I'm majoring in physics and I'm about to take a course entitled Mathematical Methods of Physics. It covers Sturm-Liouville Theory, Integral Transforms, Fourier Analysis and PDEs. I read in the thread "So you Want to be a Physicist" that ”Mathematical Methods in the Physical Science” by Mary Boas (Wiley) is good. But by the title of the book, I suspect it is a rather informal and easygoing book. As I am seriously interested in mathematics(I will pursue an academic carreer in mathematics or theoretical physics) and would like a book(probably books since the course deals spans a lot of different topics) that rigorously deals with what I am going to learn. Books made by mathematicians, and that deal with the subject the way mathematicians deal, so I can really get motivated, I don't like math textbooks that only focus on practical applications.