MALAVIYA NATIONAL INSTITUTE OF TECHNOLOGY, JAIPUR.
DEPARTMENT OF MATHEMATICS
SYLLABUS
MAT-637
Numerical Analysis
4Credits (3L+1T+0P)
Errors: Floating-point approximation of a number, Loss of significance and error
propagation, Stability in numerical computation.
Linear Systems: Gaussian elimination with pivoting strategy, LU factorization, Residual
corrector method, Solution by iteration (Jacobi and Gauss-Seidal with convergence analysis),
Matrix norms and error in approximate solution, Eigenvalue problem (Power method),
Gershgorin’s theorem (without proof). Nonlinear Equations: Bisection method, Fixed-point
iteration method, Secant method, Newton's method, Rate of convergences, Solution of a
system of nonlinear equations.
Interpolation by Polynomials: Lagrange interpolation, Newton interpolation and divided
differences, Error of the interpolating polynomials
Differentiation and Integration: Difference formulae, Some basic rules of integration.
Differential Equations: Euler method, Runge- Kutta methods, Multi-step methods, PredictorCorrector methods . Finite difference method for ordinary and Partial differential equations.
Books Recommended:1. K. E. Atkinson, An Introduction to Numerical Analysis, 2nd Edition, Wiley-India, 1989.
2. S. D. Conte and C. de Boor, Elementary Numerical Analysis - An Algorithmic Approach,
3rd Edition, McGraw-Hill, 1981.
3. R. L. Burden and J. D. Faires, Numerical Analysis, 7th Edition, Thomson, 2001.