During the past 20 years, there has been enormous productivity in theoretical as well as computational integration. Some attempts have been made to find an optimal or best numerical method and related computer code to put to rest the problem of numerical integration, but the research is continuously ongoing, as this problem is still very much open-ended. The importance of numerical integration in so many areas of science and technology has made a practical, up-to-date reference on this subject long overdue.
The Handbook of Computational Methods for Integration discusses quadrature rules for finite and infinite range integrals and their applications in differential and integral equations, Fourier integrals and transforms, Hartley transforms, fast Fourier and Hartley transforms, Laplace transforms and wavelets. The practical, applied perspective of this book makes it unique among the many theoretical books on numerical integration and quadrature. It will be a welcomed addition to the libraries of applied mathematicians, scientists, and engineers in virtually every discipline.
Preface. Notation. Preliminaries. Interpolatory Quadrature. Gaussian Quadrature. Improper Integrals. Singular Integrals. Fourier Integrals and Transforms. Inversion of Laplace Transforms. Wavelets. Integral Equations. Appendix A: Quadrature Tables. Appendix B: Figures. Appendix C: Contents of the CD-ROM. Bibliography. Index.