This book is a continuation of the book Green's Functions and Transfer Functions [35] written some ten years ago. However, there is no overlap whatsoever in the contents of the two books, and this book can be used quite independently of the previous one. This series of books represents a new kind of handbook, in which are collected data on the characteristics of systems with distributed and lumped parameters. The present volume covers some two hundred problems. Essentially, this book should be considered as a desktop handbook, intended, like [35], to give rapid "on-line" access to relevant data about problems. For each problem, the book lists all the main characteristics of the solution: standardising functions, Green's functions, transfer functions or matrices, eigenfunctions and eigenvalues with their asymptotics, roots of characteristic equations, and other data. In addition to systems described by a single differential equation, this volume also includes degenerate multiconnected systems, systems for which no Green's function or matrix exists, and other special cases which are important for applications.
Reihe
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ISBN-13
978-94-011-2062-3 (9789401120623)
DOI
10.1007/978-94-011-2062-3
Schweitzer Klassifikation
1 Characteristics of distributed systems described by individual equations.- § 1. Group (1.0.2).- § 2. Group (1.1.1).- § 3. Group (1.1.2).- § 4. Group (1.2.2).- § 5. Group (2.0.2).- § 6. Group (2.1.2).- § 7. Group (2.2.2).- § 8. Group (3.0.1).- § 9. Group (3.0.2).- § 10. Group (3.1.1).- § 11. Group (3.1.2).- § 12. Group (3.2.2).- § 13. Group (r.0.2).- § 14. Differential-difference equations.- § 15. Integral equations.- § 16. Integro-differential equations.- 2 Characteristics of interconnected distributed systems.- § 1. Systems of group (0.1.0).- § 2. Systems of group (1.0.2).- § 3. Systems of group (1.1.2).- § 4. Systems of group (1.2.2).- § 5. Systems of integral equations.- 3 On the practice of finding characteristics of distributed systems.- § 1. Introduction.- §2. Finite Integral Transforms of Greenberg and Sobolev.- § 3. On a mistake in the application of the Sobolev transform.- § 4. Greenberg transforms of some functions and expressions.- § 5. Further properties of finite integral transforms.- § 6. Application of finite integral transforms to the analysis of distributed parameter systems.- § 7. Generalised (modified) Green's functions.- § 8. On the form of presentation of the states of distributed parameter systems containing boundary conditions of the first kind.- § 9. Normal and anormal systems.- Appendix: Tables of characteristic values.
