**CHHATTISGARH SWAMI VIVEKANAND TECHNICAL UNIVERSITY, BHILAI (CG)**

**Semester B.E. III Sem. **

**Sub: Numerical Analysis & Computer Programming (C & C++)**

UNIT – I Approximation and Errors in Computation

Approximation and round of errors, truncation errors and Taylor Series, Determination of roots of

polynomials and transcendental equations by Graphical methods and Bisection, Regula-falsi, Secant and

Newton-Raphson methods, Solution of Linear simultaneous, linear algebraic equations by Gauss

Elimination Gauss-Jordan and Gauss-Siedel iteration method.

UNIT – II Empirical laws, Curve Fitting & Interpolation

Curve fitting linear and non-linear regression analysis (Method of group average and Least squares) Finite

differences, Backward, forward and central difference relation and their use in Numerical differentiation

and integration and their application in interpolation.

UNIT – III Numerical Solution of Ordinary Differential Equations

Numerical integration by Trapezoidal rule, Simpson’s (1/3

rd & 3/8th

) rule and its error estimation.

Application of difference relations in the solution of partial differential equations. Application of

difference relations in the solution of partial differential equations. Numerical solution of ordinary

differential equations by Taylor’s series, Euler, Modified Euler, Runge-Kutta and Predictor-Corrector

method.

UNIT – IV Numerical Solutions of Partial Differential Equations

Introduction, Classification of second order equations, Finite difference approximations to partial

derivatives, Elliptic equations, solution of Laplace equation, solution of Poisson’s equation, Solution of

Poisson’s equation, Solution of elliptic equations by relaxation method, Parabolic equations, Solution of

one-dimensional heat equation, Solution of two-dimensional heat equation, Solution of two-dimensional

heat equation, Hyperbolic equations, solution of wave equation.

UNIT – V Computer Programming

I/

O statement, Mathematical, Relational & Conditional Statements & Expressions. Switch Loops and

Control Statements. Introduction to one dimensional arrays and two dimensional arrays. Basics of I/O

file handling.

TEXT BOOKS

1.

Numerical Methods in Engineering & Science – Dr. B.S. Grewal – Khanna Publishers, 6th

Edn. 2004

2.

Numerical Methods – P. Kandasamy, K. Thilagavathy & K. Gunavathy – S. Chand & Co., 2nd

Rev. Edn. – 2003

REFERENCES

1.

Let us C – Yashwant Kanitkar –

2.

Introductory Methods of Numerical Analysis – S.S. Sastry, 3rd

Edn. – PHI – New Delhi, 2003

3.

Numerical Mathematical Analysis – James B. Scarborough, 6th

Edn. – Oxford & IBH Publishing Co. – New Delhi,

4.

Theory & Problems in Numerical Methods – T. Veerarajan, T. Ramchandran – TMH, New Delhi, 2004

5.

Numerical Methods for Engineers – Steven C. Chapra, Raymond P. Canale,