# Numerical Methods with Worked Examples

Springer Science & Business Media, Aug 31, 1997 - Mathematics - 273 pages
This book is for students following a module in numerical methods, numerical techniques, or numerical analysis. It approaches the subject from a pragmatic viewpoint, appropriate for the modern student. The theory is kept to a minimum commensurate with comprehensive coverage of the subject and it contains abundant worked examples which provide easy understanding through a clear and concise theoretical treatment.

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wor

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very good book if you are looking for solved examples in numerical analysis

### Contents

 Linear equations 1 11 INTRODUCTION 2 13 GAUSSIAN ELIMINATION 6 14 SINGULAR SYSTEMS 16 15 SYMMETRIC POSITIVE DEFINITE SYSTEMS 18 16 ITERATIVE REFINEMENT 19 17 ITERATIVE METHODS FOR SPARSE SYSTEMS 24 18 EXERCISES 29
 65 INTEGER PROGRAMMING 144 66 DECISION PROBLEMS 148 67 THE TRAVELLING SALESMAN PROBLEM 150 68 THE MACHINE SCHEDULING PROBLEM 152 69 EXERCISES 156 Optimization 163 71 INTRODUCTION 164 73 GOLDEN SECTION SEARCH 167

 Nonlinear equations 35 21 INTRODUCTION 36 22 BISECTION METHOD 37 23 RULE OF FALSE POSITION 40 24 THE SECANT METHOD 42 25 THE BUS AND DEKKER METHOD 45 26 NEWTONRAPHSON METHOD 47 27 COMPARISON OF METHODS FOR A SINGLE EQUATION 50 28 NEWTONS METHOD FOR SYSTEMS OF NONLINEAR EQUATIONS 51 29 EXERCISES 58 Curve fitting 63 32 LINEAR INTERPOLATION 64 33 POLYNOMIAL INTERPOLATION 70 34 LEAST SQUARES APPROXIMATION 79 35 EXERCISES 85 Numerical integration 91 41 INTRODUCTION 92 43 INTEGRATION OF FUNCTIONS 98 44 HIGHER ORDER RULES 103 45 ADAPTIVE QUADRATURE 105 46 EXERCISES 107 Numerical differentiation 111 51 INTRODUCTION 112 53 THREEAND FIVEPOINT FORMULAE 114 54 HIGHER ORDER DERIVATIVES 117 55 CAUCHYS THEOREM 120 56 EXERCISES 123 Linear programming 129 61 INTRODUCTION 130 63 CANONICAL FORM 134 64 THE SIMPLEX METHOD 136
 74 MINIMIZATION STRATEGY FOR UNCONSTRAINED PROBLEMS 170 76 A RANKONE METHOD 174 77 CONSTRAINED OPTIMIZATION 181 78 MINIMIZATION BY USE OF A SIMPLE PENALTY FUNCTION 182 79 MINIMIZATION USING A LAGRANGIAN 184 710 A PENALTY FUNCTION FOR INEQUALITY CONSTRAINTS 187 711 EXERCISES 190 Ordinary differential equations 195 81 INTRODUCTION 196 82 FIRST ORDER EQUATIONS 198 83 HIGHER ORDER EQUATIONS 209 84 BOUNDARY VALUE PROBLEMS 212 85 FINITE DIFFERENCES 215 86 ACCURACY 217 87 EXERCISES 219 Eigenvalues and eigenvectors 227 92 THE CHARACTERISTIC POLYNOMIAL 229 93 THE POWER METHOD 231 94 EIGENVALUES OF SPECIAL MATRICES 235 95 A SIMPLE QR METHOD 237 96 EXERCISES 242 Statistics 247 101 INTRODUCTION 248 103 LEAST SQUARES ANALYSIS 256 104 RANDOM NUMBERS 260 105 RANDOM NUMBER GENERATORS 261 106 MONTECARLO QUADRATURE 264 107 EXERCISES 265 References 269 Index 271 Copyright

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Jim Hoskins is the author and editor of the popular Exploring IBM series of books. He lives and fishes in Gulf Breeze, Florida. Chris Phillips is a professional fishing guide who has fished the Gulf waters for many years. He lives in Pensacola, Florida.