mth 204

Lovely Professional University,Punjab

Course No Cours Title Course Planner Lectures Tutorial Practical CreditsMTH204 NUMERICAL ANALYSIS 14795 :: Gurpreet Kaur 3 0 2 4

Sr. No. (Web adress) (only if relevant to the courses) Salient Features9 http://math.fullerton.edu/mathews/numerical.html Complete course contents are available, user friendly, complete explanation along with

diagrammatic representation is available.10 www.efunda.com/math/num_ode/num_ode.cfm Containing numerical methods of ordinary differential equation and integration11 www.numerical-methods.com Basic terminology, algorithms are available

Sr No Jouranls atricles as compulsary readings (specific articles, Complete reference)5 Indian Journal of Applied Mathematical Sciences.6 Inernational Journal of springer berg7 Pure and Applied mathematics proceeding by national academy of science.8 IAENG International Journal of Applied Mathematics

Numerical methods for Scientific and Engineering Computation By M.K. Jain, S.R.KIyenger and R.K. Jain New age international publishers.

1Text Book:

Other Specific Book:Ferziger, J.H., Numerical methods for engineering application, John wiley, New York, 1981.2

Sastry S.S., Introductory Methods of Numerical Analysis, PrenticeHall of India.3

Forsythe, G.E., M.A.MaIcolm,and C.B. Moler, Computer methods for mathematical computations, prentice-Hall, Englewood cliffs, N.J., 1977.

4

Relevant Websites

Other Reading

Format For Instruction Plan [for Courses with Lectures and Labs

1 Approved for Autumn Session 2011-12

Detailed Plan For Lectures Week Number Lecture Number Lecture Topic Chapters/Sections of

Textbook/other reference

Pedagogical tool Demonstration/case study/images/anmation ctc. planned

Part 1Week 1 Lecture 1 Errors in numerical calculations. ->Reference :1,Ch-

1/1.1;1.2;1.3Lecture 2 Errors in numerical calculations. ->Reference :1,Ch-

1/1.3Lecture 3 Solution of algebraic and Transcendental

equations: Bisection method->Reference :1,Ch-2/2.1;2.2

..\Demo102\Demo_cd1\RESOURSE\NUM_METHOD\BisectionMethod.nbp

Week 2 Lecture 4 False position method ->Reference :1,Ch-2/2.3

http://math.fullerton.edu/mathews/a2001/Animations/RootFinding/RegulaFalsi/RegulaFalsiaa.html

Lecture 5 Newton -Raphson method(Allocation of test 1)

Lecture 6 Numerical Problems onNewton -Raphson method

..\Demo102\Demo_cd1\RESOURSE\NUM_METHOD\NewtonsMethod.nbp

Week 3 Lecture 7 Rate of Convergence ->Reference :1,Ch-2/2.5

http://math.fullerton.edu/mathews/a2001/Animations/RootFinding/NewtonMethod/Newtonaa.html

Lecture 8 Rate of ConvergenceLecture 9 Iteration method

Class Test 1

->Reference :1,Ch-2/2.6

Week 4 Lecture 10 Iteration method ->Reference :1,Ch-2/2.6


Part 2Week 4 Lecture 11 Lagrange and Newton Interpolation

(Allocation of Class Test 2)->Reference :1,Ch-4/4.2

http://math.fullerton.edu/mathews/a2001/Animations/Animations4.html

Lecture 12 Lagrange and Newton Interpolation 102\Demo_cd1\RESOURSE\NUM_METHOD\InterpolatingPolynomial.nbp

Week 5 Lecture 13 Newton's divided difference interpolation ->Reference :1,Ch-4/p-226

Lecture 14 Finite differences operator ->Reference :1,Ch-4/4.3

Lecture 15 Finite differences operator

Class Test 2Week 6 Lecture 16 Finite differences operator ->Reference :1,Ch-

4/4.3Lecture 17 Newton forward difference interpolation ->Reference :1,Ch-

4/4.4Lecture 18 Newton backward difference interpolation

Week 7 Lecture 19 Stirling interpolation ->Reference :1,Ch-4/4.4

Lecture 20 Bessel Interpolation

Lecture 21 Bessel Interpolation

MID-TERMPart 3

Week 8 Lecture 22 Solution of linear systems by GaussElimination


Lecture 23 Solution of linear systems by GaussElimination

Lecture 24 Triangularization Method ->Reference :1,Ch-3/p-120

Week 9 Lecture 25 Gauss-Seidel Iteration Method(Allocation of Class Test 3)



