COURSE OUTLINE

(1) GENERAL

SCHOOL ENGINEERING SCHOOL DEPARTMENT ELECTRICAL ENGINEERING DEPARTMENT

LEVEL OF STUDIES UNDER GRADUATE COURSE CODE 2102201 SEMESTER 2

COURSE TITLE Mathematics II

INDEPENDENT TEACHING ACTIVITIES if credits are awarded for separate components of the course, e.g. lectures,

laboratory exercises, etc. If the credits are awarded for the whole of the course, give the weekly teaching hours and the total credits

WEEKLY TEACHING

HOURS CREDITS

Lectures 4 7 Exercises 2

Total 6 Add rows if necessary. The organisation of teaching and the teaching methods used are described in detail at (d).

COURSE TYPE

general background, special background, specialised general

knowledge, skills development

General Background Course

PREREQUISITE COURSES:

LANGUAGE OF INSTRUCTION and EXAMINATIONS:

Greek

IS THE COURSE OFFERED TO ERASMUS STUDENTS

YES (in English for Erasmus students)

COURSE WEBSITE (URL) http://moodle.teipir.gr/course/view.php?id=408

(2) LEARNING OUTCOMES

Learning outcomes

The course learning outcomes, specific knowledge, skills and competences of an appropriate level, which the students will acquire with the successful completion of the course are described.

Consult Appendix A

Description of the level of learning outcomes for each qualifications cycle, according to the Qualifications Framework of the

European Higher Education Area

Descriptors for Levels 6, 7 & 8 of the European Qualifications Framework for Lifelong Learning and Appendix B

Guidelines for writing Learning Outcomes

At the end of this course students of Electrical Engineering Department will believe in the power of mathematics and develop new problem solving techniques and critical reasoning skills and they will be ready for further studies in mathematics, physical sciences, or any field of engineering.

1. Ability of getting partial derivatives and Higher order partial derivatives.

2. Ability to solve Maxima and minima problems.

3. Ability of evaluating Double and triple integrals.

4. Ability of working with vector fields.

5. Ability to solve first order’s differential equations .

6. Ability to solve higher order’s differential equations

7. Ability to solve systems of differential equations.

8. Ability to solve Differential equations with partial derivatives. General Competences Taking into consideration the general competences that the degree-holder must acquire (as these appear in the Diploma Supplement and appear below), at which of the following does the course aim?

Search for, analysis and synthesis of data and information, with the use of the necessary technology Adapting to new situations Decision-making Working independently Team work Working in an international environment Working in an interdisciplinary environment Production of new research ideas

Project planning and management Respect for difference and multiculturalism Respect for the natural environment Showing social, professional and ethical responsibility and sensitivity to gender issues Criticism and self-criticism Production of free, creative and inductive thinking …… Others… …….

The course aims at fostering the following capabilities:

1. Analysis and synthesis of math problems and engineering problems. 2. Decision making. 3. Independent work. 4. Team work. 5. Work in a multidisciplinary environment. 6. Project development.

(3) COURSE CONTENT

The theory part of the course consists of the following modules: 1st Module: Functions of several independent real variables. Limits. Continuity.

Partial derivatives. Higher order partial derivatives. Derivatives of inverse function. Chain rule I. Chain rule II. Generalized chain rule.

2nd Module: Implicit differentiation. Maxima and minima.

Lagrange multipliers for conditional extremes. Jacobian determinant.

3rd Module: Del, (reverse delta). Gradient. Directional derivative. Divergence. Curl of a

Vector field. Compressible and incompressible fields. Conservative fields. 4th Module: Double and triple integrals. Change limits of integration. Change variables. Applications. Line integrals. Green’s, Gauss, and Stake’s theorems. 5th Module: Introduction to differential equations. Slope Fields. Qualitative solutions. Applications. First order linear differential equations. Separation of variables. Homogeneous differential equations, almost homogeneous differential equations. 6th Module: Exact differential equations, Almost exact differential equations. Linear differential equations, Integrating Factor. 7th Module. Bernoulli differential equations, Riccati differential equations. Clairaut differential equations, Lagrange differential equations. Applications to circuit analysis, cooling, heating e.t.c. 8th Module Linear differential equations of higher order with constant and variable coefficients. Independent solutions of a differential equation. Wronskian Determinant. Homogeneous and nonhomogeneous differential equations. Homogeneous solution. 9th

Module: Particular solution for a nonhomogeneous problem. Method of undetermined coefficients. Method of variation of parameters. General solution. 10th Module: Systems of linear differential equations. 11th Module: Differential equations with partial derivatives.

(4) TEACHING and LEARNING METHODS - EVALUATION

DELIVERY Face-to-face, Distance learning, etc.

Lectures and exercises, Face to face

USE OF INFORMATION AND COMMUNICATIONS TECHNOLOGY

Use of ICT in teaching, laboratory education, communication with students

Teaching using ICT, Communication and Electronic Submission

TEACHING METHODS The manner and methods of teaching are described in detail. Lectures, seminars, laboratory practice, fieldwork, study and analysis of bibliography, tutorials, placements, clinical practice, art workshop, interactive teaching, educational visits, project, essay writing, artistic creativity, etc. The student's study hours for each learning activity are given as well as the hours of non-directed study according to the principles of the ECTS

Activity Semester workload

Lectures 52

Excercises 26

Individual work 22

Personal study 70

Course total 170

STUDENT PERFORMANCE EVALUATION Description of the evaluation procedure Language of evaluation, methods of evaluation, summative or conclusive, multiple choice questionnaires, short-answer questions, open-ended questions, problem solving, written work, essay/report, oral examination, public presentation, laboratory work, clinical examination of patient, art interpretation, other Specifically-defined evaluation criteria are given, and if and where they are accessible to students.

Written examination: 70% Exercises: 30%

(5) ATTACHED BIBLIOGRAPHY

1. W.E. Boyce and R.C. DiPrima, «Elementary Differential Equations and Boundary Value Problems», Publ. John Willey and Sons.

2. M.R. Spiegel, «Applied Differential Equations», Publ. Prentice Hall. 3. M. Braun, « Differential Equations and Their Applications», Publ. Springer-Verlag. 4. G. Simmons, «Differential Equations with Application and Historical Notes», Publ.

McGraw -Hill. 5. R. Haberman, « Elementary Applied Partial Differential Equations»,

Publ. . Prentice Hall. 6. K.E. Gustafson, « Partial Differential Equations», Publ. John Willey and Sons. 7. Sommerfield, « Partial Differential Equations», Publ. John Academic Press. 8. K.A. Stroud, «Engineering Mathematics», Pub. Palgrave 1970. 9. K.A. Stroud, «Further Engineering Mathematics», Pub. Palgrave 1986.