110.607 Complex Variables   --  Spring 2018

This is a first semester graduate course in functions of one complex variable. Topics to be covered include the Cauchy-Riemann equations, Cauchy Integral Formula, Liouville theorem, meromorphic functions, residues, normal families and Montel's Theorem, Riemann mapping theorem, harmonic functions, Poisson Integral Formula, subharmonic functions, Dirichlet problem, Weierstrass products, Mittag-Leffler Theorem, Blaschke products.

Instructor:

Email:

Office Hours:

Hang Xu

hxu@math.jhu.edu

TTh 1:00-2:00 at Krieger 220

TA:

Office Hours

Email:

Cheng Zhang

Wed 3-4 pm at Krieger 211 and 5-7 pm at Krieger 213.

czhang67@math.jhu.edu

Lecture Time:

TTh 10:30-11:45

Classroom:

Krieger 204

Text:

Greene & Krantz, Function Theory of One Complex Variable, Third Edition

Grading:

Grades will be based on 350 points distributed as follows: 11 homework assignments, worth 10 points each, due in the lecture on the following Thursday. The lowest score will be dropped.

                                                                                      A midterm exam (100 points) and a final exam (150 points).

Syllabus (will be updated

as the course progress):

 

week

beginning

  reading

  assignment (due the following Thursday)

1.

Jan. 30

(review Chapter 1)
2.1, 2.2, 2.4

Ch. 1: 16, 17, 36, 42, 43
Ch. 2:  5, 10, 18

2.

Feb. 6

3.1-3.3

Ch. 2: 21
Ch. 3: 9, 10, 17, 19, 20a, 21, 23

3.

Feb. 13

3.4-3.6, 4.1-4.3

Ch. 3: 32, 33, 37, 38, 39, 42, 44
Ch. 4: 5

4.

Feb. 20

4.4-4.6

Ch. 4: 9, 21, 27abc, 33abc, 34bdh, 40, 50, 59

5.

Feb. 27

4.7, 5.1-5.3

Ch. 4: 30, 31, 51, 60.
Ch. 5: 2, 3, 6, 7.

6.

Mar. 6

5.4, 5.5, 6.2

Ch. 5: 5, 8, 10acf, 12, 13, 14, 16.

Ch. 6: 17

7.

Mar. 13

6.1, 6.3

Midterm, Thursday, Mar. 15

 

Mar. 20

Spring Break

 

8.

Mar. 27

6.4-6.7

Ch. 6: 1, 2, 6, 8, 12, 13, 19, 24.

9.

Apr. 3

7.1-7.3

Ch. 6: 14, 20, 21, 23

Ch. 7: 1, 2, 10, 12.

10.

Apr. 10

7.4-7.6

Ch. 7: 13, 14, 17, 18b, 19, 20, 23, 30

11.

Apr. 17

7.7, 7.8

Ch. 7: 41, 46, 50, 69

12.

Apr. 24

8.1, 8.2

Ch. 8: 1, 4, 5, 12

13.

May. 1

8.3, 9.1

Take-Home Final