Course Home Syllabus Calendar Homework

The calendar here is tentative, and the topics discussed and specific dates are subject to change. Numbers in parentheses denote the corresponding section from Gamelin, Complex Analysis.

Week 1:
Wed. 1/22 Complex numbers (I.1-2)
Fri. 1/24 Stereographic projection, square and square root (I.3-4)
Week 2:
Mon. 1/27 Exponential and logarithm functions (I.5-6)
Wed. 1/29 Complex limits and continuity (II.1)
Fri. 1/31 Complex differentiation and analyticity (II.2)
Week 3:
Mon. 2/3 Cauchy-Riemann equations (II.3)
Wed. 2/5 Jacobians and inverse function theorem (II.4)
Fri. 2/7 Harmonic functions (II.5)
Week 4:
Mon. 2/10 Conformal mappings (II.6)
Wed. 2/12 Fractional linear transformations (II.7)
Fri. 2/14 Line integrals and Green's theorem (III.1)
Week 5:
Mon. 2/17 No class
Wed. 2/19 Midterm 1 review
Fri. 2/21 Midterm 1
Week 6:
Mon. 2/24 Closed and exact forms, harmonic functions (III.2-3)
Wed. 2/26 Mean value property (III.4)
Fri. 2/28 Maximum principle (III.5)
Week 7:
Mon. 3/3 Complex line integrals (IV.1-2)
Wed. 3/5 Cauchy's theorem (IV.3)
Fri. 3/7 Cauchy's integral formula (IV.4)
Week 8:
Mon. 3/10 Liouville's theorem (IV.5)
Wed. 3/12 Complex power series (V.1-3)
Fri. 3/14 Power series for analytic functions, manipulation of power series (V.4)
Week 9:
Mon. 3/17 Manipulation of power series (V.6)
Wed. 3/19 Orders of zeroes of analytic functions (V.7)
Fri. 3/21 Laurent series (VI.1)
Week 10:
Mon. 3/31 Isolated singularities (VI.2)
Wed. 4/2 Partial fraction decompositions (VI.4)
Fri. 4/4 Midterm 2 review
Week 11:
Mon. 4/7 Midterm 2
Wed. 4/9 Residue theorem (VII.1)
Fri. 4/11 Applications of residue theorem (VII.2-3)
Week 12:
Mon. 4/14 More residue theorem (VII.3-4)
Wed. 4/16 More residue theorem (VII.5)
Fri. 4/18 Jordan's lemma (VII.7)
Week 13:
Mon. 4/21 Argument principle (VIII.1)
Wed. 4/23 Rouche's Theorem (VIII.2)
Fri. 4/25 Open mapping and inverse function theorem (VIII.4)
Week 14:
Mon. 4/28 Gamma and zeta functions
Wed. 4/30 Chebyshev function and the prime number theorem
Fri. 5/2 Laplace transforms, proof of prime number theorem
RRR Week:
Mon. 5/5 Review Session 1
Wed. 5/7 Review Session 2
Final Examinations:
Wed. 5/14 Final exam 7-10pm

Last modified 27 April 2014.