computer based numerical techniqe by manish goyal

Chapter 1 Introduction 3—30
1.1 Introduction to Computers 4
1.2 Definitions 4
1.3 Introduction to “C” Language 6
1.4 Advantages/Features of ‘C’ language 7
1.5 ‘C’ Character Set 7
1.6 ‘C’ Constants 8
1.7 “C” Variables 9
1.8 ‘C’ Key Words 10
1.9 “C Instructions” 10
1.10 Hierarchy of Operations 11
1.11 Escape Sequences 12
1.12 Basic Structure of ‘‘C’’ Program 12
1.13 Decision Making Instructions in “C” 14
1.14 Loop Control Structure 17
1.15 Arrays and String 18
1.16 Pointers 19
1.17 Structure and Unions 20
1.18 Storage Classes in ‘C’ 21
Chapter 2 Errors 31—76
2.1 Errors and Their Analysis 31
2.2 Accuracy of Numbers 32
2.3 Errors 34
2.4 A General Error Formula 42
2.5 Errors in Numerical Computations 43
2.6 Inverse Problems 46
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vi CONTENTS
2.7 Error in a Series Approximation 56
2.8 Mathematical Preliminaries 60
2.9 Floating Point Representation of Numbers 61
2.10 Arithmetic Operations with Normalized Floating Point Numbers 63
2.11 Machine Computation 71
2.12 Computer Software 72
Chapter 3 Algebraic and Transcendental Equations 77—196
3.1 Bisection (or Bolzano) Method 77
3.2 Algorithm 78
3.3 Flow-Chart 79
3.4 Program Writing 80
3.5 Order of Convergence of Iterative Methods 80
3.6 Order of Convergence of Bisection Method 80
3.7 Convergence of a Sequence 81
3.8 Prove that Bisection Method Always Converges 81
3.9 Program to Implement Bisection Method 84
3.10 Iteration Method—(Successive Approximation Method) 94
3.11 Sufficient Condition for Convergence of Iterations 95
3.12 Theorem 95
3.13 Convergence of Iteration Method 96
3.14 Algorithm for Iteration Method 96
3.15 Flow-Chart for Iteration Method 98
3.16 Computer Program 99
3.17 The Method of Iteration for System of Non-Linear Equations 111
3.18 Method of False Position or Regula-Falsi Method 113
3.19 Algorithm 114
3.20 Flow-Chart 116
3.21 Convergence of Regula-Falsi Method 130
3.22 Secant Method 132
3.23 Lin-Bairstow’s Method or Method for Complex Root 135
3.24 Muller’s Method 141
3.25 Algorithm of Muller’s Method 142
3.26 Flow-Chart for Muller’s Method 144
3.27 The Quotient-Difference Method 152
3.28 Horner’s Method 156
3.29 Newton-Raphson Method 158
3.30 Convergence 159

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