Lecture 
Date 
Topics covered 
Remarks 
Week 1 
1 
Wed Sept 26 
Introduction: complex numbers 

2 
Fri Sept 28 
Convergence of sequences and series 

Week 2 

3 
Mon Oct 1 
Complex exponential and polar coordinates 

4 
Wed Oct 3 
Discussion 

5 
Fri Oct 5 
Nth Roots and the complex logarithm 
HW 1 due 
Week 3 

6 
Mon Oct 8 
Topoogy of the complex numbers 

7 
Wed Oct 10 
Discussion 

8 
Fri Oct 12 
Continuous functions 
HW 2 due 
Week 4 

9 
Mon Oct 15 
Multivalued functions; complex differentation 

10 
Wed Oct 17 
CauchyRiemann equations 

11 
Fri Oct 19 
Discussion 

Week 5 
12 
Mon Oct 22 
Complex integration and contour integrals 
HW 3 due 
13 
Wed Oct 24 
Contour integrals 

14 
Fri Oct 26 
Cauchy's Integral Theorem for triangles 

Week 6 

15 
Mon Oct 29 
Discussion 

16 
Wed Oct 31 
Cauchy's Integral Theorem for Convex Sets 
HW 4 due 
17 
Fri Nov 2 
Midterm 

Week 7 

18 
Mon Nov 5 
Cauchy's Integral Theorem revisited; Cauchy's Integral Formula 

19 
Wed Nov 7 
Cauchy's Integral Formula and Index functions 

20 
Fri Nov 9 
Properties of the index function 

Week 8 

Mon Nov 12 
No classVeterans Day 

21 
Wed Nov 14 
Uniform convergence 
HW 5 due 
22 
Fri Nov 16 
Power series and convergence 

Week 9 

23 
Mon Nov 19 
Power series are analytic 

24 
Wed Nov 21 
Discussion 


Fri Nov 23 
No classThanksgiving 

Week 10 
25 
Mon Nov 26 
Power series expansions of analytic functions 
HW 6 due 
26 
Wed Nov 28 
Louiville's theorem and the fundamental theorem of algebra 

27 
Fri Nov 30 
Zeroes of analytic functions 

Week 11 
28 
Mon Dec 3 
Singularities of analytic functions 

29 
Wed Dec 5 
Review 

30 
Fri Dec 7 
No class 
HW 7 due 
Final 


Wed Dec 12 
Final examination, 2:30  4:20 pm 
