Table of Contents: Handbook of Integration

• Preface
• Introduction
• How to Use This Book

Applications of Integration

1. Differential Equations: Integral Representations
2. Differential Equations: Integral Transforms
3. Extremal Problems
4. Function Representation
5. Geometric Applications
6. MIT Integration Bees
7. Probability
8. Radon Transform
9. Summations: Combinatorial
10. Zeros of Functions
11. Miscellaneous Applications

Concepts and Definitions

1. Definitions
2. Integral Definitions
3. Caveats
4. Changing Order of Integration
5. Convergence of Integrals
6. Exterior Calculus
7. Feynman Diagrams
8. Finite Part of Integrals
9. Fractional Integration
10. Liouville Theory
11. Mean Value Theorems
12. Path Integrals
13. Principal Value Integrals
14. Transforms: To a Finite Interval
15. Transforms: Multidimensional Integrals
16. Transforms: Miscellaneous

Exact Analytical Methods

1. Change of Variable
2. Computer Aided Solution
3. Contour Integration
4. Convolution Techniques
5. Differentiation and Integration
6. Dilogarithms
7. Elliptic Integrals
8. Frullanian Integrals
9. Functional Equations
10. Integration by Parts
11. Line and Surface Integrals
12. Look Up Technique
13. Special Physical Forms
14. Special Integration Techniques
15. Stochastic Integration
16. Tables of Integrals

Approximate Analytical Methods

1. Asymptotic Expansions
2. Integral Inequalities
3. Integration by Parts
4. Interval Analysis
5. Laplace's Method
6. Stationary Phase
7. Steepest Descent
8. Approximations: Miscellaneous

Numerical Methods: Concepts

1. Introduction to Numerical Methods
2. Numerical Definitions
3. Error Analysis
4. Romberg Integration
5. Software Libraries: Introduction
6. Software Libraries: Taxonomy
7. Software Libraries: Excerpts from GAMS
8. Testing Quadrature Rules
9. Truncating an Infinite Interval

Numerical Methods: Techniques

1. Tables: Formulas for Integrals
2. Tables: Numerical Methods
3. Tables: Numerically Evaluated Integrals
4. Adaptive Quadrature
5. Clenshaw-Curtis Rules
6. Compound Rules
7. Cubic Splines
8. Using Derivative Information
9. Gaussian Quadrature: Generalized
10. Gaussian Quadrature: Kronrod's Extension
11. Gaussian Quadrature
12. Lattice Rules
13. Monte Carlo Method
14. Number Theoretic Methods
15. Parallel Computer Methods
16. Polyhedral Symmetry Rules
17. Polynomial Interpolation
18. Product Rules
19. Recurrence Relations
20. Symbolic Methods
21. Tschebyscheff Rules
22. Wozniakowski's Method

• Index