Math 412 - Mathematical Analysis II
Description
Math 412 is the second course in the honors analysis sequence, 411/412. The course starts from where 411 left off, which is usually the Riemann–Stieltjes integral or sequences of functions, and continues from there.
Topics covered
Topics usually covered in Math 412 include:
- Riemann–Stieltjes integral
- Sequences of functions
- Fourier series
- Differentiation of functions of several variables
- Inverse and implicit function theorems
- Integration of functions of several variables
- Vector calculus and differential forms
Note that the exact list of topics may vary by instructor and semester. Additional topics may include spaces as completions of spaces of Riemann integrable functions, power series, and the Lebesgue measure theory.
Comments on prerequisites
Background on inner product spaces and normed vector spaces (topics seen in courses such as 350) may be helpful, but students without this background are not going to be at much of a disadvantage.
Resources
Textbook
The usual textbook for the class is Principles of Mathematical Analysis by Walter Rudin. Lecture notes from when the course was last taught by Zheng-Chao Han, which he uses as a second reference (and is the main source he uses for later portions of the class) may be found online at https://zhengchao-han-math.github.io/math412/.
Additional materials
Calculus on Manifolds by Michael Spivak may be useful as a supplementary source.