Book recommendations for Fourier Series, Dirac Delta Function and Differential Equations? I'm a second-year undergrad and currently taking a course in Mathematical Physics which covers the topics of Dirac delta functions, Fourier series, Fourier transforms and Differential equations. They recommended using Boas' "Mathematical Methods in Physical Sciences" book. However, I find the book too "wishy-washy" and focusing on irrelevant points for my taste. I was wondering if anyone can suggest any book which explains the concepts in the most straightforward and to the point manner, with real-world examples?
 A: For a down to earth  but rigorous account distributions and delta functions (but not so much differential equations) you can't beat James Lighthill's Introduction to Fourier analysis and generalised functions, Cambridge University Press. ISBN 978-0-521-05556-7.
The book is quite thin, only 70 pages or so. It is written at the undergraduate level. Although he  uses test function  (He calls them "good functions") to define how distributions work ---  just as in advanced books for mathematicians---  there  is not much sophisticated mathematical formalism and what there is, is well matched to what physics students learn.
The book has many applications to Fourier series and Fourier integrals of exactly the type one meets in physics papers and that are not often explained  in regular mathematical methods classes. Lighthill is a great expositor (I took his "Waves in fluids" class when I was an undergrad and it was one of the best classes I had) and the book is well set out  for self study. Amazon has used copies for about $14.
A: In my opinion the Schaum series offers a wide variety of questions and examples. They probably have different books for differential equations and Fourier series. They'll handle Dirac Delta in the differential equations one.
