This book is a compilation of the most important and widely applicable methods for evaluating and approximating integrals. It is an indispensable time saver for engineers and scientists needing to evaluate integrals in their work. From the table of contents: - Applications of Integration - Concepts and Definitions - Exact Analytical Methods - Approximate Analytical Methods - Numerical Methods: Concepts - Numerical Methods: Techniques
Author(s): Daniel Zwillinger
Edition: First Edition
Publisher: Jones and Bartlett
Year: 1992
Language: English
Pages: 381
Tags: Математика;Математический анализ;
Cover ......Page 1
Contents ......Page 4
Preface ......Page 7
Introduction ......Page 9
How to Use This Book ......Page 11
1 Differential Equations: Integral Representations ......Page 14
2 Differential Equations: Integral Transforms ......Page 19
3 Extremal Problems ......Page 27
4 Function Representation ......Page 33
5 Geometric Applications ......Page 37
6 MIT Integration Bee ......Page 41
7 Probability ......Page 43
8 Summations: Combinatorial ......Page 44
9 Summations: Other ......Page 47
10 Zeros of Functions ......Page 53
11 Miscellaneous Applications ......Page 58
12 Definitions ......Page 60
13 Integral Definitions ......Page 64
14 Caveats ......Page 71
15 Changing Order of Integration ......Page 74
16 Convergence of Integrals ......Page 77
17 Exterior Calculus ......Page 80
18 Feynman Diagrams ......Page 83
19 Finite Part of Integrals ......Page 86
20 Fractional Integration ......Page 88
21 Liouville Theory ......Page 92
22 Mean Value Theorems ......Page 96
23 Path Integrals ......Page 99
24 Principal Value Integrals ......Page 105
25 Transforms: To a Finite Interval ......Page 108
26 Transforms: Multidimensional Integrals ......Page 110
27 Transforms: Miscellaneous ......Page 116
28 Change of Variable ......Page 122
29 Computer Aided Solution ......Page 130
30 Contour Integration ......Page 142
31 Convolution Techniques ......Page 153
32 Differentiation and Integration ......Page 155
33 Dilogarithms ......Page 158
34 Elliptic Integrals ......Page 161
35 Frullanian Integrals ......Page 170
36 Functional Equations ......Page 173
37 Integration by Parts ......Page 175
38 Line and Surface Integrals ......Page 177
39 Look Up Technique ......Page 183
40 Special Integration Techniques ......Page 194
41 Stochastic Integration ......Page 199
42 Tables of Integrals ......Page 203
43 Asymptotic Expansions ......Page 208
44 Asymptotic Expansions: Multiple Integrals ......Page 212
45 Continued Fractions ......Page 216
46 Integral Inequalities ......Page 218
47 Integration by Parts ......Page 228
48 Interval Analysis ......Page 231
49 Laplace's Method ......Page 234
50 Stationary Phase ......Page 239
51 Steepest Descent ......Page 243
52 Approximations: Miscellaneous ......Page 253
53 Introduction to Numerical Methods ......Page 256
54 Numerical Definitions ......Page 257
55 Error Analysis ......Page 259
56 Romberg Integration / Richardson Extrapolation ......Page 263
57 Software Libraries: Introduction ......Page 267
58 Software Libraries: Taxonomy ......Page 271
59 Software Libraries: Excerpts from GAMS ......Page 273
60 Testing Quadrature Rules ......Page 285
61 Truncating an Infinite Interval ......Page 288
62 Adaptive Quadrature ......Page 290
63 Clenshaw-Curtis Rules ......Page 294
64 Compound Rules ......Page 296
65 Cubic Splines ......Page 298
66 Using Derivative Information ......Page 300
67 Gaussian Quadrature ......Page 302
68 Gaussian Quadrature: Generalized ......Page 305
69 Gaussian Quadrature: Kronrod's Extension ......Page 311
70 Lattice Rules ......Page 313
71 Monte Carlo Method ......Page 317
72 Number Theoretic Methods ......Page 325
73 Parallel Computer Methods ......Page 328
74 Polyhedral Symmetry Rules ......Page 329
75 Polynomial Interpolation ......Page 332
76 Product Rules ......Page 336
77 Recurrence Relations ......Page 338
78 Symbolic Methods ......Page 342
79 Tschebyscheff Rules ......Page 345
80 Wozniakowski's Method ......Page 346
81 Tables: Numerical Methods ......Page 350
82 Tables: Formulas for Integrals ......Page 353
83 Tables: Numerically Evaluated Integrals ......Page 361
Mathematical Nomenclature ......Page 364
Index ......Page 366
Back Cover ......Page 381
