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Excellent Introduction for Applied Scientists,
Rezension bezieht sich auf: Symmetries and Differential Equations (Gebundene Ausgabe)
This is a book on applied mathematics as it should be. It is written in classical language and avoids abstract notation, that is not necessary for a correct and readable deduction of the matter.
Starting with the presentation of scale transformations it introduces the reader step by step to the theory of continuous transformations. The concept of prolongation of the group action is presented first for one dependend and one independend variable. Then gradually more independend and dependend variables are introduced. This avoids confusion arising from an unnecessary abstract notation. Applications to ordinary and partial differential equations follow. At the present for me the hihglight of the book is the introduction of Lie-Backlund-Symmetries.
The deductions are presented very clearly and the introduced concepts are well motivated. Helpful examples prevent a misunderstanding of the theory. The exercises frequently refer to original publications, thereby making solutions available, so that no reader is left struggling with umanageable exercises. In the later chapters proofs are frequently skipped and left as exercises, but the reader will realize that these proofs can be obtained as slight variations of earlier ones.
This book is indispenseable for applied scientist as a bridge to more mathematically oriented texts like Olver's. After having completed my second tour through this delicious text I am looking forward to find some more time to read again some parts and to look more carefully at some aspects.