ABSTRACT

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 - Appro

chapter 3|6 pages

Extremal Problems

chapter 4|4 pages

Function Representation

chapter 5|4 pages

Geometric Applications

chapter 6|2 pages

MIT Integration Bee

chapter 7|1 pages

Probability

chapter 8|3 pages

Summations: Combinatorial

chapter 9|6 pages

Summations: Other

chapter 10|5 pages

Zeros of Functions

chapter 11|2 pages

Miscellaneous Applications

chapter 12|4 pages

Definitions

chapter 13|7 pages

Integral Definitions

chapter 14|3 pages

Caveats

chapter 15|3 pages

Changing Order of Integration

chapter 16|3 pages

Convergence of Integrals

chapter 17|3 pages

Exterior Calculus

chapter 18|3 pages

Feynman Diagrams

chapter 19|2 pages

Finite Part of Integrals

chapter 20|4 pages

Fractional Integration

chapter 21|4 pages

Liouville Theory

chapter 22|3 pages

Mean Value Theorems

chapter 23|6 pages

Path Integrals

chapter 24|3 pages

Principal Value Integrals

chapter 25|2 pages

Transforms: To a Finite Interval

chapter 26|6 pages

Transforms: Multidimensional Integrals

chapter 27|6 pages

Transforms: Miscellaneous

chapter 28|8 pages

Change of Variable

chapter 29|12 pages

Computer Aided Solution

chapter 30|11 pages

Contour Integration

chapter 31|2 pages

Convolution Techniques

chapter 32|3 pages

Differentiation and Integration

chapter 33|3 pages

Dilogarithms

chapter 34|9 pages

Elliptic Integrals

chapter 35|3 pages

Frullanian Integrals .

chapter 36|2 pages

FUnctional Equations

chapter 37|2 pages

Integration by Parts

chapter 38|6 pages

Line and Surface Integrals

chapter 39|11 pages

Look Up Technique

chapter 41|4 pages

Stochastic Integration

chapter 42|5 pages

Tables of Integrals

chapter 43|4 pages

Asymptotic Expansions

chapter 44|4 pages

Asymptotic Expansions: Multiple Integrals

chapter 45|2 pages

Continued Fractions

chapter 46|10 pages

Integral Inequalities

chapter 47|3 pages

Integration by Parts

chapter 48|3 pages

Interval Analysis

chapter 49|5 pages

Laplace's Method

chapter 50|4 pages

Stationary Phase

chapter 51|10 pages

Steepest Descent

chapter 52|3 pages

Approximations: Miscellaneous

chapter 53|1 pages

Introduction to Numerical Methods

chapter 54|2 pages

Numerical Definitions

chapter 55|4 pages

Error Analysis

chapter 57|4 pages

Software Libraries: Introduction

chapter 58|2 pages

Software Libraries: Taxonomy

chapter 59|12 pages

Software Libraries: Excerpts from G AMS

chapter 60|3 pages

Testing Quadrature Rules

chapter 61|2 pages

Truncating an Infinite Interval

chapter 62|4 pages

Adaptive Quadrature

chapter 63|2 pages

Clenshaw-Curtis Rules

chapter 64|2 pages

Compound Rules

chapter 65|2 pages

Cubic Splipes

chapter 66|2 pages

Using Derivative Information

chapter 67|3 pages

Gaussian Quadrature

chapter 68|6 pages

Gaussian Quadrature: Generalized

chapter 69|2 pages

Gaussian Quadrature: Kronrod's Extension

chapter 70|4 pages

Lattice Rules

chapter 71|8 pages

Monte Carlo Method

chapter 72|3 pages

Number Theoretic Methods

chapter 73|1 pages

Parallel Computer Methods

chapter 74|3 pages

Polyhedral Symmetry Rules

chapter 75|4 pages

Polynomial Interpolation

chapter 76|2 pages

Product Rules

chapter 77|4 pages

Recurrence Relations

chapter 78|3 pages

Symbolic Methods

chapter 79|1 pages

Tschebyscheff Rules

chapter 80|4 pages

Wozniakowski's Method

chapter 81|3 pages

Tables: Numerical Methods

chapter 82|8 pages

Tables: Formulas for Integrals

chapter 83|3 pages

Tables: Numerically Evaluated Integrals

chapter |2 pages

Mathematical Nomenclature