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Thirupathi Gudi
Professor
Department of Mathematics
Indian Institute of Science
Bangalore - 560 012

Phone: +91 - 80 - 2293 3208

E-mail: gudi [AT] iisc[dot]ac[dot]in

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Fall 2023:

Course number: UMC 202

Course name: Numerical Methods

Venue: F12, OPB.

Course meetings: Theory: Mon, Wed, Fri, during 10:00 AM -10:50 AM

Lab: Thu, during 2:00PM - 5:30 PM (Venue wil be known soon)

UMC 202: Numerical Methods (Credits: 3:1)

Numerical solution of algebraic and transcendental equations, Iterative algorithms, Convergence, Newton Raphson procedure, Solutions of polynomial and simultaneous linear equations, Gauss method, Relaxation procedure, Error estimates, Numerical integration, Euler-Maclaurin formula. Newton-Cotes formulae, Error estimates, Gaussian quadratures, Extensions to multiple integrals. Numerical integration of ordinary differential equations: Methods of Euler, Adams, Runge-Kutta and predictor – corrector procedures, Stability of solution. Solution of stiff equations. Solution of boundary value problems: Shooting method with least square convergence criterion, Galerkin Method (Finite Element) Solution of partial differential equations: Finite-difference techniques, Stability and convergence of the solution, Finite element methods.

Texts:
1. Richard L. Burden and J. Douglas Faires, Numerical Analysis: Theory and Applications, India Edition, Cengage Brooks-Cole Publishers, 2010.
2. Press, W.H., Teukolsky, S.A., Vetterling, W.T., and Flannery, B.P., Numerical Recipes in C/FORTRAN, Prentice Hall of India, New Delhi, 1994.
3. Borse, G.J., Numerical Methods with MATLAB: A Resource for Scientists and Engineers, PWS Publishing Co., Boston, 1997.
4. Conte, S. D. and Carl de Boor., Elementary Numerical Analysis, McGraw-Hill, 1980.
5. Hildebrand, F. B., Introduction to Numerical Analysis, Tata McGraw-Hill, 1988.
6. Froberg, C. E., Introduction to Numerical Analysis, Wiley, 1965.