# Numerical Methods(NM) Syllabus

 Title Numerical Methods Short Name NM Course code CACS252 Nature of course Theory + Practical Semester fourth-semester Full marks 60 + 20 + 20 Pass marks 24 + 8 + 8 Credit Hrs 3 Elective/Compulsary Compulsary

### Course Description

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.

### Units and Unit Content

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.

### Lab and Practical works

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.