Mathematics of Classical and Quantum Physics (Dover Books on Physics) by Frederick W. Byron (PDF)

Description

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.

User’s Reviews

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

⭐This book is nothing short of a mathematical symphony! One of the best books on the subject of Hilbert Spaces and Inner Product Spaces (in addition to Fourier series and transform). The subject of inner product spaces is a subtle one and the authors do a superb job in developing it piece by piece in the most elegant way I’ve seen (so far). Chapters 3, 4, and 5 are devoted to the development of the subjects of inner product spaces, Hilbert Spaces, and related concepts such as Linear Transformations, Eigenvalues and Eigenvectors, and Orthogonality and Completeness. For a physics student, the materials in the these three chapters is all they’d need to manage through a Quantum Mechanics course at the level of both Griffiths’ Introduction to Quantum Mechanics and Shankar’s Principles of Quantum Mechanics and similar books (such as my favorite book on quantum mechanics: A Modern Approach to Quantum Mechanics by John Townsend). All the polynomials such Hermite, Legendre, and Laguerre polynomials which are necessary to understand the derivations of the various eigen-functions in QM are nicely developed early on in the book. I should also mention that the first two chapters of the book dealing with mathematics of Classical Mechanics are also extremely useful. Chapter two introduces the student to Calculus of Variation and related applications in Classical Mechanics. The book is divided into two volumes: chapters 1 through 5 together form the first volume and the rest (chapters 6 to 10) form the second volume. Chapter 7 is devoted to Green’s function while chapter 10 is devoted to Group Theory.The book isn’t easy! For a gentler introduction to the subjects of inner product spaces and Hilbert spaces, I would highly recommend Linear Algebra and Matrix Theory by Gilbert and Gilbert. It’s an excellent book on the subject and a really easy book to read. The chapters are short, the problems and examples are sufficient, and the development is complete. If you’re a physics undergrad, then this is really all you’d need.

⭐This book is a rigorous approach to many of the math subjects relevant to physics: vector and Hilbert spaces, Special functions (Sturm-Liouville theory), Complex analysis, Group theory, and Green’s functions, etc.Make no mistake, it is indeed first and foremost a math book, not a physics one. It has a high level of rigor, being very precise and thorough with definitions and using those definitions in subsequent, detailed proofs of important theorems. At the same time however, the theorems that this book proves, examples used, and guiding philosophy is very much based in what a physicist would find interesting and relevant to coursework in upper division courses highlighted in a way that is a bit more informative than what one would find in a physics textbook.Its strength lies in teaching math to a physics student interested in learning the proofs and underlying framework for the math used in a “whole, from the ground up” approach rather than the rather piecemeal approach to math in physics courses. However, one can also skip the proofs and just read the theorems and examples to get at the important information needed to calculate “stuff”.

⭐Had a siper time reading it. Author knows his stuff. I learned a lot of math and some applications. Worth my time spent.

⭐This book gives an excellent coverage of mathematical physics from the standpoint of a vector space. It takes all of the mathematics that would normally be spread out over many courses and brings it together in one book. The treatment given here is concise and complete. It is well written and easy to follow unlike some texts.As other reviewers have said, this book is for advanced students. People with a strong mathematical background should gain a lot from this book. Undergraduates would probably find most of this book too hard. However, because this book is so good, undergraduates with an interest in mathematical physics could also gain a lot from this book.Coming from Dover this book is not only very good, it is very cheap, which makes it extremely good value. I highly recommend it.

⭐If you are like so me, you have spent years torturing yourself with horrific books like Matthews and Walker or Arfken. But almost by accident I came across this absolute gem, this masterpiece of balance between rigor and informality. The book presents mathematical physics on a level that is exactly at the level of graduate physics. The notation, the viewpoint and the emphasis are exactly what you need to master just about all the mathematics in graduate physics. This is all done not as Afken or Matthews and Walker do it, by slapping together hodgepodges of this and that into a cookbook, but by unifying mathematical physics into a beautiful tapestry, with the underlying fabric of linear vector spaces.This book would be worth it if the price were 10 times more than it is.

⭐This book contains an enormous amount of insight into a great amount of mathematics that is largely taken for granted in undergraduate courses on the subjects of Classical and Quantum Physics. This book, despite it’s age, does a wonderful job of filling the gaps between undergraduate math courses in Linear Algebra and Calculus, and the mathematics that is used in these two foundational fields of physics. I highly recommend this book for any aspiring graduate student in physics, particularly after one has taken a good number of math courses and both classical and quantum physics at the undergraduate level, in preparation for graduate studies. In particular, it is best for someone who is interested in the details of the thoeries. It helped me a lot.

⭐This should be mandatory reading for any students embarking on the study of quantum mechanics as the mathematical backbone required is a little stouter than is typically provided to a junior level undergrad student.

⭐I don’t normally write reviews but for this, I had to. It is the best maths book I have ever read.I have just finished my first year of my physics degree at Oxford, this is the prefect level going forward. Its explanation of grad, div and curl are the best (it even derives the expressions and informally proves associated theorems) ive seen (better than Lang anyway). Calculus of variations is also exceptional.

⭐This book was first published in 1969.I don’t understand why they cannot write like this anymore…

⭐The product is as described. Delivery was quick.

⭐love mathematics so love this book

⭐Arrived as expected. Fine

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