Mathematical Methods for Physicists
George B. Arfken and Hans J. Weber
George Arfken 's text is one of the more useful of its type, simply because it is very clear and easy to understand. The book is one of a few that I could recommend for the reason that they are easy to understand. Many of the new modern math physics texts are written in a non precise style that is friendly, but does not teach. Strang's mathematics texts come to mind - although they are generally regarded as very good, I don't think the student gets a clear understanding from them.
Older textbooks, like Morse and Feshbach, Courant and Hilbert are complete and rigorous, but are not very student friendly. They are written for non novices.
Arfken's book, like that of Butkov, and Byron and Fuller, are less formal,
but not too informal, and rigorous enough to give a solid understanding of the material. They are perfect for first year graduate work, or even senior level undergraduate study, and most importantly for people working in the field who need to learn something in a relatively short time, and so they can actually use it in their work. I cannot say that for the older classic books like Morse and Feshbach an the modern texts like Strang.
Arfken has very good discussions on Vector and Tensor analysis, Matrix and Group theory, infinite series, Differential Equations, Sturm Lioville Theory and Function Space, Special Functions, 2 large portions of Complex Variables, Fourier Series, integral transofrms, Integral equations and variational calculus. Lots of worked examples, and problems to solve, and good figures. This is a worthwhile book for students of Engineering, Physics, Applied Mathematicians and workers in these fields. Butkov and Byron & Fuller are also very similar and very valuable. Byron & Fuller is a little more difficult to read, but spending the time on it is worth it.
Note: I added others book of the same field. Enjoy!
