An introduction to invariant imbedding - Bellman, Richard 1920-1984 (Society for Industrial and Applied Mathematics (SIAM, 3600 Market Street, Floor 6, Philadelphia, PA 19104), 1992)
Mode of access: World Wide Web. - System requirements: Adobe Acrobat Reader
Includes bibliographical references and indexes
Chapter 1. Fundamental concepts -- Chapter 2. Additional illustrations of the invariant imbedding method -- Chapter 3. Functional equations and related matters -- Chapter 4. Existence, uniqueness, and conservation relations -- Chapter 5. Random walk -- Chapter 6. Wave propagation -- Chapter 7. Time-dependent problems -- Chapter 8. The calculation of Eigenvalues for Sturm-Liouville type systems -- Chapter 9. Schrodinger-like equations -- Chapter 10. Applications to equations with periodic coefficients -- Chapter 11. Transport theory and radiative transfer -- Chapter 12. Integral equations -- Author index -- Subject index
Here is a book that provides the classical foundations of invariant imbedding, a concept that provided the first indication of the connection between transport theory and the Riccati Equation. The reprinting of this classic volume was prompted by a revival of interest in the subject area because of its uses for inverse problems. The major part of the book consists of applications of the invariant imbedding method to specific areas that are of interest to engineers, physicists, applied mathematicians, and numerical analysts. A large set of problems can be found at the end of each chapter. Numerous problems on apparently disparate matters such as Riccati equations, continued fractions, functional equations, and Laplace transforms are included. The exercises present the reader with "real-life" situations. The material is accessible to a general audience, however, the authors do not hesitate to state, and even to prove, a rigorous theorem when one is available. To keep the original flavor of the book, very few changes were made to the manuscript; typographical errors were corrected and slight changes in word order were made to reduce ambiguities