FS-719 Numerical Methods PDF
FS-719 Numerical Methods PDF
FS-719 Numerical Methods PDF
Objective:
The Objective of this course is to help student to understand basic concepts in numerical methods and
able to solve engineering as well as social problems.
COURSE DESCRIPTION:
Text Books:
1. Balagurusamy, E., “Numerical Methods”, Tata McGraw-Hill Pub.Co.Ltd, New Delhi, 1999.
2. S.S. Sastry, “Introductory Methods of Numerical Analysis”, PHI learning Pvt Ltd.
3. Curtis F. Gerald and Patrick O.Wheatley, “Applied Numerical Analysis”, Pearson Education Ltd
4. Gerald, C.F, and Wheatley, P.O, “Applied Numerical Analysis”, Sixth Edition, Pearson Education Asia,
New Delhi, 2002.
5. Higher Engineering Mathematics by Dr. B.S. Grewal, 36th Edition, Khanna Publishers.
6. S.C. Chapra and R.P. Canale, “Numerical Methods for Engineers with Programming and Software
Applications”, McGraw-Hill, Newyork – 1998
7. Kandasamy, P., Thilagavathy, K. and Gunavathy, K., “Numerical Methods”, S.Chand Co. Ltd., New
Delhi, 2003.
8. Burden, R.L and Faires, T.D., “Numerical Analysis”, Seventh Edition, Thomson Asia Pvt. Ltd.,
Singapore, 2002.
Course Plan:
Week Unit Topics Hours
Theory Practical Tutorial
1 I Introduction to Numerical solutions of algebraic and 3 0 1
transcendental equations: Newton-Raphson and
Regula-Falsi methods.
2 I Solution of linear simultaneous equations: Gauss 3 0 1
elimination and Gauss Jordon methods.
3 I Iterative methods: Gauss Jacobi and Gauss-Seidel 3 0 1
methods.
4 I Definition of Eigen values and Eigen vectors of a 3 0 1
square matrix. Computation of largest Eigen value
and the corresponding Eigen vector by Rayleigh’s
power method.
5 II Finite differences (Forward and Backward 3 0 1
differences) Interpolation, Newton’s forward and
backward interpolation formulae.
6 II Divided differences: Newton’s divided difference 3 0 1
formula. Lagrange’s interpolation and inverse
interpolation formulae.
7 III Numerical differentiation using Newton’s forward 3 0 1
and backward interpolation formulae.
8 III Numerical Integration: Simpson’s one third and 3 0 1
three eighth’s value, Boole’s rule, Weddle’s rule
9 III Romberg’s method, two and Three point Gaussian 3 0 1
quadrature formulas.
10 III Double integrals using trapezoidal and Simpson’s 3 0 1
rules.
11 IV Single-step explicit methods: Taylor series method, 3 0 1
Euler and modified Euler methods,
12 IV simultaneous equations by Euler’s and Picard’s
method
13 IV Fourth order Runge Kutta method for solving first 3 0 1
and second order equations.
14 IV Single-step implicit methods, multistep linear 3 0 1
methods,
15 IV Milne’s and Adam’s predictor and corrector 3 0 1
methods.
16 Revision 3 0 1