
Math 8051: Schedule and Homework Assignments
The schedule below will be gradually filled out as
the class progresses.
Day 
Topic 
Book pages 
Homework 
8/28  Properties of complex numbers  Chapter I 
 8/30  Metric space basics 
P. 1113  Homework 1, due 9/6
 9/4  No class  Labor Day  
 9/6  Connectedness 
P. 1417  Homework 2, due 9/13
 9/11  Compactness; sequences  P. 18, 2023 
 9/13  Continuous functions 
P. 2428 
 9/18  Uniform convergence, power series  P. 2933  Homework 3, due 9/27
 9/20  No class  
 9/25  Complex differentiation  P. 3338 
 9/27  Logarithms; CauchyRiemann equations  P. 3942 
 9/29  Harmonic functions; conformal mapping  P. 4247  Play
with demo
 10/2  Riemann sphere; Möbius transformations
 P. 89, 4749  Homework 4, due 10/11
 10/4  Line integrals  P. 6165 
 10/9  Power series representations  P. 6872 
 10/11  Zeros of an analytic function  P. 73,
7679  Homework 5, due 10/18
 10/16  Winding numbers  P. 7983 
 10/18  Homotopy and integrals 
P. 8795  Homework 6, due 10/25
 10/23  Cauchy's theorem and integral formula  P.8386 
 10/25  Counting zeros, open mapping theorem  P. 9799 
 10/30  Midterm exam   Solutions
 11/1  Poles and removable singularities 
P. 103106  Homework 7, due 11/8
 11/6  Essential singularities  P. 106110 
 11/8  Residue Theorem  P. 112116  Homework
8, due 11/15
 11/13  Integrals using residues  BN, P. 144151 
 11/15  Sums using residues  BN,
P. 151154  Homework
9, due 11/29
 11/27  The Argument Principle  P. 123125 
 11/29  Rouche's theorem; Maximum Modulus  P. 125126,
128130  Homework
10, due 12/6
 12/4  Schwarz's Lemma  P. 130132 
 12/6  Conformal maps of the
disk   Suggested problems, not due
 12/11  Review  
 12/15  Final exam (10:3012:30)  

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Last modified: Fri Aug 21 15:35:22 PDT 2009
