Mathematical Methods for Physicists: A Comprehensive Guide

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!

George Arfken’s original publication, “Mathematical Methods for Physics” is in this reviewer’s opinion, one of the most comprehensive textbooks of this topic and an excellent reference source for engineers and physicists. It has gone through several editions with the additional authors, first Weber and now Harris. Although I have and use Arfken’s first edition, this 7th edition has additional material and is consistent with the intent of Arfken’s original text. I recommend this text to any engineering student at the college or university level as it will assist them in their studies and provides an excellent approach to solving problems or explaining topics found in electrical engineering, mechanical engineering, and physics. The book will also be useful when the engineering student is confronted with problems in lecture that may not be clear in their class room text.

Whether you need it as a reference (tho, online works just as well) or a book to work through to learn or improve skill sets this book is great. It does present some issues if you're only using it as a text as sometimes it's referring to things stated previously and you have to hunt down what the authors are talking about. I had to use this for class, but getting more use out of it as a reference that sits at my desk

I got this book for a graduate level class I am taking next semester (Fall 2017), so I have not really looked at the content in this book at all yet and have no comment on the content. I will update this review if I have antyhing to say on the content after going through it this next semester. My main purpose of this review at this moment is to comment on the quality of the international edition. I ordered the international edition from an Amazon seller called Lowcost Bukz, and the international edition seems to be a decent quality and not an extraordinarily bad quality as some reviews on here make it seem. While, as I read in a review, the paper does seem a bit thin and "newspaper-like", the printing is clear and readable. I ordered it new and it came a bit beat up, but that is not a huge problem and likely to be expected with most international editions. Overall, the book is usable and readable and seems like it should stand up well as long as one is not too rough with the book. Also, with a bit of Googling you can likely find a PDF copy of it as a back up should something happen to the international edition. Overall, I would recommend ordering the international edition of this book if you want to save a bit of money (roughly $30+) and want a physical book (it tends to be easier to flip around in the book, such as if you need to refer to information earlier in the book for doing a problem, with a physical copy than with a PDF). I do not think given the quality of the international edition that it is worth spending a lot more money for the U.S. edition. I will update this review if I notice anything else about the quality or if I have comments in the future about the content.Update 12/23/2017:After finishing the semester, the book seemed to hold up well. It is still intact though the cover is now a bit bent. I did not travel to often with it and the bends in the soft cover mostly came from when I did do the traveling. I have put clear contact paper on a number of my soft covers which helps them stay sturdy, and I did not get the chance to put the contact paper on this book, so it likely would have held up even better with that added protection. As far as the content, I found the writing to be rather dry. However, reading the text was still useful and there are numerous practice problems, a few even with answers given. The course I took covered complex integration, series solutions of differential equations, integral equations, orthogonality, Green's functions, and group theory. I found Mary Boas' Mathematical Methods in the Physical Sciences to be helpful in my course, as well. It covers many of the same topics as this book and Boas' book often covered the topics more clearly, so if you have the extra cash to purchase Boas' book or if you can find a PDF copy of it, I would highly recommend that book in addition to this one.

Used Arfken's 3rd edition text almost 40 years ago in grad school. Decided to replace my old falling apart textbook. This newer 7th edition has preliminary and matrix sections in the beginning which is helpful. Like the earlier editions, the topics are in as good order as possible.

I learned these things a long time ago. I purchased it for curiosity to refresh my memory and to see what is new in the field. The book came very promptly in a perfect shape. A+++ for the seller.