / Congressmen: requirements, elections, rights and duties, vacancy and suspension.

9. JUDICIARY POWER Organization / Functions / Principles and rights / Judge: requirements, rights and duties, limitations /

10. ECONOMIC REGIME Market social economy / Free initiative / Free competition / Economic pluralism / Rights and consumer protection.

11. TAX AND BUDGET REGIME Taxes. Principles and types / Government annual budget

V. METHODOLOGY

The course takes place in theory sessions. Faculty present the concepts, methods and principles on 1993 Peruvian constitution, and promote active student participation and discussion.

VI. GRADING FORMULA The Final Grade PF is calculated as follow:

PF = (EP + EF) / 2

EP: Mid-Term Exam EF: Final Exam

VII. BIBLIOGRAPHY

1. RUBIO M., BERNALES E. Constitution and Political Society PUCP Editions, Lima, Peru, 1994

2. RUBIO M. 1993 Peruvian Constitution PUCP Editions, Lima, Peru, 1994




SA818 – COSTS AND BUDGETS

I. GENERAL INFORMATION CODE : SA818 Costs and Budgets SEMESTER : 8-10 CREDITS : 3 HOURS PER WEEK : 4 (Theory, Practice) PREREQUISITES : EC717 Construction Processes

CONDITION : Elective

II. COURSE DESCRIPTION The course prepares students in the understanding and application of the methods of costs accumulation systems in manufacturing industry, identifying all resources required in a production process including raw materials and work force, considering and efficient and rational use of the resources. Students calculate direct and indirect costs using several costing methods. Likewise students determine the required budget to complete a project in a given time, as well as the required investment. Specialized software is used for determining costs, budgets, cash flow and investment plans. III. COURSE OUTCOMES At the end of the course, students:

1. Identify the required resources to fabricate a product and determine to costs of each component.

2. Determine the direct and indirect costs of a product or service. 3. Elaborate budgets to complete a project in a given period of time making an efficient use

of raw materials, work force and other required resources. 4. Plan and determine short-term and long-term investment required to complete a project,

and take into account the time value of money.

IV. LEARNING UNITS

1. INTRODUCTION AND GENERAL CONCEPTS Introduction to cost systems / Business economic-financial information / Costs behavior / Costs as management and decision tools / Expense, cost and income / Functions of a manufacturing company / Organization structural chart / Cost flow of final product.

2. COSTS Elements of a cost system / Production cost / Cost classification / Resources cost / Human resources cost / Direct and indirect fabrication costs / Fixed, variable and semi-variable costs / Batch process costs and continuous process cost / Real, historic and pre-determined costs / Absorption costs / Manufacturing, marketing, administration, financial costs / Opportunity cost.

3. RAW MATERIALS AND RESOURCES Materials cost and control / Process of using raw materials / Materials purchase, use and control / Methods of materials costing / Inventory period based costing / Human resources

costa and control / Working times / Human resources cost assignation by departments / Learning curve.

4. COSTING METHODS Fabrication indirect costing and control / Included costs / Estimation of total indirect costs / Estimation of production levels / Determination of rates of indirect costs / Work order based costing / Determination of indirect costs by work order / Process based costing / Cost flow / Unit cost and total cost / Standard cost / Standard types / Costs standards / Variation analysis

5. BUDGET Budget, concepts and applications / Project planning / Master budget / Operating budget / Sales budget / Production budget / Purchase of direct materials / Direct work force / Indirect fabrication costs / Sales budget / Administration cost budget / Income forecast.

6. CAPITAL BUDGET Planning of long term investment / Capital budget program / Investment evaluation methods / Investment control / Money value over time / Interest rate.

V. METHODOLOGY The course takes place in theory and practice sessions. In theory sessions, faculty presents the concepts and methods. In practice sessions, students solve different problems related to costing, budget and investment. Students work in groups to complete a report on costs and budgets of a given industrial company. Student’s active participation is promoted throughout the course.

VI. GRADING FORMULA The Final Grade PF is calculated as follow:

PF = (EP + EF + PL) / 3

EP: Mid-term Exam. EF: Final Exam. PL: Average grade of Practice Works.

