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.
Author(s): R. Bellman, G. M. Wing
Series: Classics in applied mathematics 8
Publisher: Society for Industrial and Applied Mathematics
Year: 1987
Language: English
Pages: 267
City: Philadelphia
CLASSICS IN APPLIED MATHEMATICS:An Introduction to Invariant Imbedding......Page 1
Preface......Page 6
Preface to the Classic Edition......Page 12
Contents......Page 14
1 FUNDAMENTAL CONCEPTS......Page 20
2 ADDITIONAL ILLUSTRATIONS OF THE INVARIANT IMBEDDING METHOD......Page 41
3 FUNCTIONAL EQUATIONS AND RELATED MATTERS......Page 58
4 EXISTENCE,UNIQUENESS,AND CONSERVATION RELATIONS......Page 73
5 RANDOM WALK......Page 86
6 WAVE PROPAGATION......Page 107
7 TIME-DEPENDENT PROBLEMS......Page 127
8 THE CALCULATION OF EIGENVALUES FOR STURM-LIOUVILLE TYPE SYSTEMS......Page 152
9 SCHROBINGER-LIKE EQUATIONS......Page 166
10 APPLICATIONS TO EQUATIONS WITH PERIODIC COEFFICIENTS......Page 188
11 TRANSPORT THEORY AND RADIATIVE TRANSFER......Page 205
12 INTEGRAL EQUATIONS......Page 238
AUTHOR INDEX......Page 264
SUBJECT INDEX......Page 266
