NM

MTH 214.3 (Credit hours 3, Practical 3)

Numerical Methods

BCA, Second Year,  Fourth Semester

Course Objectives:

This course aims to provide familiarity with the theory of numerical analysis for solving algebraic and transcendental equations, solution of ordinary and partial differential equations related to engineering problems, numerical differentiation and integration.

Course Contents:

1. Solution of Nonlinear Equations                                                                                      10 hours

Review of calculus and Taylor's theorem, Errors in numerical calculations, Trial and error method, Bisection method, Newton's method, Secant method and their convergence,  Fixed point iteration and is convergence

2. Solution of Linear Algebraic Equations                                                                          10 hours

Review of the existence of solutions and properties of matrices, Gaussian Climination method, pivoting, ill conditioning, Gauss-Jordan method, Inverse of matrix using Gauss elimination method, Method of factorization, Dolittle algorithm, Cholesky's factorization, Iterative solutions, Solving eigen value problems using power method

3. Numerical Differentiation and Integration                                                                      6 hours

Newton's differentiation formulas, Maxima and minima of tabulated function, Netwon-ote's quadrature formulas, Gaussian integration algorithm, Romberg integration formulas

4. Interpolation and Approximation                                                                                    8 hours

Lagrange's polynomials, Newton's interpolation using difference and divided differences. Cubic spline interpolation, Least squares method for linear and nonlinear data

5. Solution of Ordinary Differential Equations                                                                   8 hours

Review of differential equations, initial value problem, Taylor series method picard'smethod, Euler's method and its accuracy, Henu's method, Runge-Kutta methods, Solution of the higher order equations, Boundary value problems, Shooting method and its algorithm

6. Solution of Partial Differential Equations                                                                       6 hours

Review of partial differential equations, Deriving difference equations, Laplacian equation and Poisson's equation, engineering examples

Text Book:

1. C.F. Gerald and P.O. Wheatly: Applied Numerical Analysis, 4th Edition, addison Wesley publishing Company, New York.

Reference Book:

1. W. Chency and D. Kinciad: Numerical Mathematics and Computing, 2nd Edition, Brooks Cole Publishing Co, 1985.
2. W.H. Press, B.P. Flannery et.al.: Numerical Recipes in C, 1st Edition, Cambridge press, 1988.
3. S. Yakwitz and F. Szidarovszky: An Introduction to Numerical Computations, 2nd Edition, Macmillan Publishing Co., New York.  

 

2. Gauss Jordan Method