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 |