Last updated 29 Sep.
| Week of | Sections | Main topics | Suggested problems | Lecture notes | Remarks |
| 17 Aug | I.1-I.3 | Basics on complex numbers, the sterographic projection | I.1: 1, 3, 5, 6, 8 I.2: 1, 2, 4, 8 I.3: 1, 2 | I.1, I.2 + I.3 | |
| 24 Aug | I.4-I.8 | Complex functions, roots and logarithms, trigonometric functions | I.4: 1, 2 I.5: 1, 2, 3 I.6: 1, 2, 4 I.7: 1, 3 I.8: 2, 3 | ||
| 31 Aug | II.1, II.2 | Analysis recap, analytic functions | II.1: 1, 2, 10, 12, 15, 18 II.2: 1, 3, 4, 5 | II.2 | |
| 7 Sep | II.3-II.6 | Cauchy-Riemann equations, the inverse mapping theorem, harmonic functions, conformal mappings | II.3: 1, 3, 4, 6 II.4: 1, 3 II.5: 1, 2, 7 II.6: 1, 2, 4, 5 | II.3, II.4 | |
| 14 Sep | II.7, III.1 | Fractional linear transformations, line integrals | II.7: 1, 2, 3, 4, 5 III.1: 1, 2, 4, 6 | II.7, III.1 | Mandatory assigment 1 posted 17 Sep |
| 21 Sep | III.2-III.5 | Path independence of integrals, harmonic conjugates, the maximum principle | III.2: 1, 2, 3 III.3: 1, 2, 3 III.4: 1 III.5: 1, 2, 4 | III.2, III.3-III.5 | |
| 28 Sep | III.6, IV.1, IV.2 | Applications to fluid dynamics, complex line integrals, the fundamental theorem of calculus for analytic functions | III.6: 1, 3, 4 IV.1: 1, 2, 3, 4, 5 IV.2: 1, 2, 5 | III.6 | Mandatory assigment 1 submission due 1 Oct |
| 5 Oct | IV.3, IV.4, IV.5, V.1 | The Cauchy integral formula, Liouville's theorem, series | IV.3: 1, 5 IV.4: 1, 4 IV.5: 1, 2, 3 V.I: 1, 2, 7 | IV.3-IV.4 IV.5, V.1 | |
| 12 Oct | V.2-V.4 | Convergence of sequences of functions, power series of an analytic functions | V.2, 1, 2, 8, 9 V.3: 1, 2, 3, 6 V.4: 1, 2, 3, 7 | V.2-V.3 V.4 | Mandatory assignment 2 posted 15 Oct |
| 19 Oct | V.5–V.7, VI.1 | Power series at infinity, Zeros of an analytic function, Laurent series | V.5: 1, 3 V.6: 1, 3 V.7: 1, 2, 9 VII.1: 1, 2 | ||
| 26 Oct | VI.2–VI.4, IX.1 | Isolated singularities of analytic functions, partial fractions decomposition, the Schwarz lemma | VI.2: 1, 2, 3, 7, 8 VI.3: 1, 2 VI.4: 1, 2, 3 IX.1: 1, 2, 3 | Lecture Tuesday 27 Oct, no exercise session Mandatory assignment 2 due 29 Oct | |
| 2 Nov | VII.1–VII.3, VIII.1 | The residue theorem, definite integrals via complex analysis, the argument principle | VII.1: 1, 2, 3 VII.2: 1, 2, 6, 8, 9 VII.3: 1, 2, 3 VIII.1: 1, 2 | ||
| 9 Nov | VIII.2, VIII.4, VIII.6, VIII.8 | Rouché's theorem, the open mapping theorem, winding numbers, simply-connected domains | VIII.2: 1, 4, 6 VIII.4: 5 VIII.6: 1, 2, 5 VIII.8: 1 | ||
| 16 Nov | Revision | ||||
| 23 Nov | Revision | ||||
| 30 Nov | No lectures, exam 3 Dec | ||||