VII. BIBLIOGRAPHY

1. CASHIN James Fundamentals and Techniques of Costs Accounting Mc Graw Hill, Mexico, 2012

2. BACKER Morton Costs Accounting Mc Graw Hill, Mexico, 2012

3. BLANCK Leland Economics Engineering Mc Graw Hill, Mexico, 1998




EP305 – ECONOMICS ENGINEERING

I. GENERAL INFORMATION CODE : EP305 Economics Engineering SEMESTER : 8-10 CREDITS : 3 HOURS PER WEEK : 4 (Theory – Practice) PREREQUISITES : MA074 Financial Mathematics CONDITION : Elective II. COURSE DESCRIPTION This course is theoretical and practical and its general objective is to provide students with the conceptual and practical framework regarding the analysis and solutions approach to technical-economic problems in the Mechanical Engineering field. It deals with financial mathematics, cost-benefit analysis, economic and financial assessment of mechanical engineering projects. III. COURSE OUTCOMES

1. Identify and analyze technical-economic problems in businesses and projects belonging to the civil engineering field.

2. Apply financial mathematics and the principles of the cost-benefit analysis in the technical-economic assessment of the alternatives of solution in engineering surveys.

3. Develop creativity, rationality, effectiveness and economy in the analysis and assessment of the engineering solutions, seeking environmental quality and preservation.

4. Apply the cost-benefit analysis principles and procedures to guide and assess projects of basic applied research.

5. Analyze the possible the project operation conditions assessing its advantages and disadvantages. 6. Assess the feasibility of private investment projects and understand the importance of the social

assessment of the public projects.

IV. LEARNING UNITS 1. TECHNICAL-ECONOMIC PROBLEMS AND PREINVESTMENT STUDIES / 4 HOURS Mechanical Engineering sphere / Types of technical-economic problems, variables involved. Rational process of problem solving. Problem tree and solution tree. Investment projects. General process of project development. Preinvestment studies importance, objectives and characteristics. Contents of the study.

2. FINANCIAL MATHEMATICS / 4 HOURS Economic value of time. Financial formulas and deductions. Nominal interest rate and effective interest rate. Inflation effect. Interest rate. 3. GENERAL THEORY OF PROJECTS ASSESSMENT / 28 HOURS Costs in the execution and operation of projects. Investment costs and operation costs. Schedule of Investments and operation costs budget. Projects benefits and income. Project assessment. Cost-benefit principle. Project viability levels. Project assessment indexes. Types of indexes. Cost-benefit temporal flow. Cost-benefit temporal graph. Net current value. Index concept, calculation and application. Application

cases. Internal rate of return. Index concept, calculation and application. Application cases. Opportunity cost of capital. Shares in Peru. Relationship between Net current value and Internal rate of return. Application of thee net current value for assets assessment. Annual equivalent cost, application cases. Present value of costs. 4. BUSINESSS ASSESSMENT AND PROJECTS FINANCING / 16 HOURS Economic assessment of projects: Project economic flow, business profitability before and after taxes. Civil engineering projects financing. Types of financing. Financing structure. Loan characteristics. Project financing management. Financing quantitative aspects. Application of the internal rate of return in the financing alternatives assessment. Credit effective interest. Leasing financing. Real state project promotion. Market study. Product definition. Technical and economic aspects of the promotion. Schedule. Financing alternatives. Project cash flow. Concession system. 5. PROJECT SOCIAL ASSESSMENT / 8 HOURS Project social assessment: Similarities and differences regarding business assessment. Externalities and social prices. Social profitability of public projects. Cost effectiveness. National investment system. System phases. Minimal content of Preinvestment studies. 6. UNCERTAINTY ANALYSIS IN PROJECTS ASSESSMENT / 4 HOURS Project risk and uncertainty: Sensitivity analysis and other methods. Montecarlo’s method.

