Math 185. Complex Analysis

Department of Mathematics
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.

Announcements

• 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.

Lectures

Location: Evans Hall, Room 70

Times: 2:00–3:00 PM on Mon/Wed/Fri

Course staff

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

Syllabus

• 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 assignments

• 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

Supplementary materials

• 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.

• Some common algebraic structures.

• Some notes on sets, logic, and mathematical language (courtesy of George Bergman).

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

Textbooks

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.