Abstract: The first half of the course of methods of mathematical physics, complex functions, is mainly mathematical background technically needed for the second half. Students tend to take it as abstract and irrelevant with physics. Using Fourier series as a demo, it is shown how they directly treat problems in everyday life and physics. Presenting it in physical scenarios, i.e., substantializing the physics related, helps students essentially understand it. More importantly, this will directly connect the Fourier transform with major physics, and give students command of mathematics via physical pictures, which favors flexible applications of them in subsequential courses.

Key words: methods of mathematical physics, Fourier series, physical pictures