Math 185 - Introduction to Complex Analysis - Spring 2015

Instructor:    Jason Murphy   (for contact info click here)

GSI: Edward Scerbo (853 Evans, office hours Monday through Friday 4pm–6pm)

Lecture:   TuTh 9:30–11am in   3 Evans

Office hours:   Tues. 2–3:30pm, Thurs. 3:30–5pm in 857 Evans

Piazza:   For discussion boards etc. you can find a Piazza signup link here.

Course control number:    54239

Prerequisites:    Math 104

Textbook:   Complex Analysis by Elias Stein and Rami Shakarchi

Additional resources: Syllabus:    The official course description includes the following topics:
analytic functions of a complex variable, Cauchy's integral theorem, power
series, Laurent series, singularities of analytic functions, the residue theorem
with application to definite integrals, additional topics such as conformal mapping.

Grading:   Grades will be determined using the following: Your grade will be computed by using the best of the following schemes: Course policies:   It is your responsibility to know the policies stated below. Contact info: The best way to reach me is by email — murphy (at) math (dot) berkeley (dot) edu.
Please check the course webpage for information before writing.

Class schedule:    The following table will be updated throughout the semester.

Date   Lecture   Topics   References
(Stein Shakarchi)  		 Remarks  
1/20 1 Review of analysis and topology Ch 1, Sections 1.1–2.1
1/22 2 Review of analysis and topology
The complex plane 		Ch. 1, Sections 1.1–2.1, p.88  
1/27 3 Cauchy–Riemann equations
Power series		 Ch.1, Sections 2.2, 2.3
1/29 4 Power series
Curves in the plane 		Ch. 1, Sections 2.3, 3
2/3 5 Curves in the plane
Integration over curves		 Ch. 1, Section 3
Appendix B 		Homework 1 Due 
2/5 6 Goursat's theorem
Cauchy's theorem 		Ch. 2, Sections 1–3
Ch. 3, Section 5
2/10 7 Cauchy's theorem
Cauchy integral formula 		Ch. 2, Section 4
2/12 8 Corollaries of Cauchy integral formula   Ch. 2, Sections 4, 5 Homework 2 Due  
2/17 9 Corollaries of Cauchy integral formula  
Isolated singularities 		Ch. 2, Sections 4, 5
Ch. 3, Sections 1–3
2/19 10 Isolated singularities
Meromorphic functions 		Ch. 3, Sections 1–3
2/24 11 Meromorphic functions
Ch. 3, Sections 1–3
Ch. 2, Section 3 		Homework 3 Due
2/26 12 The residue theorem
Evaluation of some integrals 		Ch. 2, Section 3
Ch. 3, Section 2
3/3 13 The argument principle
and applications		 Ch. 3, Section 4
3/5 14 The complex logarithm
Review 		Ch. 3, Section 6 Homework 4 Due
3/10 Midterm
3/12 15 Infinite products
Weierstrass's theorem 		Ch. 5, Sections 1–5
3/17 16 Weierstrass's theorem
Functions of finite order 		Ch. 5, Sections 1–5
3/19 17 Functions of finite order
Hadamard's factorization theorem 		Ch. 5, Sections 1–5 Homework 5 Due
3/23–3/27 Spring break
3/31 18 Conformal mappings Ch. 8, Sections 1–3
4/2 19 Conformal mappings
Introduction to groups 		Ch. 8, Sections 1–3
4/7 20 Möbius transformations Ch. 8, Sections 1–3 Homework 6 Due
4/9 21 Automorphisms of the disk
and upper half plane		 Ch. 8, Sections 1–3
4/14 22 Normal families Ch. 8, Sections 1–3
4/16 23 Riemann mapping theorem Ch. 8, Sections 1–3 Homework 7 Due
4/21 24 Prime number theorem Gamelin Ch. XIV
4/23 25 Prime number theorem Gamelin Ch. XIV
4/28 26 Prime number theorem Gamelin Ch. XIV Homework 8 Due 
4/30 27 Prime number theorem Gamelin Ch. XIV  
5/4 RRR Week  
5/5 RRR Week
5/6 RRR Week
5/7 RRR Week Homework 9 due
5/8 RRR Week


Homework assignments:

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