Date |
Reading |
Topics |
Tu, Sep 7, 2021 |
Refer to Advanced Calculus and Methods of Mathematical Physics from the first year |
Review of calculus on normed vector spaces: norm, point-set topology (open, closed, compact sets), continuity and differentiability, Riemann integration of vector-valued functions |
We, Sep 8, 2021 |
Stein, Ch 1, Sec 2.2 |
Holomorphic functions: Definition, Cauchy-Riemann equations, examples |
We, Sep 15, 2021 |
Stein, Ch 1, Sec 2.3 |
Power series, curves (elementary definitions) |
Th, Sep 16, 2021 |
Stein, Ch 1, Sec 3; Ch 2, Sec 1+2 |
Integration along curves, Goursat’s theorem, local existence of primitives |
We, Sep 22, 2021 |
Stein, Apx B (parts); Ch 2, Sec 3 |
General Cauchy theorem, applications |