College of the Holy Cross, Spring 2022
Syllabus for Math 305 (Complex Analysis)
Professor Hwang, (rhymes with song)
Do not make travel plans that conflict with the midterm tests or your final exam. If an emergency prevents you from taking the final exam at the allotted time, speak to your Class Dean immediately to arrange for an incomplete grade, and to me to schedule a make-up exam.
The schedule below is subject to minor changes. Any substantial corrections will be announced by email and/or in class.
| Day | Date | Section | Topics |
| M | Jan 24 | Advising | |
| W | Jan 26 | Section 1.1 | The complex field |
| F | Jan 28 | Section 1.2 | Rectangular and polar form |
| M | Jan 31 | Section 1.3 | Conjugation, the triangle inequalities |
| W | Feb 2 | Section 1.4 | Elementary topology |
| F | Feb 4 | Section 2.1 | Limits and continuity |
| M | Feb 7 | Section 2.1 | Limits and continuity |
| W | Feb 9 | Section 2.2 | Differentiability |
| F | Feb 11 | Section 2.2 | Differentiability |
| M | Feb 14 | Section 2.3 | The Cauchy-Riemann equations |
| W | Feb 16 | Section 2.4 | Constant functions |
| F | Feb 18 | Midterm 1 | |
| M | Feb 21 | Section 3.1 | Möbius transformations |
| W | Feb 23 | Section 3.2 | The projective line |
| F | Feb 25 | Section 3.3 | Stereographic projection |
| M | Feb 28 | Section 3.4 | Exponential and circular functions |
| W | Mar 2 | Section 3.5 | Logarithms |
| F | Mar 4 | Section 4.1 | Complex integration |
| M | Mar 7 | Spring Break | |
| W | Mar 9 | Spring Break | |
| F | Mar 11 | Spring Break | |
| M | Mar 14 | Section 4.2 | Antiderivatives |
| W | Mar 16 | Section 4.3 | Cauchy's theorem |
| F | Mar 18 | Section 4.4 | The Cauchy integral formula |
| M | Mar 21 | Section 4.4 | Winding numbers |
| W | Mar 23 | Section 5.1 | More about Cauchy's theorem |
| F | Mar 25 | Midterm 2 | |
| M | Mar 28 | Section 5.2 | Existence of antiderivatives |
| W | Mar 30 | Section 5.3 | The fundamental theorem of algebra |
| F | Apr 1 | Section 6.1 | Harmonic functions |
| M | Apr 4 | Section 7.1-7.2 | Sequences and series |
| W | Apr 6 | Section 7.3 | Sequences of functions |
| F | Apr 8 | Section 7.3 | Sequences of functions |
| M | Apr 11 | Section 7.4 | Regions of convergence |
| W | Apr 13 | Section 8.1 | Power series |
| F | Apr 15 | Easter | |
| M | Apr 18 | Easter | |
| W | Apr 20 | Section 8.1 | The general Cauchy integral formula |
| F | Apr 22 | Section 8.2 | Zeros of holomorphic functions |
| M | Apr 25 | Section 8.3 | Laurent series |
| W | Apr 27 | Academic Conference | |
| F | Apr 29 | Section 9.1 | Isolated singularities |
| M | May 2 | Midterm 3 | |
| W | May 4 | Section 9.2 | Residues |
| F | May 6 | Section 9.2 | Residues |
| M | May 9 | Section 9.3 | Rouché's theorem |