This course gives a basic introduction to Numerical Analysis.
Errors in computation: Representation and arithmetic of numbers, source of errors, error propagation, error estimation. Numerical solution of non-linear equations: Bisection method, Secant method, Newton-Raphson method, Fixed point methods, Muller’s method. Interpolations: Lagrange interpolation, Newton divided differences, Hermite interpolation, Piecewise polynomial interpolation. Approximation of functions: Weierstrass and Taylor expansion, Least square approximation. Numerical Integration: Trapezoidal rule, Simpson’s rule, Newton-Cotes rule, Guassian quadrature. Numerical solution of ODE: Euler’s method, multi-step methods, Runge-Kutta methods, Predictor-Corrector methods. Solutions of systems of linear equations: Gauss elimination, pivoting, matrix factorization, Iterative methods – Jacobi and Gauss-Siedel methods. Matrix eigenvalue problems: power method.