V. CONTINUOUS EVALUATION Quiz 1: Project definition. Market identification. Quiz 2: Demand and offer projections. Technical optimization. Quiz 3: Economical and financial evaluation. Social evaluation. Quiz 4: Sensibility and risks analysis. VI. METHODOLOGY An active method in the learning-teaching process is used in this course. Students participate in this method every class either individually or in work groups. The instructor exposes and gives examples to complement the students’ activity, using the available audiovisual aids. Cases are analyzed through debate and dialogs, apart from reflexive readings. Classroom work, with the help of the computers, is complemented with homework given by the instructor which students should expose. VII. EVALUATION FORMULA The average grade PF is calculated as follows: PF = 0.5 PP + 0.5 TE

PP: Average of five quizzes TE: Average of three reports VIII. BIBLIOGRAPHY

1. SAPAG CHAIN NASSIR

Investment projects, Formulation and Assessment Pearson-Prentice Hall Editorial, Mexico, 2012

1




PA425 – PROJECT DESIGN AND EVALUATION I. GENERAL INFORMATION

CODE : PA425 Project Design and Evaluation SEMESTER : 8-10 CREDITS : 4 HOURS PER WEEK : 6 (Theory–Practice) PREREQUISITES : AA226 Economic Theory, MA074 Financial Mathematics CONDITION : Elective

II. COURSE DESCRIPTION

The course prepares students to understand the general concepts of projects. Project size. Location of the project. Project technology. Investment and financing. Studies of costs and revenues. Evaluation. Organization, administration and legal framework. Final engineering studies and submission guidelines. During the course, the processing of feasibility studies and the development of a final project are presented.

III. COURSE OUTCOMES

1. Interprets the applicable technical standards and criteria for lead or participate in the conception and development of projects.

2. Understand the technical, economic and financial viability of projects. 3. Identify the components of the final study. 4. Organize the technical documentation for the execution of engineering projects.

IV. LEARNING UNITS 1. GENERAL CONCEPTS PROJECTS / 12 hours

Course Focus. Methodology. General concepts of projects: meaning of engineering projects. Types of Projects. Definition and project stages: preliminary study, pre-feasibility, feasibility, implementation and installation, commissioning and operation.

2. MARKET STUDY OF A PROJECT / 04 hours Market study: product demand, supply and price. Market research.

3. TECHNICAL STUDY OF A PROJECT / 12 hours Locating a project: location factors and choice of alternative locations. Project size: previous studies, product definition to produce, production process, diagrams of plant and production capacity. Technology of the project: Study of distribution of machines and equipment. Determination of installed capacity.

4. PROJECT EVALUATION / 12 hours Investment and financing. Definitions. Investment and Financing structures. Cost study. Classification of operating costs. Depreciation. Determination of income. Breakeven. Project evaluation: economic evaluation. Financial evaluation. Sensitivity analysis.

2

5. PROJECT MANAGEMENT / 04 hours Organization, administration and legal framework of the project.

6. FINAL PROJECT AND GUIDELINES FOR PRESENTATION / 12 hours Final Engineering Study. Basic engineering and detail engineering. Guidelines for submission of final engineering studies: descriptive memory, technical specifications, quantities, budgets, project schedules and plans. Guidelines for presentation of engineering reports. Presentation of engineering services. Engineering services mode. Guidelines for submitting proposals for economic and, technical services.

V. METHODOLOGY The course takes place in theory and practice sessions. In the theory sessions the teacher presents the concepts and explains the applications. In the practice sessions, case studies are analyzed. Halfway through the development of the course students must submit a feasible project and at the end of the course students must submit and present an integrated project. In all sessions the active student participation is encouraged.

VI. EVALUATION FORMULA The Average Grade PF is calculated as follow: PF = ( EX1 + EX2 + TF ) / 3 EX1: Exam 1 EX2: Exam 2 TF: Final Report / Final Project

VII. BIBLIOGRAPHY 1. SAPAG CHAIN, NASSIR

Formulation and Evaluation of Investment Projects, Mc Graw Hill. Fifth Edition, 2012.

2. PMBOK Project Management Body of Knowledge Project Management Institute PMI 2014




SA713 – ACCIDENTS AND SAFETY

I. GENERAL INFORMATION CODE : SA713 Accidents and Safety SEMESTER : 9-10 CREDITS : 4 HOURS PER WEEK : 6 (Theory – Practice) PREREQUISITES : SA633 Industrial Hygiene CONDITION : Elective II. COURSE DESCRIPTION This course is designed to allow students develop a solid preventive culture, complementing the knowledge already acquired in the career with tools that facilitate the exercise an effective and efficient control of the constant risks in every industrial process, revealing the importance of labor risks preventions during the development of a work and its close ties with the concepts of quality and productivity. III. COURSE OUTCOMES

1. Interpret and apply national technical regulations and rules regarding current labor risks prevention in the industry sector.

