Unit 1: Solution of Nonlinear Equations (10 hrs)
Introduction, Types of Equation, Errors in Computing, The Bisection Method; The Method of False Position, Newton- Raphson Method, Solution of System of Nonlinear Equation, Fixed Point Iteration and Convergence
Unit 2: Interpolation and Approximation (10 hrs)
Introduction, Errors in Polynomial Interpolation, Lagrange's Polynomials, Newton's Interpolation using Difference and Divided Differences, Cubic Spline Interpolation, Least Squares Method for Linear and Non-linear Data.
Unit 3: Numerical Differentiation and Integration (5 hrs)
Introduction to Numerical Differentiation, Newton's Differentiation Formulas, Numerical Integration (Trapezoidal Rule, Simpson's 1/3 rule, 3/8 rule); Romberg Integration; Numerical Double Integration.
Unit 4: Solution of Linear Algebraic Equations (10 hrs)
Review of the existence of solutions and properties of matrices. Consistency of a Linear System of Equations, Gaussian Elimination Method, Gauss-Jordan Method, Inverse of matrix using Gauss Elimination Method, Method of factorization, Iterative Methods(Jacobi & Gauss-Seidel Iteration),Power Method.
Unit 5: Solution of Ordinary Differential Equations (7 hrs)
Introduction to Differential Equations, Initial Value Problem, Taylor Series Method, Picard's Method, Euler's Method and Its Accuracy, Heun's method, Runge-Kutta Methods, Solutions of Higher Order Equations, Boundary Value Problems, Shooting Method and Its Algorithm.
Unit 6: Solution of Partial Differential Equations (5 hrs)
Introduction to Partial Differential Equations, Deriving Differences Equations, Laplacian Equation and Poisson's Equation.