Math 185: Complex Analysis, Fall 2015

Instructor: Nikhil Srivastava, email: firstname at

Lectures: MWF 4-5pm, 9 Evans Hall.

Office Hours: Tuesday and Wednesday, 10:15am-11:45am, 1035 Evans Hall.

GSI: Christopher Wong, office hours MW 10:30am-12:30pm and TTh 4:30pm-6:30pm, 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.


Readings and Homework Schedule

# Date Topic Readings HW Notes
1 W 8/26 introduction, complex numbers 1-8
2 F 8/28 Euler's identity, arguments, roots.
regions, functions, stereographic projection.
9-14 HW1 out
3 M 8/31 limits, continuity, differentiation. 15-20
4 W 9/2 Cauchy-Riemann equations, chain rule 21-24, 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. 25-27 HW1 solutions
7 F 9/11 exp, log, powers, trig functions 30-40 HW2 due
HW3 out
8 M 9/14 integration 41-47
9 W 9/16 antiderivatives 48-49 HW2 solutions
10 F 9/18 Cauchy-Goursat I 50-53 HW4 out
11 M 9/21 Cauchy-Goursat II, review50-53 HW3 solutions
12 W 9/23 Midterm 1
13 F 9/25 Cauchy Goursat III, deformation theorem 50-53 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 55-58 rewrite due
HW4 solutions
16 F 10/2 fundamental theorem of algebra, max modulus principle 58-59HW5 due
HW6 out
17 M 10/5 sequences, series 60-63HW5 solutions
18 W 10/7 Taylor's theorem, uniform convergence 62-63, 69-70
19 F 10/9 Manipulation of series, examples 71-73, 64HW6 due
HW7 out
20 M 10/12 zeros of analytic functions, identity principle, Laurent series 82, 28, 65-68
21 W 10/14 Proof of Laurent expansion 65-68
22 F 10/16 isolated singularities 74, 78, 83-84HW8 out
HW6 solutions
23 M 10/19 residue theorem, residues at poles 75-81
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, 85-87HW8 solutions
27 W 10/28 review for midterm 50-84, 93-94HW9 solutions
28 F 10/30 Midterm 2
29 M 11/2 Jordan's lemma, indented contours 88-89HW10 out
30 W 11/4 integration around a branch point / through a branch cut 90-91Guest 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 notesHW11 out
W 11/11 holiday HW10 solutions
33 F 11/13 Mobius Transformations 96-101 HW12 out
watch this video
34 M 11/16 Conformal Mapping 102-103, 112-113
35 W 11/18 Inverse Function Theorem, Harmonic Functions114,115HW11 solutions
36 F 11/20 Dirichlet Problem 116-117, 119
supplementary notes
HW13 out
37 M 11/23 Analytic Continuation, Gamma Function lecture notes
38 M 11/30 Prime Number Theorem lecture notesHW14 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.