MATH 8701 - Complex Analysis - Fall 2013

| Class Lecture Notes | Homework | Moodle | HW Solutions | Further Reading |

General Information

Time MWF, 2:30--3:20 p.m.
Location Vincent Hall, Room 206
Professor Ben Brubaker (brubaker@math.umn.edu)
Office: Vincent Hall, Room 233
Office Phone: 5-6380
Office Hours: W 1-2, Th 12:30-1:30, and always available by appointment
Textbook Lars Ahlfors, Complex Analysis (3rd. Ed., McGraw-Hill)
Course
Assignments 		Weekly problem sets (35% of total grade), a midterm (20%), an integration quiz (10%) and a final exam (35%).
Syllabus
Syllabus II
Syllabus III 		(linked at left as PDF files) The first syllabus is an outline of the course through the first midterm on Wednesday, October 16. The second is through the integration quiz on Monday, November 18.

Take-Home Final Exam

Midterm I

    Here is the review sheet of problems for the first midterm, one of which will appear on the test itself.

    There will be one question on the midterm asking you to state and prove one of the following results:
    • Differentiability is equivalent to the Cauchy-Riemann equations (p. 26)
    • Open sets are connected iff joined by a rectilinear path (p. 56)
    • Cauchy's theorem for rectangles (p. 109)
    • Cauchy's theorem for disks (p. 113)
    • Liouville's theorem (p. 122)

Homework

All section and problem numbers in the following assignments refer to Ahlfors' book.

  • Problem Set 1 (Due Friday, Sept. 13):
    • Find the fifth roots of 3 + 3i.
    • Section 1.1.4 (p. 9): 3, 4
    • Section 1.1.5 (p. 11): 1, 4
    • Section 1.2.2 (p. 16): 5
    • Section 1.2.3 (p. 17): 1, 2
    • Section 1.2.4 (p. 20): 1, 2
  • Problem Set 2 (Due Friday, Sept. 20):
    • Section 2.1.2 (p. 28): 2, 4, 7
    • Section 2.1.4 (p. 32): 2, 3, 6
    • Section 2.2.3 (p. 37): 3, 5
    • Section 2.2.4 (p. 41): 2, 4, 6, 8
  • Problem Set 3 (Due Friday, Sept. 27):
    • Section 2.3.2 (p. 44): 1
    • Section 2.3.4 (p. 47): 5, 6, 10
    • Section 3.1.2 (p. 53): 1, 7
    • Section 3.1.3 (p. 58): 3, 4
    • Section 3.1.4 (p. 63): 3, 4
    • Section 3.1.5 (p. 66): 1, 3
    • Section 3.2.2 (p. 66): 1, 2
  • Problem Set 4 (Due Friday, Oct. 4):
    • Section 4.1.3 (p. 108): 1, 2, 3, 4, 6
    • Section 4.2.2 (p. 120): 1, 3
  • Problem Set 5 (Due Friday, Oct. 11):
    • Section 4.2.3 (p. 123): 1, 2, 3, 5
    • Section 4.3.2 (p. 130): 1, 2, 3, 4 (DUE: Nov. 8)
  • Problem Set 6 (Due Friday, Oct. 25):
    • Section 4.3.3 (p. 133): 1, 2
    • Section 4.3.4 (p. 136): 1, 2
  • Problem Set 8 (Due Friday, Nov. 8):
    • Section 4.3.2 (p. 130): 1, 2, 3, 4
    • As a linked pdf
  • Problem Set 9 (Due Friday, Nov. 15):
    • Section 4.5.2 (p. 154): 1, 2 (assigned previously)
    • Section 4.5.3 (p. 161): 1 (b,e,f only), 3 (c,d,e,g,h)
  • Problem Set 10 (Now Due Monday, Dec. 9):
    • One extra problem as a linked pdf
    • Section 5.1.2 (p. 184): 3
    • Section 5.1.3 (p. 186): 4
    • Section 5.2.1 (P. 190): 1, 5
  • Problem Set 10, PART II (Also Now Due Monday, Dec. 9):
    • Section 5.2.2 (p. 193): 1
    • Section 5.2.3 (p. 197): 1, 3
    • Section 5.2.4 (p. 200): 1, 2

Homework Solutions

Further Reading