NUMERICAL METHODS CSE Syllabus for
MA-202 NUMERICAL METHODS [3 1 0 4]
Roots of algebraic and transcendental equations, Bisection method, Regula – Falsi method, Newton –Raphson method, Bairstow’s method and Graeffe’s root squaring method.
Solution of simultaneous algebraic equations, matrix inversion and eigen-value problems, triangularisation method, Jacobi’s and Gauss-Siedel iteration method, partition method for matrix inversion, power method for largest eigen-value and Jacobi’s method for finding all eigen-values.
Finite differences, interpolation and numerical differentiation, forward, backward and central differences, Newton’s forward, backward and divided difference interpolation formulas, Lagrange’s interpolation formula, Stirling’s and Bessel’s central difference interpolation formulas, numerical differentiation using Newton’s forward and backward difference formulas and numerical differentiation using Stirling’s and Bessel’s central difference interpolation formulas.
Numerical integration, Trapezoidal rule, Simpson’s one-third rule and numerical double integration using Trapezoidal rule and Simpson’s one-third rule.
Taylor’s series method, Euler’s and modified Euler’s methods, Runge-Kutta fourth order methods for ordinary differential equations, simultaneous first order differential equations and second order differential equations.
Boundary value problems, finite difference methods for boundary value problems.
Partial differential equations, finite difference methods for elliptic, parabolic and hyperbolic equations.
1. S S Sastry, Introductionary Methods of Numerical Analysis, 3rd Edition, Prentice Hall of India Pvt.Ltd., New India -1999
2. S C Chapra and R P Canale, Numerical Methods for Engineers, 2nd Edition, McGraw Hill Book Company, Singapore 1990.
3. Grewal, B S, ”Numerical Methods”, Khanna Publishers ,Delhi.
4. Kalavathy S., “Numerical Methods”, Cengage Publishers, New Delhi.
5. Burden Richard L. , Faires J. Douglas, “Numerical Anlaysis” , Cengage Learning , New Delhi.