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