MA8491 – NOTES & QP
MA8491 – SYLLABUS
UNIT I SOLUTION OF EQUATIONS AND EIGENVALUE 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 method — Iterative methods of Gauss Jacobi and Gauss Seidel — Eigenvalues of a matrix by Power method and Jacobi?s method for symmetric matrices.
UNIT II INTERPOLATION AND APPROXIMATION
Interpolation with unequal intervals — Lagrange?s interpolation — Newton?s divided difference interpolation — Cubic Splines — Difference operators and relations — Interpolation with equal intervals — Newton?s forward and backward difference formulae.
UNIT III NUMERICAL DIFFERENTIATION AND INTEGRATION
Approximation of derivatives using interpolation polynomials — Numerical integration using Trapezoidal, Simpson?s 1/3 rule — Romberg?s Method — Two point and three point Gaussian quadrature formulae — Evaluation of double integrals by Trapezoidal and Simpson?s 1/3 rules.
UNIT IV INITIAL VALUE PROBLEMS FOR ORDINARY DIFFERENTIAL EQUATIONS
Single step methods — Taylor?s series method — Euler?s method — Modified Euler?s method — Fourth order Runge — Kutta method for solving first order equations — Multi step methods — Milne?s and Adams — Bash forth predictor corrector methods for solving first order equations.
UNIT V BOUNDARY VALUE PROBLEMS IN ORDINARY AND PARTIAL
Finite difference methods for solving second order 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.