Lecture Notes
- Lecture 0 (01/10/2022)
Complex numbers: addition, multiplication, modulus, argument and conjugate.
- Lecture 1 (01/11/2022)
Geometric meaning of multiplication, de Moivre's formula, n-th roots, triangle inequality.
- Lecture 2 (01/12/2022)
Exponential and trigonometric functions.
- Lecture 3 (01/13/2022)
Logarithm and power function. Some subsets of the complex plane.
- Lecture 4 (01/14/2022)
Open, closed and (path) connected subsets of the complex plane.
- Lecture 5 (01/18/2022)
Accumulation points, interior points, closure, boundary. Sequences
and limits.
- Lecture 6 (01/19/2022)
Compact sets. Bolzano-Weierstrass and Heine-Borel thms.
- Lecture 7 (01/20/2022)
Functions: limits and continuity.
- Lecture 8 (01/21/2022)
Limits at infinity. Stereographic projection. Cauchy-Riemann
equations