# Numerical Methods for Science and Engineering

295

Author: Dr R Muthucumaraswamy

ISBN Print Book: 9789391549565

Copy Right Year: 2024

Pages: 234

Binding: Soft Cover

Publisher:  Yes Dee Publishing

SKU: 9789391549565 Category:

## Description

This book is designed for a one semester course on Numerical Methods taught across all branches of Engineering. This book has simple and step by step explanation with a wide variety of solved examples, which enables the students to understand the course in depth. The author has taken care to maintain an optimum depth in covering all the topics, which fulfills the requirements of both students and faculty. This book is also useful in preparing for GATE and other competitive examinations.

Key Features

• Comprehensive coverage of all topics
• Wide variety of solved problems and standard questions
• Application of the topics are discussed in each chapter
• MCQ’s and problems for practice are included in each chapter

Chapter 1 Solution of Algebraic and Transcendental Equations

1.1 Introduction

1.2 Gauss Elimination Method (Direct Method)

Solved Problems 1.1 to 1.2

1.3 Gauss-Jordan Method (Direct Method)

Solved Problems 1.3 to 1.6

1.4 Inverse of a Matrix by Gauss-Jordan Method (Direct Method)

Solved Problems 1.7 to 1.10

1.4.1 Errors

1.5 Iterative Method

1.5.1 Gauss-Jacobi Iterative Method

Solved Problems 1.11 to 1.13

1.5.2 Gauss-Seidel Iterative Method

Solved Problems 1.14 to 1.15

1.6 Method of Successive Approximation (Simple Iteration Method)

Solved Problems 1.16 to 1.19

1.7 Newton-Raphson Iterative Method

Solved Problems 1.20 to 1.24

1.7.1 Criterion for Convergence in Newton-Raphson Method

Solved Problems 1.25 to 1.27

1.8 EigenValue of a Matrix by Power Method

Solved Problems 1.28 to 1.32

1.9 Thomas Algorithm for Tridiagonal System of Equations

Solved Problems 1.33 to 1.35

Exercise

Multiple-Choice Questions

Exercise Problems

Chapter 2 Interpolation and Approximation

2.1 Introduction

2.2 Lagrange’s Interpolation Formula for Equal as Well as Unequal Intervals

Solved Problems 2.1 to 2.3

2.2.1 Inverse Interpolation

Solved Problem 2.4

2.3 Difference Operators

2.4 Newton’s Forward Interpolation Formula

2.5 Newton’s Backward Interpolation Formula

Solved Problems 2.5 to 2.9

2.6 Newton’s Divided Difference Formula for Interpretation

Solved Problems 2.10 to 2.12

Multiple-Choice Questions

Exercise Problems

Chapter 3 Numerical Differentiation and Integration

3.1 Introduction

3.2 Newton’s Forward Formula for Differentiation

3.3 Newton’s Backward Formula for Differentiation

Solved Problems 3.1 to 3.3

3.4 Numerical Differentiation for Unequal Intervals

Solved Problems 3.4 to 3.7

3.5 Numerical Integration

3.5.1 Trapezoidal Rule

3.5.2 Simpson’s 1/3 Rule

3.5.3 Simpson’s 3/8 Rule

Solved Problems 3.8 to 3.15

3.6 Romberg Integration

Solved Problem 3.16

3.7 Double Integration

Solved Problems 3.17 to 3.23

3.8 Two-Point and Three-Point Gaussian Quadrature Formula

Solved Problems 3.24 to 3.30

Multiple-Choice Questions

Exercise Problems

Chapter 4 Numerical Solution of Ordinary Differential

Equations

4.1 Introduction

4.2 Taylor Series Method

Solved Problems 4.1 to 4.4

4.2.1 Point wise Method in Taylor’s Series

Solved Problem 4.5

4.3 Euler’s Method

Solved Problems 4.6 to 4.8

4.4 Modified Euler’s Method

Solved Problems 4.9 to 4.10

4.5 RungeKutta Method of Fourth Order

Solved Problems 4.11 to 4.13

4.5.1 RungeKutta Method for Simultaneous First Order Differential Equation

Solved Problems 4.14 to 4.15

4.5.2 RungeKutta Method for Second Order Differential Equation

Solved Problem 4.16

4.6 Multi Step Methods

4.6.1 Milne’s Predictor-Corrector Method

Solved Problems 4.17 to 4.20

Solved Problem 4.21

Multiple-Choice Questions

Exercise Problems

Chapter 5 Numerical Solution of Partial Differential

Equation

5.1 Introduction

5.2 Classification

Solved Problems 5.1 to 5.3

5.3 Difference Quotient

5.4 Finite Difference Formula for Two-Dimensional Heat Equation

Solved Problems 5.4 to 5.7

5.5 Poisson Equation

Solved Problems 5.8 to 5.9

5.6 One-Dimensional Wave Equation Numerical Solution

(Hyperbolic Equation)

Solved Problems 5.10 to 5.13

5.7 One-Dimensional Heat Equation

5.7.1 Finite Difference Solution of One-Dimensional Heat Equation

5.7.2 Explicit Method

Solved Problems 5.14 to 5.15

5.7.3 Implicit Method

5.8 Crank Nicolson Method

Solved Problems 5.16 to 5.17

Multiple-Choice Questions

Exercise Problems