University of California, Berkeley

Fall 2008

This is an introductory course on complex analysis.

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

- 12/12/08: Solutions to Problem Set 10 posted.
- 12/06/08: Extra office hours 12:15–1:15 daily from Mon, Dec 15 to Thu, Dec 18.
- 12/06/08: Final exam to be held 5–8, Thu, Dec 18 in LeConte Hall, Room 3.
- 12/05/08: Solutions to Problem Set 9 posted.
- 12/04/08: Problem Set 10 posted. See the footnote for instruction on how to turn it in.
- 12/01/08: Revision lecture on Friday, Dec 05, 5–7PM, in Evans Hall, Room 9.
- 11/30/08: Problem Set 9 posted.
- 11/24/08: Solutions to Problem Set 8 posted.
- 11/14/08: Solutions to Problem Set 7 posted.
- 11/08/08: Solutions to Problem Set 6 posted.
- 11/08/08: Problem Set 7 posted.
- 11/01/08: Problem Set 6 posted.
- 10/25/08: Solutions to Problem Set 5 posted.
- 10/25/08: Solutions to Problem Set 4 posted.
- 10/25/08: Solutions to Problem Set 3 posted.
- 10/17/08: Problem Set 5 posted.
- 10/17/08: Office hours on Mon, Oct 20 moved to 4–5.
- 10/10/08: Problem Set 4 posted.
- 10/04/08: Lecture on Fri, Oct 31 as per normal.
- 10/04/08: Midterm exam to be held Mon, Oct 27 (Part I) and Wed, Oct 29 (Part II) in LeConte Hall, Room 3.
- 10/04/08: Solutions to Problem Set 2 posted.
- 10/03/08: Problem Set 3 posted.
- 10/01/08: Office hours changed to Mon 3–4, Wed 3–5.
- 09/26/08: Problem Set 2 posted.
- 09/26/08: Solutions to Problem Set 1 posted.
- 09/12/08: Problem Set 1 posted.
- 08/27/08: Check this page regularly for announcements.

**Location:** Evans Hall,
Room 70

**Times:** 2:00–3:00 PM on Mon/Wed/Fri

**Instructor:** Lek-Heng
Lim

Evans Hall, Room 873

`lekheng(at)math.berkeley.edu`

(510) 642-8576

**Office hours:** 3:00–4:00 PM, Mon and 3:00–5:00 PM, Wed

- 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 05; due: Dec 12); Solutions: PDF (posted: Dec 12)
- Problem Set 9: PDF (posted: Nov 30; due: Dec 05); Solutions: PDF (posted: Dec 05)
- Problem Set 8: PDF (posted: Nov 15; due: Nov 21); Solutions: PDF (posted: Nov 24)
- Problem Set 7: PDF (posted: Nov 08; due: Nov 14); Solutions: PDF (posted: Nov 14)
- Problem Set 6: PDF (posted: Nov 01; due: Nov 07); Solutions: PDF (posted: Nov 08)
- Problem Set 5: PDF (posted: Oct 17; due: Oct 24); Solutions: PDF (posted: Oct 25)
- Problem Set 4: PDF (posted: Oct 10; due: Oct 17); Solutions: PDF (posted: Oct 25)
- Problem Set 3: PDF (posted: Oct 3; due: Oct 10); Solutions: PDF (posted: Oct 25)
- Problem Set 2: PDF (posted: Sep 26; due: Oct 3); Solutions: PDF (posted: Oct 4)
- Problem Set 1: PDF (posted: Sep 12; due: Sep 19); Solutions: PDF (posted: Sep 26)

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

- J.D. Gray and S.A. Morris,
"When is a function that satisfies the
Cauchy-Riemann equations analytic?,"
*American Mathematical Monthly*,**85**(1978), no. 4, pp. 246–256.

- M.G. Arsove,
"On the definition of an analytic function,"
*American Mathematical Monthly*,**62**(1955), no. 1, pp. 22–25.

- Course homepage from Fall 2007.

**Final Exam**: 5:00–8:00 PM, Thu, Dec 18. Venue: LeConte Hall, Room
3.

**Midterm Exam**: 2:00–3:00 PM, Mon, Oct 27 (Part I) and
2:00–3:00 PM, Wed, Oct 29 (Part II). Venue: LeConte Hall, Room
3.

**Grade composition:** 40% Homework, 20% Midterm, 40% 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.