Week 9 Lecture 26 Numerical Differentiation using LinearInterpolation


http://math.fullerton.edu/mathews/a2001/Animations/Derivative/ForwardD1f/ForwardDfaa.html

Lecture 27 Numerical Differentiation using QuadraticInterpolation

http://math.fullerton.edu/mathews/a2001/Animations/Derivative/CentralD2.1f/CentralD1faa.html

Week 10 Lecture 28 Numerical Integration: Trapezoidal Rule ->Reference :1,Ch-5/5.7

http://math.fullerton.edu/mathews/a2001/Animations/Quadrature/Trapezoidal/Trapezoidalaa.html

Part 4Week 10 Lecture 29 Simpson Rule

Class Test 3


http://math.fullerton.edu/mathews/a2001/Animations/Quadrature/Simpson/Simpsonaa.html

Lecture 30 Gauss-quadrature method ->Reference :1,Ch-5/p-360

..\Demo102\Demo_cd1\RESOURSE\NUM_METHOD\GaussianQuadrature.nbp

Week 11 Lecture 31 Solution of initial value problem usingTaylor series method


..\Demo102\Demo_cd1\RESOURSE\NUM_METHOD\NumericalMethodsForDifferentialEquations.nbp

Lecture 32 Euler's Method ->Reference :1,Ch-6/6.3

Lecture 33 Numerical problems on Euler's MethodWeek 12 Lecture 34 Runge-Kutta Method(Second order) ->Reference :1,Ch-

6/6.4Lecture 35 Runge-Kutta Method(Third order)

Lecture 36 Runge-Kutta Method(fourth order)


Spill OverWeek 13 Lecture 37 Geometrical Interpretation of

Newton -Raphson method->Reference :1,Ch-2/2.3

Lecture 38 Jacobi Iteration Method ->Reference :1,Ch-3/3.4

Lecture 39 Euler's Modified Method ->Reference :1,Ch-6/6.3

http://math.fullerton.edu/mathews/a2001/Animations/OrdinaryDE/MEuler1/MEuleraa.html

Details of homework and case studies Homework No. Objective Topic of the Homework Nature of homework

(group/individuals/field work

Evaluation Mode Allottment / submission

WeekClass Test 1 To increase the

efficiency of the students

Errors in numerical calculations,,Solution of algebraic and Transcendental equations,Iteration methods ,Bisection method, iteration method, Method of false position, Newton -Raphson method,Rate of convergence

Individual Evaluation of test marks

2 / 3

Class Test 2 To increase efficiency of students

Iteration Method, Lagrange and Newton Interpolations, Newtons divided difference interpolation,Finite differences operator,Newton forward difference interpolation


4 / 5

Class Test 3 To increase the efficiency of students

Gauss-elimination method (using Pivoting strategies) Triangularization method, Gauss-Seidel Iteration method. Numerical differentiation using linear and quadratic interpolation


9 / 10

Scheme for CA:out of 100*Component Frequency Out Of Each Marks Total MarksClass Test 2 3 10 20

Total :- 10 20

* In ENG courses wherever the total exceeds 100, consider x best out of y components of CA, as explained in teacher's guide available on the UMS

*Each experiment of the lab will be evaluated using following relative scheme:


Component % of MarksWR 50J/E 20VIVA 30

List of experiments :-Lecture Number

Lecture Topic Pedagogical Tools Or Equipment Planned lab Manual

Group 1 WAP on Bisection Method, False Position Method C Compiler Not ApplicableGroup 2 WAP on Newton Raphson Method, Iteration Method C Compiler Not ApplicableGroup 3 WAP on Lagrange and Newton Interpolation, Newtons

divided differenceinterpolation

C Compiler Not Applicable

Group 4 WAP on Newton forward difference interpolation,Newton backward differenceinterpolation

C Compiler Not Applicable

Group 5 WAP on Stirling interpolation, Bessel Interpolation C Compiler Not ApplicableGroup 6 WAP on Gauss Elimination Method C Compiler Not Applicable

Mid TermGroup 7 WAP on Triangularization Method,Gauss-Seidel

Iteration MethodC Compiler Not Applicable

Group 8 WAP on Trapezoidal Rule, Simpson Rule C Compiler Not ApplicableGroup 9 WAP on Gauss-quadrature method C Compiler Not ApplicableGroup 10 WAP on Taylor series method, Eulers Method C Compiler Not ApplicableGroup 11 WAP on Runge-Kutta Method C Compiler Not Applicable


mth 204

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