Handbook of Integration - Daniel Zwillinger, Jones and Bartlett

Description: Handbook of Integration by Daniel Zwillinger Jones and Bartlett Publishers, 1992, 0867202939, Hardcover without Jacket, Fine condition, no marks, no underlining, no highlighting, like new condition. 367 pages. This book is a compilation of the most important and widely applicable methods for evaluating and approximating integrals. As a reference book, it provides convenient access to these methods and contains examples showing their use. The book is divided into five parts. The first part lists several applications of integration. The second part contains definitions and concepts and has some useful transformations of integrals. This section of the book defines many different types of integrals, indicates what Feynman diagrams are, and describes many useful transformations. The third part of the book is a collection of exact analytical evaluation techniques for integrals. For nearly every technique the following are given: •the types of integrals to which the method is applicable •the idea behind the method •the procedure for carrying out the method •at least one simple example of the method •notes for more advanced users •references to the literature for more discussion or examples. The material for each method has deliberately been kept short to simplify use. Proofs have been intentionally omitted. CONTENTS Preface Introduction How to Use This Book I Applications of Integration 1Differential Equations: Integral Representations. . 2Differential Equations: Integral Transforms 3Extremal Problems 4Function Representation 5Geometric Applications 6MIT Integration Bee 7Probability 8Summations: Combinatorial 9Summations: Other 10Zeros of Functions 11Miscellaneous Applications II Concepts and Definitions 12Definitions 13Integral Definitions 14Caveats 15Changing Order of Integration 16Convergence of Integrals 17Exterior Calculus 18Feynman Diagrams 19Finite Part of Integrals 20Fractional Integration 21Liouville Theory 22Mean Value Theorems 23Path Integrals 24Principal Value Integrals 25Transforms: To a Finite Interval 26Transforms: Multidimensional Integrals 27Transforms: Miscellaneous III Exact Analytical Methods 28Change of Variable 29Computer Aided Solution 30Contour Integration 31Convolution Techniques 32Differentiation and Integration 33Dilogarithms 34Elliptic Integrals 35Frullanian Integrals 36Functional Equations 37Integration by Parts 38Line and Surface Integrals 39Look Up Technique 40Special Integration Techniques 41Stochastic Integration 42Tables of Integrals IV Approximate Analytical Methods 43Asymptotic Expansions 44Asymptotic Expansions: Multiple Integrals 45Continued Fractions 46Integral Inequalities 47Integration by Parts 48Interval Analysis 49Laplace's Method 50Stationary Phase 51Steepest Descent 52Approximations: Miscellaneous V Numerical Methods: Concepts 53Introduction to Numerical Methods 54Numerical Definitions 55Error Analysis 56Romberg Integration / Richardson Extrapolation . . . 57Software Libraries: Introduction 58Software Libraries: Taxonomy 59Software Libraries: Excerpts from GAMS 60Testing Quadrature Rules 61Truncating an Infinite Interval VI Numerical Methods: Techniques 62Adaptive Quadrature 63Clenshaw—Curtis Rules 64Compound Rules 65Cubic Splines 66Using Derivative Information 67Gaussian Quadrature 68Gaussian Quadrature: Generalized 69Gaussian Quadrature: Kronrod's Extension 70Lattice Rules 71Monte Carlo Method 72Number Theoretic Methods 73Parallel Computer Methods 74Polyhedral Symmetry Rules 75Polynomial Interpolation 76Product Rules 77Recurrence Relations 78Symbolic Methods 79Tschebyscheff Rules 80Wozniakowski's Method 81Tables: Numerical Methods 82Tables: Formulas for Integrals 83Tables: Numerically Evaluated Integrals Mathematical Nomenclature Index nthdegree books

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