University of California, Berkeley

Fall 2007

This is an introductory course on complex analysis.

The official prerequisite for taking this course is Math 104: Introduction to Analysis.

- 12/14/07: Extra office hours 12–2 on Mon, Dec 17.
- 12/14/07: Solutions to Problem Set 10 posted.
- 12/11/07: Solutions to Problem Sets 8 and 9 posted.
- 12/11/07: Final exam will take place in 9 Evans Hall, 8–11, Tue, Dec 18.
- 12/10/07: Extra office hours 12–2 on Wed, Dec 12.
- 12/06/07: Extra office hours 12–2 on Fri, Dec 07.
- 12/06/07: Problem Set 10 posted.
- 11/29/07: Problem Set 9 posted.
- 11/17/07: Extended office hours 12–4 on Mon, Nov 19.
- 11/15/07: Problem Set 8 posted.
- 11/14/07: Solutions to Problem Set 7 posted.
- 11/08/07: Problem Set 7 posted.
- 11/05/07: Extra office hours 12–1 on Tue, Nov 06.
- 11/01/07: Solutions to Problem Set 6 posted.
- 10/27/07: Solutions to Problem Set 5 posted.
- 10/25/07: Problem Set 6 posted.
- 10/24/07: Midterm II will take place in 170 Barrows Hall, 4–5, Wed, Nov 07.
- 10/21/07: Solutions to Problem Set 4 posted.
- 10/18/07: Problem Set 5 posted.
- 10/17/07: Extra office hours 12–1 on Fri, Oct 19.
- 10/17/07: Deadline for Problem Set 4 postpone till Fri, Oct 19.
- 10/13/07: Solutions to Problem Set 3 posted.
- 10/11/07: Problem Set 4 posted.
- 09/30/07: Problem Set 3 posted.
- 09/29/07: Read Timothy Gowers's blog for entry on Cauchy's theorem. Remember to check out Terence Tao's comments.
- 09/24/07: Wed's office hours brought forward to 11–1, Tue, Sep 25. Office hours will go back to normal after midterm.
- 09/24/07: Solutions to Problem Set 2 posted.
- 09/19/07: Midterm I will take place in 210 Wheeler Hall, 4–5, Wed, Sep 26.
- 09/19/07: Problem 5(e) in Problem Set 2 corrected.
- 09/19/07: Solutions to Problem Set 1 posted.
- 09/17/07: Problem Set 2 posted.
- 09/08/07: Problem Set 1 has been updated with the two additional questions.
- 09/07/07: Problem Set 1 posted. Please check back later for an updated version with questions 6 & 7.
- 09/05/07: Problem Set 1 will be posted on Friday (Sep 7), due in class the following Friday (Sep 14); not Wednesdays as announced earlier.
- 08/27/07: Check this page regularly for announcements.

**Location:** Evans Hall,
Room 75

**Times:** 4:00 AM–5:00 PM on Mon/Wed/Fri

**Instructor:** Lek-Heng
Lim

Evans Hall, Room 873

`lekheng(at)math.berkeley.edu`

(510) 642-8576

Office hours 12:00–2:00 PM every Monday and
2:00–4:00 PM every Wednesday

**Graduate Student Instructor:** David
Penneys

Evans Hall, Room 891

`dpenneys(at)math.berkeley.edu`

Office hours: 8:00–10:00 AM, 1:00–4:00 PM every Monday and
12:30–3:00 PM, 5:00–7:30 PM every Tuesday

- Analytic functions of a complex variable
- Cauchy's integral theorem
- Power series
- Laurent series
- Singularities of analytic functions
- Residue theorem with application to definite integrals
- Additional topics

Homework will be assigned once a week and will be due the following week (except possibly in the weeks when there is a midterm). Collaborations are permitted but you will need to write up your own solutions.

- Problem Set 10: PDF (posted: Dec 06; due: Dec 10); Solutions: PDF (posted: Dec 14)
- Problem Set 9: PDF (posted: Nov 29; due: Dec 6); Solutions: PDF (posted: Dec 11)
- Problem Set 8: PDF (posted: Nov 15; due: Nov 21); Solutions: PDF (posted: Dec 11)
- Problem Set 7: PDF (posted: Nov 08; due: Nov 14); Solutions: PDF (posted: Nov 14)
- Problem Set 6: PDF (posted: Oct 24; due: Oct 31); Solutions: PDF (posted: Nov 01)
- Problem Set 5: PDF (posted: Oct 18; due: Oct 24); Solutions: PDF (posted: Oct 27)
- Problem Set 4: PDF (posted: Oct 11; due: Oct 19); Solutions: PDF (posted: Oct 21)
- Problem Set 3: PDF (posted: Sep 30; due: Oct 10); Solutions: PDF (posted: Oct 13)
- Problem Set 2: PDF (posted: Sep 17; due: Sep 24); Solutions: PDF (posted: Sep 24)
- Problem Set 1: PDF (posted: Sep 07; due: Sep 14); Solutions: PDF (posted: Sep 19)

**Bug report** on the problem sets or the solutions:
`lekheng(at)math.berkeley.edu`

- Timothy Gowers's blog entry on Cauchy's theorem. Remember to check out Terence Tao's comments.

**Midterm I grade distribution:** median = 28,
mean = 27, max = 35, min = 15, stdev = 5.7, max possible marks = 40.

**Grade composition:** 40% Homework, 15% Midterm I, 15% Midterm II,
30% Final

The second book is optional. As a whole, it is more advanced than the first book but Part I of the book covers the same basic materials.

- Joseph Bak and Donald Newman,
*Complex Analysis*, 2nd Ed., Springer, 1997.

- Serge Lang,
*Complex Analysis*, 4th Ed., Springer, 1999.