MA5470 Numerical Analysis

Course Details

Linear and nonlinear systems : (13 lectures) Norms of vectors and matrices, Linear systems: direct and iterative schemes, Ill conditioning and convergence analysis; Numerical schemes for Non-linear Systems,

Interpolation : (10 lectures) Interpolation and Error, Hermite interpolation, Piecewise polynomial (Spline) interpolation, Numerical differentiation, Newton-cotes and Gaussian quadrature,

Numerical solution to ordinary differential eqns : (17 lectures) Difference equations, Numerical solution of IVPs: Single step and multi-step methods: order, consistency, stability and convergence analysis, Two point boundary value problems: Shooting and finite difference methods, Eigenvalue Location, Power Method, Jacobi Method.

Course References:

Text Books:
1. D. Kinciad & W. Cheney, Numerical Analysis and mathematics of Scientific Computing, Brooks/Cole, 1999.
2. K. E. Atkinson, An Introduction to Numerical Analysis, John-Wiley & Sons, 2nd Edition, 1989.

Reference Books:
1. R. L. Burden & J. D. Faires, Numerical Analysis, 7th Edition, Cengage Learning (India), 2008.
2. B. Bradie, A Friendly Introduction to Numerical Analysis, Pearson Education (India), 2007.
3. C. E. Gerald & P. O. Whealtley, Applied Numerical Analysis, Pearson Education (India), 2006.
4. S. S. Sastry, Introductory Methods of Numerical Analysis, PHI. 2009.
5. S. D. Conte & C. De Boor, Elementary Numerical Analysis, TATA Mcgraw-Hill, 2010.
6. J. Stoer & R. Bulirsch, Introduction to Numerical Analysis by Springer (India), 2009.
7. F. B. Hildebrand, Introduction to Numerical Analysis, Dover Publication, South Asia Edition, 2008.
8. A. Iserles, A First Course in the Numerical Analysis of Differential Equations, Cambridge University Press, 1996.
9. J. H. Mathews, Numerical Methods for Mathematics, Science and Engineering, PHI, 1994.
10. V. S. Ryabenkii & S. V. Tsykkov, A theoretical Introduction to Numerical Analysis by, Chapman & Hall/CRC, 2010