Course Title: Numerical Methods (3 Cr)
Course Code: CACS252
Class Load: 6 Hrs. / Week (Theory: 3 Hrs, Tutorial: 1, Practical: 2 Hrs.)

Unit I Solution of Nonlinear Equations

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 

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

 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 

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(Jacohi & Gauss-Seidel Iteration),Power Method. 

 Unit 5 Solution of Ordinary Differential Equations 

Introduction to Differential Equations Value Problem, Taylor Series Method. Picard's Method, Eater's Method and Its Accuracy, Heun's method, Runge-Kutta Methods. Solution of Higher Order Equations. Boundary Value Problems, Shooting Method and Its Algorithm. 

Unit 6 Solution of Partial Differential Equations 

Introduction to Partial Differential Equations. Deriving Difference Equations. Laplacian Equation and Poisson's Equation.