| Week | Date | Contents |
| 1 | 0906 |
Labour Day |
| 0908 | Outline §1.1 algebra of complex numbers |
|
| 0910 | §1.2 complex plane, absolute value, distance, complex conjugate §1.3 vector viewpoint and sum, triangle inequality, argument |
|
| 2 | 0913 | §1.3 polar form and product of complex
numbers §1.4 complex potentials, Euler's formula by Taylor series, De Moivre's formula |
| 0915 | §1.5 powers and roots §1.6 open sets |
|
| 0917 | §1.6 connected sets, interior and boundary |
|
| 3 | 0920 | §2.1 functions of a complex variable, domain and range |
| 0922 | §2.2 limits of complex sequences, limits of functions of
a complex variable |
|
| 0924 | §2.2 continuity of functions of
a complex variable §2.3 differentiability and analyticity of functions of a complex variable |
|
| 4 | 0927 | §2.3 examples of analyticity §2.4 analyticity and Cauchy-Riemann equations |
| 0929 | §2.4 proof of theorems, examples |
|
| 1001 |
§2.5 harmonic functions, harmonic conjugate |
|
| 5 | 1004 |
§2.5 level set of harmonic functions and their
conjugates §3.1 polynomials: zeros and factorization |
| 1006 |
§3.1 polynomials: Fundamental Theorem of Algebra;
Taylor form; rational functions: zeros, poles and partial fraction |
|
| 1008 |
finding coefficients of partial
fraction §3.2 exponential function, fundamental region of; sin z and cos z |
|
| 6 | 1011 |
Thanksgiving |
| 1013 |
§3.2 sin z, cos z, sinh z and cosh z §3.3 multi-valued function, log z and its principle value |
|
| 1015 |
Midterm Exam |
|
| 7 | 1018 |
§3.5 complex powers |
| 1020 |
§3.5 inverse trigonometric functions |
|
| 1022 |
arccos(2i) §4.1 smooth curves and contours on plane |
|
| 8 | 1025 |
Jordan's curve
theorem §4.2 contour integrals over a smooth curve |
| 1027 |
§4.2 integrals over contours, upper bound §4.3 Independence of path |
|
| 1029 |
§4.3 three equivalent properties for functions with
antiderivatives §4.4 continuous deformation of loops |
|
| 9 | 1101 |
§4.4 examples, deformation invariance theorem
|
| 1103 |
§4.4 corollaries and examples (§4.4(b) is
skipped) §4.5 Cauchy's integral formula |
|
| 1105 |
§4.5 examples, corollaries, derivative formulas |
|
| 10 | 1108 |
§4.5 an example §4.6 interior derivative bound, Liouville theorem |
| 1110 |
§4.6 Fundamental Theorem of Algebra, mean value theorem, maximum modulus theorem | |
| 1112 |
§5.1 convergence of series, comparison and
ratio tests |
|
| 11 | 1115 |
§5.1 alternating series, integral test, uniform
convergence §5.2 Taylor series |
| 1117 |
§5.2 Convergence of Taylor series of analytic
functions |
|
| 1119 |
§5.2 Taylor series of derivatives and products of
analytic
functions
|
|
| 12 | 1122 |
§5.3 power series, radius and disk of
convergence |
| 1124 |
§5.3 analyticity of power series (§5.4
is
skipped) §5.5 Laurent series for analytic functions in an annulus |
|
| 1126 |
§5.5 Examples §5.6 removable singularity |
|
| 13 |
1129 |
§5.6 zeros and poles of finite order, essential
singularity §6.1 residue and Cauchy's residue theorem |
| 1201 |
§6.1 residue formulas for poles of finite order,
examples |
|
| 1203 |
old final exam review |
|
| 1207 |
Final Exam |