Mathematical Methods for Physicists: A Comprehensive Guide 7th Edition by George B. Arfken (PDF)

Description

Now in its 7th edition, Mathematical Methods for Physicists continues to provide all the mathematical methods that aspiring scientists and engineers are likely to encounter as students and beginning researchers. This bestselling text provides mathematical relations and their proofs essential to the study of physics and related fields. While retaining the key features of the 6th edition, the new edition provides a more careful balance of explanation, theory, and examples. Taking a problem-solving-skills approach to incorporating theorems with applications, the book’s improved focus will help students succeed throughout their academic careers and well into their professions. Some notable enhancements include more refined and focused content in important topics, improved organization, updated notations, extensive explanations and intuitive exercise sets, a wider range of problem solutions, improvement in the placement, and a wider range of difficulty of exercises.Revised and updated version of the leading text in mathematical physicsFocuses on problem-solving skills and active learning, offering numerous chapter problemsClearly identified definitions, theorems, and proofs promote clarity and understanding New to this edition:Improved modular chaptersNew up-to-date examplesMore intuitive explanations

User’s Reviews

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

⭐There are several books in the market that give a good overview about the mathematical methods that Physicists must learn in their undergraduate formation at University. Some of them are Boas “Mathematical Methods in the physical science”, Cahill “Physical Mathematics”, Hassani “Mathematical Physics” and of course Arfken ,Weber and Harris with “Mathematical Methods of Physics” This last one is my favorite. I must say that I have all of them but I have only gone very deep on the last two. Hassani is very terse, it covers much more than Arfken but is not an easy reading at all. That’s why I recommend to every physics student Arfken, after a first chapter that touches and make contact with what one sees on the calculus courses this is infinite series, vectors, derivatives, integrals, Dirac’s delta function, complex numbers and induction there follows a second chapter that reminds the reader about some of the topics that are covered in a Linear Algebra course which are matrices and determinants. The third chapter is basically a Calculus III review where all about curvilinear coordinates, transformations coordinates and the typical Integral theorems of Gauss, Stokes and Green identities are covered. Chapter four begins with new stuff for the student, with a full chapter on Tensors and Differential forms. Chapters 5 and 6 are again a Linear algebra course for vector spaces and the eigen value problem. Chapter 7 is about ordinary differential equations which usually are seen in a different a previous course just on ODEs. Chapter 8 is about Sturm Liouville theory which is new stuff for the undergraduate where you learn about self adjoint differential operators, chapter 9 deal with Partial Differential Equations (PDEs) where you learn about some of the methods to deal with this awesome subject like the separation of variable and you treat the Laplace, Poisson, Heat and Wave equations for example. Chapter 10 is about Green’s functions which are the solutions to any differential equation as a response to the Dirac delta function. Chapter 11 and 12 are about complex analysis these are a MUST seen by the student for the methods of complex variable are used nearly everywhere in advanced Physics, chapter 13 introduces the Gamma Function it is HERE that I learned everything I know about the Gamma Function, its functional equation, its various representations, its zeros, poles and analytic continuation etc. Chapter 14 you have Bessel Functions, these functions are a bit terse to treat but are fundamental in Physics they not only satisfy recurrence relations but you have a whole Zoo of them, first kind second kind , modified, spherical etc. Their orthogonality is given and also various integral representations. Chapter 16 is about Angular Momentum which is vital introduction to what one sees on a Quantum Mechanics course for the solution of the Hydrogen Atom. Chapter 17 is about Group Theory, chapter 18 gives more special functions other than the Gamma and Bessel like the Chebyshev polynomials, Hermite functions, Laguerre functions and the Hypergeometric function, all off these functions pop up as different solutions of classic ODEs that appear in Physics. Chapter 19 is about Fourier Series which are a basic tool to treat PDEs, Chapter 20 is about Integral Transforms which are used as another method to solve ODEs and PDEs, The Laplace Transform for ODEs and typically The Fourier Transform for PDEs. Chapter 21 treats Integral Equations, Chapter 22 Calculus of Variations, here is presented the Euler-Lagrange equation fundamental for High energy physics and finally chapter 23 is about probability and Statistics which should be covered as usual in a separate course but these is a resume. All in all a great textbook to learn the mathematics a Physicists needs in order to acquire its undergraduate title, more important the exercises are doable and in case you are doing self study as me, you can find on the internet its solution manual with the answers to every single question and exercise, it is a delight for me, my favorite!

⭐i bought this edition because it included some topics i wasn’t very familiar with. i also have the 5th (from which i took a class 20+ years ago). It’s been a while since i did anything remotely approaching math, so i decided to work through the 7th ed as a refresher. Comparing the online-version of Ch1 of the 7th edition to chapter 5 from the 5th edition (both chapters on infinite series) i was stunned at how poor the exposition is in this edition vs. the earlier one. the arguments in 5th edition are more complete and much more easily followed. the explanations of the same topics in the 7th ed are, well, crap by comparison. looks like i should have stuck with the 5th and found other sources for the additional topics (i.e. forms). glad i bought the international edition and didn’t waste the full hardcover price.

⭐It has everything you need for those long nights alone.

⭐It was exactly what it said it was! Detailed, Matter of fact, Great Reference, etc. I’m a happy Camper.

⭐Good as a new

⭐The material in this book is difficult for me, even though I have a PhD in Engineering and an MS in Computational Mathematics.On the contrary, I believe that Kreyszig’s Advanced Engineering Mathematics is accessible to anyone with a “rusty” calculus.As a result, if anyone finds Arfken’s book too difficult to read, I recommend reading Riley’s book (Riley-Hobson-Bence) first.Starting with Kreyszig’s book is also a good idea. It includes topics like Fourier Analysis and PDE, Complex Analysis, Linear Algebra and Vector Calculus, but excludes Tensors, Hilbert Spaces, and Calculus of Variations.

⭐It’s an important book to get a clear and broad view on many mathematical topics that are regularly used in engineering and physics applications. Authors did a great job to put everything in a single book and it’s well written. It helped me a lot. Both Undergrad and grad students can have it.

⭐necessary reference for any physicist who is not a mathematical genius. doesnt replace a good course in math but close enough for most physicists need in understanding the material

⭐Comprehensive mathematics and clear text. The line drawings throughout rather basic. But overall a 5 star quality book which would suit advanced students.

⭐Excellent content but the pages are so thin!!!

⭐Immense detail, and use of advanced methods of calculation. Includes calculus. Covers all the major arras of advanced mathematics. Relates theory to individual examples.

⭐Seems like a very solid book, time will tell.

⭐1st time I ordered it, I received a children’s coloring book. I return requested it the same day and I received the actual book yesterday (as of the day of typing).. Now I open it to study and the first 6 pages are missing i.e. the contents.Also, I ordered a new book and this one looks battered and slightly worn. Not exactly used, but not particularly new either.This is saddening. (Attached picture is of the 1st book received)

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