An Introduction to Invariant Imbedding

Here is a book that describes 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. 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. 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.

Richard Bellman (1920-1984) authored 44 books and over 600 published research papers during his lifetime. His last position was as professor of mathematics, electrical engineering, biomedical engineering, and medicine at the University of Southern California in Los Angeles. His contributions resulted in numerous awards including honorary doctorates from universities in various countries. He was elected to the National Academy of Engineering, the National Academy of Sciences, and was a Fellow of the American Academy of Arts and Sciences.

Dr. G. M. Wing is retired from the Los Alamos National Laboratory. His career has included professorships in mathematics at leading universities and staff positions in industry. He is the author of three other books and more than 75 research papers and articles. Dr. Wing is a member of the Editorial Board of Transport Theory and Statistical Physics, and is a past associate editor of the Journal of Mathematical Analysis and Applications.