The Handbook of Integration
by Zwillinger; DanielFormat: Hardcover
Pub. Date: 1992-11-02
Publisher(s): A. K. Peters
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Summary
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
Table of Contents
| 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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