In the Calculus 1 course that I am currently taking, we only discussed functions given in polar coordinates as some sort of side note, but I am eager to explore them more thoroughly. Namely, what I am looking for is some book, or video lectures in which there is a detailed description on
1. How to find the domain
2. Analyze the symmetry of a polar function with respect to the pole and the polar axis
3. Determine the existence of asymptotes
4. Existence of branches that cross the pole
5.Concavity and convexity
6.Table of values
7.Sketch the graph(of functions which are more complicated than, e.g. a simple sine function.)
I have been searching the internet a lot, but found mostly trivial examples of such functions.