Numerical Methods(NM) Syllabus

Course Description 

This course covers solution of nonlinear equations, interpolation and approximation, numerical differentiation and integration and solution of linear algebraic equation, ordinary differential equations and partial difrential equations. it provides knowledge for numerical analysis.

Course Objectives 

The general objectives of this subject are to make students familiar with the 

theory of numerical analysis for solving algebraic and transcendental equations, 

solution of ordinary and partial differential equations, numerical di fferentiation 

and integration.

1. Solution of Nonlinear Equations

teaching hours: 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

2. Interpolation and Approximation

teaching hours: 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.

3. Numerical Differentiation and Integration

teaching hours: 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.

4. Solution of Linear Algebraic Equations

teaching hours: 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.

5. Solution of Ordinary Differential Equations

teaching hours: 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.

6. Solution of Partial Differential Equations

teaching hours: 5 hrs

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

Laboratory Works 

Laboratory works will consist of program development and testing of Non-linear Equations, Interpolation, Numerical Differentiation and Integration, Linear Algebraic Equations, Ordinary and Partial Differential Equations using C or C+ I Builder.