UNIT I SOLUTION OF EQUATIONS AND EIGENVALUE PROBLEMS

1.1 Solution of algebraic and transcendental equations

1.2 Fixed point iteration method

1.3 Newton Raphson method

1.4 Solution of linear system of equations

1.5 Gauss elimination method

1.6 Pivoting

1.7 Gauss Jordan method

1.8 Iterative methods of Gauss Jacobi and Gauss Seidel

1.9 Matrix Inversion by Gauss Jordan method

1.10 Eigen values of a matrix by Power method

UNIT II INTERPOLATION AND APPROXIMATION

2.1 Interpolation with unequal intervals - Lagrange's interpolation

2.2 Newton’s divided difference interpolation

2.3 Cubic Splines

2.4 Interpolation with equal intervals - Newton’s forward and backward difference formula

UNIT III NUMERICAL DIFFERENTIATION AND INTEGRATION

3.1 Approximation of derivatives using interpolation polynomials

3.2 Numerical integration using Trapezoidal, Simpson’s 1/3 rule – Romberg’s method

3.3 Two point and three point Gaussian quadrature formula

3.4 Evaluation of double integrals by Trapezoidal and Simpson’s 1/3 rules

UNIT IV INITIAL VALUE PROBLEMS FOR ORDINARY DIFFERENTIAL EQUATIONS

4.1 Single Step methods

4.2 Taylor’s series method

4.3 Euler’s method - Modified Euler’s method

4.4 Fourth order Runge-Kutta method for solving first order equations

4.5 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 DIFFERENTIAL EQUATIONS

5.1 Finite difference methods for solving two-point linear boundary value problems

5.2 Finite difference techniques for the solution of two dimensional Laplace’s and Poisson’s equations on rectangular domain

5.3 One dimensional heat flow equation by explicit and implicit (Crank Nicholson) methods

5.4 One dimensional wave equation by explicit method