Instructor: Nikhil Srivastava, email: firstname at math.berkeley.edu
Lectures: MWF 45pm, 9 Evans Hall.
Office Hours: Tuesday and Wednesday, 10:15am11:45am, 1035 Evans Hall.
GSI: Christopher Wong, office hours MW 10:30am12:30pm and TTh 4:30pm6:30pm, 1039 Evans Hall.
Text: Brown and Churchill, Complex Variables and Applications, 9e.
Supplementary Text: Gamelin, Complex Analysis. Available online for Berkeley students at Springerlink.
Syllabus: We will cover the first 9 chapters of Brown and Churchill and some additional topics, such as infinite products and applications of conformal mapping.
Piazza: This is an excellent place to ask and answer questions about the material. The website is here and you can sign up here.
Announcements
Readings and Homework Schedule
#  Date  Topic  Readings  HW  Notes 
1  W 8/26  introduction, complex numbers  18  
2  F 8/28  Euler's identity, arguments, roots. regions, functions, stereographic projection.  914  HW1 out  
3  M 8/31  limits, continuity, differentiation.  1520  
4  W 9/2  CauchyRiemann equations, chain rule  2124, lecture notes on asymptotic notation and the chain rule  
5  F 9/4  an application to infinite series.  Prof. Hammond's notes  HW1 due HW2 out  Guest lecture by Prof. Alan Hammond 
M 9/7  holiday, no class  
6  W 9/9  analyticity, Laplace's equation and harmonic functions.  2527  HW1 solutions  
7  F 9/11  exp, log, powers, trig functions  3040  HW2 due HW3 out  
8  M 9/14  integration  4147  
9  W 9/16  antiderivatives  4849  HW2 solutions  
10  F 9/18  CauchyGoursat I  5053  HW4 out  
11  M 9/21  CauchyGoursat II, review  5053  HW3 solutions  
12  W 9/23  Midterm 1  
13  F 9/25  Cauchy Goursat III, deformation theorem  5053  HW4 due  
14  M 9/28  Cauchy integral formula  54  HW5 out.  
15  W 9/30  extension of CIF, Morera's theorem, Liouville's Theorem  5558  rewrite due HW4 solutions  
16  F 10/2  fundamental theorem of algebra, max modulus principle  5859  HW5 due HW6 out  
17  M 10/5  sequences, series  6063  HW5 solutions  
18  W 10/7  Taylor's theorem, uniform convergence  6263, 6970  
19  F 10/9  Manipulation of series, examples  7173, 64  HW6 due HW7 out  
20  M 10/12  zeros of analytic functions, identity principle, Laurent series  82, 28, 6568  
21  W 10/14  Proof of Laurent expansion  6568  
22  F 10/16  isolated singularities  74, 78, 8384  HW8 out HW6 solutions  
23  M 10/19  residue theorem, residues at poles  7581  
24  W 10/21  argument principle  93  
25  F 10/23  Rouche's theorem, open mapping theorem  94 lecture notes  HW9 out HW7 solutions  
26  M 10/26  applications to definite integrals  92, 8587  HW8 solutions  
27  W 10/28  review for midterm  5084, 9394  HW9 solutions +handwritten  
28  F 10/30  Midterm 2  
29  M 11/2  Jordan's lemma, indented contours  8889  HW10 out  
30  W 11/4  integration around a branch point / through a branch cut  9091  Guest lecture by Prof. Gang Liu 

31  F 11/6  the Basel problem, the point at infinity  lecture notes  
32  M 11/9  residues at infinity, the Fibonacci sequence  lecture notes  HW11 out  
W 11/11  holiday  HW10 solutions  
33  F 11/13  Mobius Transformations  96101  HW12 out watch this video  
34  M 11/16  Conformal Mapping  102103, 112113  
35  W 11/18  Inverse Function Theorem, Harmonic Functions  114,115  HW11 solutions  
36  F 11/20  Dirichlet Problem  116117, 119 supplementary notes  HW13 out  
37  M 11/23  Analytic Continuation, Gamma Function  lecture notes  
38  M 11/30  Prime Number Theorem  lecture notes  HW14 out  
39  W 12/2  Prime Number Theorem  HW 13 due HW12 solutions  
40  F 12/2  Prime Number Theorem / review  interesting article  HW13 solutions 
Please read the assigned sections before class. All section numbers are from Brown and Churchill, except those marked with a G, which are from Gamelin.
Grading: 20% Homework, 40% Midterms, 40% Final. The lower midterm score will be replaced by the final exam score, if it helps.
Homework will be assigned every Friday and due the following Friday at the end of class. Solutions to selected problems will be posted on this page, and late homework will not be accepted.
Michael Hutchings on writing proofs (which will be required) and on
academic dishonesty (which will not be tolerated).
Writing homework solutions in LaTeX is encouraged.