Mathematics of Classical and Quantum Physics
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- Type：Epub+TxT+PDF+Mobi
- Create Date：2021-04-30 08:55:05
- Update Date：2025-09-06
- Status：finish
- Author：Frederick W. Byron Jr.
- ISBN：048667164X
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Summary
This textbook is designed to complement graduate-level physics texts in classical mechanics， electricity， magnetism， and quantum mechanics。 Organized around the central concept of a vector space， the book includes numerous physical applications in the body of the text as well as many problems of a physical nature。 It is also one of the purposes of this book to introduce the physicist to the language and style of mathematics as well as the content of those particular subjects with contemporary relevance in physics。
Chapters 1 and 2 are devoted to the mathematics of classical physics。 Chapters 3， 4 and 5 — the backbone of the book — cover the theory of vector spaces。 Chapter 6 covers analytic function theory。 In chapters 7， 8， and 9 the authors take up several important techniques of theoretical physics — the Green's function method of solving differential and partial differential equations， and the theory of integral equations。 Chapter 10 introduces the theory of groups。 The authors have included a large selection of problems at the end of each chapter， some illustrating or extending mathematical points， others stressing physical application of techniques developed in the text。
Essentially self-contained， the book assumes only the standard undergraduate preparation in physics and mathematics， i。e。 intermediate mechanics， electricity and magnetism， introductory quantum mechanics， advanced calculus and differential equations。 The text may be easily adapted for a one-semester course at the graduate or advanced undergraduate level。
Chapters 1 and 2 are devoted to the mathematics of classical physics。 Chapters 3， 4 and 5 — the backbone of the book — cover the theory of vector spaces。 Chapter 6 covers analytic function theory。 In chapters 7， 8， and 9 the authors take up several important techniques of theoretical physics — the Green's function method of solving differential and partial differential equations， and the theory of integral equations。 Chapter 10 introduces the theory of groups。 The authors have included a large selection of problems at the end of each chapter， some illustrating or extending mathematical points， others stressing physical application of techniques developed in the text。
Essentially self-contained， the book assumes only the standard undergraduate preparation in physics and mathematics， i。e。 intermediate mechanics， electricity and magnetism， introductory quantum mechanics， advanced calculus and differential equations。 The text may be easily adapted for a one-semester course at the graduate or advanced undergraduate level。
Reviews
Richard Marney
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A review reading of selected topics for a course to be taken in the fall。 Much still to be learned！！！ 🤨This is a graduate level book in both mathematics and physics， requiring a solid grounding in both subject areas。
Dr Muhammad Zafar Iqbal
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This has been a good read。 The author has put a lot of time and effort。 Being a writer myself， I find it commendable。 The content is decent and keeps you hooked for a long time。 And some parts are simply minds blowing。 I look forward to reading more books like this。 All in all， a good experience for an avid reader like me。
WarpDrive
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A delicious smorgasbord of higher mathematics for the physical sciences。 Designed and used as a university textbook for the senior undergraduate student， or as a companion to post-graduate programs in mathematical physics， this highly informative and well structured book originally consisted of two separate volumes， bound into one single tome in this particular edition。This very appealing book is essentially self-contained， assuming the standard undergraduate preparation in physics and mathemati A delicious smorgasbord of higher mathematics for the physical sciences。 Designed and used as a university textbook for the senior undergraduate student， or as a companion to post-graduate programs in mathematical physics， this highly informative and well structured book originally consisted of two separate volumes， bound into one single tome in this particular edition。This very appealing book is essentially self-contained， assuming the standard undergraduate preparation in physics and mathematics: in particular， previous exposure to partial and ordinary differential equations， multivariate calculus， functional analysis， classical electromagnetism and quantum mechanics are absolutely essential。This book deals with several different subjects， varying from calculus of variations， introduction to tensor analysis， linear algebra and Hilbert spaces， perturbation theory， advanced complex analysis， the all-important Green's functions and integral equations （including integral equations in Hilbert space）， group and representation theory， and others。 