Numerical Methods with Worked Examples

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Springer Science & Business Media, Aug 31, 1997 - Mathematics - 273 pages
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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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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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About the author (1997)

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.

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