As a junior math major the only coordinate systems I've thus far been exposed to are Cartesian and polar (including cylindrical and spherical) coordinates. But of course these aren't the only ones. What book (online lectures, etc) can you recommend where I can study different types of coordinate systems in depth? I'm looking to learn more about coordinate systems such as bipolar, skew, triangular, and even more interesting ones like the following
Thanks in advance for any suggestions.
The subject in general should be handled somewhere between differential geometry and calculus of many variables. But usually coordinate systems are picked because they are useful for certain applications. I wrote about that here.