Course Details
Subject {L-T-P / C} : MA2305 : Numerical Analysis { 3-1-0 / 4}
Subject Nature : Theory
Coordinator : Prof. Jugal Mohapatra
Syllabus
Definitions, Sources, Propagation of errors, Floating-point arithmetic, and rounding errors. Root finding of nonlinear equations: Bisection method, Secant and Regula-falsi methods, Newton's method, Fixed point iterations, Convergence analysis of these methods. Newton's method for nonlinear systems.
Finite differences, Polynomial interpolation, Lagrange, Newton, forward/backward interpolation.
Numerical integration, Trapezoidal, Simpson's rules, Newton-Cotes formula, Gaussian quadrature.
IVP: Taylor series method, Picard’s method, Euler and modified Euler methods, Runge-Kutta methods.
Numerical methods in linear algebra: Gauss elimination, LU-Factorization, Matrix inversion Linear systems: Solution by iteration Matrix Eigenvalue problems, Inclusion of matrix Eigenvalues, Eigenvalues by iteration.
Course Objectives
- This course is an introduction to a broad range of numerical methods for solving mathematical problems that arise in Science and Engineering. The goal is to provide a basic understanding ofthe derivation, analysis, and use of these numerical methods, along with a rudimentary understanding of finite precision arithmetic and the conditioning and stability of the various problems and methods.
Course Outcomes
This will help to choose, develop and apply the appropriate numerical techniques for problems, interpret the results, and assess accuracy. The problems cover (i) systems of linear equations, (ii) eigenvalue calculation (iii) interpolation, approximation, and integration of functions (iv) initial values problems governed by ordinary differential equations (v) nonlinear equations.
Essential Reading
- K. E. Atkinson, "Introduction to Numerical Analysis", John Wiley , 2nd Edition, 1989
- R. L. Burden, J. Douglas Faires, "Numerical Analysis", Cengage Learning , 2011
Supplementary Reading
- C. F. Gerald and P. O. Wheatley, Applied Numerical Analysis, Pearson Education India , 2007
- E. Süli, D. F. Mayers, "An Introduction to Numerical Analysis", Cambridge University Press , 2003