In all cases， the authors admirably manage to strike a praiseworthy compromise between mathematical accuracy and theoretical coherence and depth on one side， and the more applicative perspectives on the other side， providing highly instructive and relevant examples of application to practical problems from the physical sciences， and a rich offering of relevant exercises of varying level of difficulty。 I also greatly appreciated that any theoretical shortcuts or approximations are clearly highlighted by the authors， and that some items whose mathematical rigor is often neglected （such as the correct definition of the Dirac Delta， which is not a regular function， but a shorthand notation for a rather complex limiting process， called a "generalized function"） are properly treated by the authors in a concise but generally accurate way。 This is compounded with a generally lucid and concise writing style， a reasonably low level of inaccuracies and typos （only a dozen that I could find， which is pretty good in an advanced mathematical text of more than 650 pages）， and a balanced pedagogical approach based on mathematical derivations that require just the right level of personal effort to make the study interesting and rewarding for the assiduous reader， without being un-necessarily discouraging。Differently to too many other university textbooks （that often appear not much more than a series of recipes）， this excellent volume provides an organic， comprehensive， well-articulated and logically connected treatment of several themes in mathematics for the physical sciences， with a focus on enabling the deeper mathematical understanding of the techniques presented in each chapter， and an overall high level perspective and analysis of the sometimes hidden commonalities between many different elements。 For example， all the so-called “special functions” of mathematical physics （such as the spherical harmonics， Legrenge， Hermite， and Laguerre polynomials）， are all treated uniformly within the framework of Hilbert spaces， rather than just as ad-hoc solutions to very specific differential equations。 Such framework is a much more general and comprehensive one， and provides a systematizing and unifying theme to an otherwise confusing and messy maze of special cases and properties。 This book is a real gem， whose only shortcomings are in the too basic and succinct introduction to tensor analysis， and the occasional usage of older approaches and terminology （for example， contemporary mathematics tend to focus more on the study and properties of compact operators， rather than just on the completely continuous operators as done in this book; this is not a big issue anyway， as compact operators on a Banach space are always completely continuous - and， in any case， the occasional appearance of some quaint， oldish element is pretty unavoidable， considering the original publication date of the book）。A more generous allocation to numerical approaches， and to themes and examples related to quantum field theory rather than just the more traditional aspects of non-relativistic quantum mechanics， would have been appreciated， but this again is just a very minor point。 Please also note that， if you want to gain a better handling of mathematical techniques for general relativity， this is probably not the book for you （there is no treatment of differential manifolds， nor of Lie groups， and tensor analysis is only addressed at embryonic level）。 I must also say that， possibly， a bit too much space has been allocated to some items of linear algebra （such as eigenvectors and eigenvalues） that would normally be treated as part of standard undergraduate courses， and therefore they are not， in my opinion， really necessary in a book aimed at senior undergraduates or post-graduates。 But all the above are just minor issues that do not compromise the high quality and value of this great book。 A pleasurable reading experience （being such a rich and densely packed book， it does required time and dedication， mind you）， very reasonably priced and a guarantee of many rewarding hours of study and learning， this book is highly recommended to the dedicated reader with the appropriate pre-requisite knowledge， and especially to the readers interested not just in a disparate collection of higher mathematical techniques， but in achieving a more unified and comprehensive understanding of the underlying beautiful mathematical world。 People with a relatively stronger mathematical background will also definitely love this book and fully appreciate its overall approach。 It is also a useful book to keep for future reference。4。5 stars， rounded up to 5 stars。 。。。more
Scott Bembenek
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To be honest， I read this book some time ago when I was in graduate school， and have been recently reviewing it at my leisure。 In addition to the usual math physics references （like Arfken）， this book really provides some extra insight。 A great example of this， is the coverage on Hilbert Space。 In short， add this book to your shelf of math physics books ASAP。
Marc
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One of the many books in my library I opened and parsed through but haven't taken the time to truly read yet。。。 One of the many books in my library I opened and parsed through but haven't taken the time to truly read yet。。。 。。。more
Stephen
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