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Anna Numerical Methods Sem-III
No Units Titles Sub Titles Chapters
1 Unit 1 Solutions of Equtions and Eigen Value Problems Solution of algebraic and transcendental equations - Fixed point iteration method - Newton- Raphson method- Solution of linear system of equations - Gauss Elimination method - Pivoting - Gauss-Jordan methods - Iterative methods of Gauss-Jacobi and Gauss-Seidel - Matrix Inversion by Gauss-Jordan method - Eigenvalues of a matrix by Power method and by Jacobi's method VIEW CHAPTERS
2 Unit 2 Interpolatation and Approximation Interpolation with unequal intervals - Lagrange interpolation - Newton's divided difference interpolation - Cubic Splines - Interpolation with equal intervals - Newton's forward and backward difference formulae - Least square method - Linear curve fitting VIEW CHAPTERS
3 Unit 3 Numerical Differentiation and Integration Approximation of derivatives using interpolation polynomials - Numerical integration using Trapezoidal, Simpson's 1/3 and Simpson's 3/8 rules - Romberg's method - Two point and three point Gaussian quadrature formulae - Evaluation of double integrals by Trapezoidal and Simpson's rules VIEW CHAPTERS
4 Unit 4 Intial Value Problems for Ordinary Differential Equation Single step-methods - Taylor's series method - Euler's method - Modified Euler's method - Fourth order Runge-Kutta method for solving first and second order equations - Multi-step methods - Milne's and Adams-Bashforth predictor-corrector methods for solving first order equations VIEW CHAPTERS
5 Unit 5 Boundary Value problem in Ordinary andPartial Differential Equations Finite difference methods for solving two-point linear boundary value problems, Finite difference techniques for the solution of two dimensional Laplace's and Poisson's equations on rectangular domain - One dimensional heat-flow equation by explicit and implicit (Crank- Nicholson) methods - One dimensional wave equation by explicit method VIEW CHAPTERS
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