The Handbook of Integration

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ISBN: 9780867202939 | 0867202939
Cover: Hardcover
Copyright: 11/2/1992

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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

Preface
Introduction
How to Use This Book
Applications of Integration
Differential Equations: Integral Representations	p. 1
Differential Equations: Integral Transforms	p. 6
Extremal Problems	p. 14
Function Representation	p. 20
Geometric Applications	p. 24
MIT Integration Bee	p. 28
Probability	p. 30
Summations: Combinatorial	p. 31
Summations: Other	p. 34
Zeros of Functions	p. 40
Miscellaneous Applications	p. 45
Concepts and Definitions
Definitions	p. 47
Integral Definitions	p. 51
Caveats	p. 58
Changing Order of Integration	p. 61
Convergence of Integrals	p. 64
Exterior Calculus	p. 67
Feynman Diagrams	p. 70
Finite Part of Integrals	p. 73
Fractional Integration	p. 75
Liouville Theory	p. 79
Mean Value Theorems	p. 83
Path Integrals	p. 86
Principal Value Integrals	p. 92
Transforms: To a Finite Interval	p. 95
Transforms: Multidimensional Integrals	p. 97
Transforms: Miscellaneous	p. 103
Exact Analytical Methods
Change of Variable	p. 109
Computer Aided Solution	p. 117
Contour Integration	p. 129
Convolution Techniques	p. 140
Differentiation and Integration	p. 142
Dilogarithms	p. 145
Elliptic Integrals	p. 148
Frullanian Integrals	p. 157
Functional Equations	p. 160
Integration by Parts	p. 162
Line and Surface Integrals	p. 164
Look Up Technique	p. 170
Special Integration Techniques	p. 181
Stochastic Integration	p. 186
Tables of Integrals	p. 190
Approximate Analytical Methods
Asymptotic Expansions	p. 195
Asymptotic Expansions: Multiple Integrals	p. 199
Continued Fractions	p. 203
Integral Inequalities	p. 205
Integration by Parts	p. 215
Interval Analysis	p. 218
Laplace's Method	p. 221
Stationary Phase	p. 226
Steepest Descent	p. 230
Approximations: Miscellaneous	p. 240
Numerical Methods: Concepts
Introduction to Numerical Methods	p. 243
Numerical Definitions	p. 244
Error Analysis	p. 246
Romberg Integration / Richardson Extrapolation	p. 250
Software Libraries: Introduction	p. 254
Software Libraries: Taxonomy	p. 258
Software Libraries: Excerpts from GAMS	p. 260
Testing Quadrature Rules	p. 272
Truncating an Infinite Interval	p. 275
Numerical Methods: Techniques
Adaptive Quadrature	p. 277
Clenshaw-Curtis Rules	p. 281
Compound Rules	p. 283
Cubic Splines	p. 285
Using Derivative Information	p. 287
Gaussian Quadrature	p. 289
Gaussian Quadrature: Generalized	p. 292
Gaussian Quadrature: Kronrod's Extension	p. 298
Lattice Rules	p. 300
Monte Carlo Method	p. 304
Number Theoretic Methods	p. 312
Parallel Computer Methods	p. 315
Polyhedral Symmetry Rules	p. 316
Polynomial Interpolation	p. 319
Product Rules	p. 323
Recurrence Relations	p. 325
Symbolic Methods	p. 329
Tschebyscheff Rules	p. 332
Wozniakowski's Method	p. 333
Tables: Numerical Methods	p. 337
Tables: Formulas for Integrals	p. 340
Tables: Numerically Evaluated Integrals	p. 348
Mathematical Nomenclature	p. 351
Index	p. 353
Table of Contents provided by Blackwell. All Rights Reserved.

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The Handbook of Integration

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