2. Learn main labor risk factors in industrial works. 3. Work out risk analysis: identify dangers; assess risks and operational control mechanisms. 4. Design, implement, manage and assess labor risks prevention plans in industrial works. 5. Research work accidents: assess consequences, identify causes and establish corrective actions. 6. Identify, assess and control the most frequent significant environmental aspects in industrial works.

IV. LEARNING UNITS 1. RISK FACTORS AND REGULATION FRAMEWORK Safety and health conditions in construction works in Peru. Risk factors in construction works. Work accidents, causes and consequences. National technical regulations and rules regarding to safety and health, applicable to industrial works. Individual protection equipment (IPE) and collective protection systems (CPS). Technical specifications. Technical-economic assessment. IPE / CPS selection. Signs. National and international rules.

2. OPERATIONAL RISKS IN INDUSTRIAL WORKS Safety in industrial works. Risks generated from the use of manual machines and tools. Risks generated from the operation and use of materials. Risks generated from the use of electricity. Risks in specific activities: demolitions, excavations, land movement (heavy equipment), formwork, removal of formwork. Concrete placement and production. Steel placement and preparation. Metal working jobs (electric, oxyacetylene and compressed gas cylinder welding), working in confined spaces, mechanical lifting of loads.

Industrial hygiene in construction works. Concepts. Chemical agent, explosion control, use of dangerous chemical products. Physical agents, noise, vibrations and radiations. 3. OPERATIONAL RISKS MANAGEMENT IN INDUSTRIAL WORKS Risk analysis. Identification of dangers, risk assessment, operational control mechanisms. Elaboration of standards and work procedures. Management of non-conformities. Verification mechanisms, identification, assessment and register of non-conformities. Establishment of corrective action, work accident investigation. Determination of causes (analysis methods), mitigation and corrective actions. Work accident statistics. Performance indicators analysis and formulation of line actions for continuous improvement. Response planes in emergencies: design, implementation, testing (Drills) and adjustment. 4. DEVELOPMENT OF PREVENTIVE BEHAVIOR IN WORKERS, RISKS PREVENTION PLAN Behavior change fundamentals. REAZON – WILLPOWER, key binomial. Training as tools to achieve the preventive behavior in the worker. Communication techniques. How to design an effective training program in keeping with the work? Work head leadership. Command line responsibilities (engineers and foremen). Safety committee as key element of an intrinsically safe production process. System concept for the design, implementation, management and assessment of the risks prevention plan in mining and construction works.

V. LABORATORY EXPERIENCES Visit to work 1: Identification of risks. Visit to work 2: Safety plan assessment. Visit to work 3: Control and management system assessment. VI. METHODOLOGY Expository-Interactive method: instructor lecture, student exposition. Guided discussion method: managing of the group to approach situations and come to conclusions and recommendations. Demonstration method: Execution. The instructor executes to show how and what it has to be done with, and the students execute it to prove they have learned. VII. EVALUATION FORMULA The average grade PF is calculated as follows: PF = (EP+EF+((P1+P2+P3+P4+P5+P6)/5)/3

EP: Mid-Term Exam EF: Final Exam P#: Quizzes

VIII. BIBLIOGRAPHY

1. ALEJANDRO MENDOZA PLAZA Implementing the Business Preventive Culture. Achieve Zero Accidents. AMeP and Safe-Pro Method (Spanish) Confemental Foundation, 2012

2. OSHA 2202 PUBLICATION Construction Industry Digest Revised in 2012, 105 pp

3. CESAR MINGUES FERNANDEZ Prevention planning and execution, Risk Assessment in Industry (Spanish) Escuela de la Edificación Foundation, 3rd Edition, 2011

4. Ed. CEP Labor Risks Prevention Handbook, Industry and Construction Sector and Related Matters (Spanish), CEP Editorial, 2010

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