Probability- Axioms of probability –Discrete and continuous random variables – Moment generating functions – Binomial distribution – Poisson distribution– Uniform distribution –Exponential distribution - Normal distribution.

Newton Raphson method –Pivoting — Gauss Jordan method- Iterative methods of Gauss Jacobi and Gauss Seidal- LU decomposition method – Matrix Inversion by Gauss – Jordan method – Eigenvalues of a matrix by power method.

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

Approximation of derivatives using interpolation polynomials – Numerical integration using Trapezoidal, Simpson’s 1/3rd, 3/8th rule– Two point and three point Gaussian quadrature formulae – Evaluation of double integrals by Trapezoidal and Simpson’s 1/3 rules

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