I am planning to teach (unofficially, I am a Grad student) a course in real analysis.
Aim of the course is to understand the convergence of Fourier series.
I want to start with the notion of sequence of real numbers, their convergence, metric space, convergence of sequence in metric space and so on...
Has any one tried such a course with the time bound of 20 lectures, 1.5 hours each? Any suggestions are welcome.
I want to teach derivatives and integration. 30 hours may be less for usual course in real analysis that start with definition of convergence of sequence of real numbers to reach till the definition of Fourier series. What I had in mind is some of the topics can be skipped without breaking the flow. So, I am asking what would be a sequence of topics that starts with notion of limit, continuity and ends with convergence of Fourier series. This is for the benifit of students who take physics as major in their undergraduate. They might not take more courses in analysis in their undergraduate but use the setup of Fourier series without being sure if that makes sense or not.