Mathematical Physics: Classical Mechanics (UNITEXT Book 109) by Andreas Knauf (PDF)

Description

As a limit theory of quantum mechanics, classical dynamics comprises a large variety of phenomena, from computable (integrable) to chaotic (mixing) behavior. This book presents the KAM (Kolmogorov-Arnold-Moser) theory and asymptotic completeness in classical scattering. Including a wealth of fascinating examples in physics, it offers not only an excellent selection of basic topics, but also an introduction to a number of current areas of research in the field of classical mechanics. Thanks to the didactic structure and concise appendices, the presentation is self-contained and requires only knowledge of the basic courses in mathematics.The book addresses the needs of graduate and senior undergraduate students in mathematics and physics, and of researchers interested in approaching classical mechanics from a modern point of view.

User’s Reviews

Reviews from Amazon users which were colected at the time this book was published on the website:

⭐This text has a very specific audience and the organization is very odd.The audience in my opinion would be senior/junior level students in mathematics and graduate students of physics. I can only speak to my level of experience with undergraduate physics at my university. In my opinion the level of mathematics required is too advanced for an undergraduate physics major (topology, differential forms, abstract algebra, etc). While the very interested and advanced student could learn and read the text, I think they would have a little bit of a harder time than a student of mathematics. The text does cover these topics via various appendices and examples, and I am sure it is sufficient to complete the text and understand the material. Keep in mind that it is a lot of material packed very densely, with no exercises to practice the mathematics the author is trying to teach you. There are examples and proofs, however.Finally I do not understand why the sections on topology, differential forms, etc have been exiled to the appendix. The author spends three chapters on differential equations, which the reader should already be familiar with. And while these sections are not to be taken lightly, (they are probably more along the lines of what you would see in a graduate level ODE course) the reader should have already seen the material, while the majority of math and overwhelming majority of physics majors will not have seen topology even once! I do not wish that the three chapters were not there, but I do not understand why those three chapters are part of the text while the sections on topology and algebra aren’t. I believe that these sections of the text should be expanded upon slightly, and added to the main text. This is not a reason why someone should or shouldn’t buy the book, but it does irritate me and frankly, doesn’t make sense at all.I do not think the book is bad, but the author does take a while to expose physical concepts at a high mathematical level. These issues are not severe, I am writing this review as an FYI to other people interested in this text

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