### Numerical Analysis - I

UNIVERSITY OF SARGODHA

DEPARTMENT OF MATHEMATICS

COURSE OUTLINE                                                                                                  FALL 2020

Course Tittle: NUMERICAL ANALYSIS-I

Course Code: MATH-401

Credit Hours: 03

Email: [email protected]

DESCRIPTION & OBJECTIVES

This course is designed to teach the students about numerical methods and their theoretical bases. The course aims at inculcating in the students the skill to apply various techniques in numerical analysis, understand and do calculations about errors that can occur in numerical methods and understand and be able to use the basics of matrix analysis. It is optimal to verifying numerical methods by using computer programming (MatLab, Maple, C++, etc).

Recommended Books:

1. Gerald C.F.  and Wheatley P.O., Applied Numerical Analysis, Pearson Education,     Singapore, 2005.

2. Burden R. L. and Faires J. D.: Numerical Analysis, latest edition, PWS Pub. Co.

3. Mathews J.H., Numerical Methods for Mathematics, latest Edition, Prentice Hall     International.

4. Chapra S. C. and Canale R. P.: Numerical Methods for Engineers, 6th edition, McGraw Hill.

5. Sankara K. Numerical Methods for Scientists and Engineers. 2nd ed. New  Delhi:      Prentice Hall, 2005.

CONTENTS

Floating point arithmetic, approximations and errors. Bisection method, regula-falsi method, fixed point iteration method, Newton-Raphson method, secant method, error analysis for iterative methods. Direct methods: Gaussian elimination method for solving system of equations, Gauss-Jordan method; matrix inversion; LU-factorization; Doolittle’s, Crout’s and Cholesky’s methods, Iterative methods: Jacobi, Gauss-Seidel and SOR. Introduction, Power Method, Jaccobi's Method. The use of software packages/ programming languages for above mentioned topics is recommended.

COURSE SCHEDULE

Week

## Dates

1.

Floating point arithmetic

Oct 12-16, 2020

2.

approximations and errors

Oct 19-23, 2020

3.

Bisection method

Oct 26-30, 2020

regula-falsi method

Nov 2-6, 2020

5.

fixed point iteration method

Nov 9-13, 2020

6

Newton-Raphson method

Nov 16-20, 2020

7.

secant method

Nov 23-27, 2020

8.

error analysis for iterative methods

Nov 30-Dec 4, 2020

9.

Gauss-Jordan method

Dec 7-11, 2020

10.

Mid Term Exam

Dec 14-18, 2020

11.

Direct methods: Gaussian elimination method for solving system of equations

Dec 21-25, 2020

12.

Winter Break

Dec 28-, 2020– Jan 1,2021

13.

Winter Break

Jan 4-8 , 2021

14.

matrix inversion LU-factorization, , Crout’s and Cholesky’s methods

Jan 11-15, 2021

15.

Iterative methods

Jan 18-22. 2021

16.

Jacobi, Gauss-Seidel and SOR. Introduction, Power Method

Jan 25-29, 2021

17.

, Jaccobi's Method.

Feb 1-5, 2021

18.

Final term Exam

Feb 8-12, 2021

RESEARCH PROJECT

N/A

ASSESSMENT CRITERIA

Mid exam:       30

Sessional:        20

Project:            --

Assignments:   10

Presentation:   10

Final exam:     50

Total:               100

RULES AND REGULATIONS

75% attendance is compulsory to appear in Final Term exam.