Ebook: Wave Propagation: An Invariant Imbedding Approach
- Tags: Analysis, Theoretical Mathematical and Computational Physics, Numeric Computing
- Series: Mathematics and Its Applications 17
- Year: 1985
- Publisher: Springer Netherlands
- Edition: 1
- Language: English
- pdf
Approach your problems from the right end It isn't that they can't see the solution. It is and begin with the answers. Then one day, that they can't see the problem. perhaps you will find the final question. G. K. Chesterton. The SCQlldIII of Father 'The Hermit Clad in Crane Feathers' in R. Brown 'The point of a Pin'. van Gu!ik's The Chinese Maze Murders. Growing specialization and diversification have brought a host of monographs and textbooks on increasingly specialized topics. However, the "tree" of knowledge of mathematics and related fields does not grow only by putting forth new branches. It also happens, quite often in fact, that branches which were thought to be completely disparate are suddenly seen to be related. Further, the kind and level of sophistication of mathematics applied in various sciences has changed drastically in recent years: measure theory is used (non trivially) in regional and theoretical economics; algebraic geometry interacts with . physics; the Minkowsky lemma, coding theory and the structure of water meet one another in packing and covering theory; quantum fields, crystal defects and mathematical programming profit from homotopy theory; Lie algebras are relevant to filtering; and prediction and electrical engineering can use Stein spaces. And in addition to this there are such new emerging subdisciplines as "experimental mathematics", "CFD", "completely integrable systems", "chaos, synergetics and large-scale order", which are almost impossible to fit into the existing classification schemes. They· draw upon widely different sections of mathematics.
Content:
Front Matter....Pages i-xiv
Introduction....Pages 1-20
Eikonal Equation and the WKB Approximation....Pages 21-37
Invariant Imbedding....Pages 38-59
Application to the Wave Equation....Pages 60-94
The Bremmer Series....Pages 95-109
Generalization ....Pages 110-129
Time Dependent Processes....Pages 130-158
Asymptotic Properties....Pages 159-190
Operator Techniques....Pages 191-214
Variational Principles....Pages 215-258
Dynamic Programming and Solution of Wave Equations....Pages 259-309
Approximations....Pages 310-334
Back Matter....Pages 335-367
Content:
Front Matter....Pages i-xiv
Introduction....Pages 1-20
Eikonal Equation and the WKB Approximation....Pages 21-37
Invariant Imbedding....Pages 38-59
Application to the Wave Equation....Pages 60-94
The Bremmer Series....Pages 95-109
Generalization ....Pages 110-129
Time Dependent Processes....Pages 130-158
Asymptotic Properties....Pages 159-190
Operator Techniques....Pages 191-214
Variational Principles....Pages 215-258
Dynamic Programming and Solution of Wave Equations....Pages 259-309
Approximations....Pages 310-334
Back Matter....Pages 335-367
....