# 640:403 - Introductory Theory of Functions of a Complex Variable

### Resources:

Web sites:
Course web site `http://sites.math.rutgers.edu/~asbuch/complex_s18/`
Homework and exam scores

Text:
Stephen D. Fisher, Complex Variables (2nd edition)
Lev A. Borisov, Notes on the Gamma and Zeta functions

Syllabus

Lectures:
Tuesday and Thursday 1:40 - 3:00 PM in SEC-212 (Busch)

Office hours:
Tuesday 3-4 PM and Wednesday 11-12 noon in HILL-234 (Busch). Plus Thursday after class until everyone leaves.

David Bau's Complex Function Graph Viewer (Short explanation)
Thanks to Scott Harman for showing me this!

Midterm 1, Tuesday February 20 in class, 22%
Midterm 2, Tuesday April 3 in class, 22%
Final Exam, May 4, 8-11 AM, 44%
Weekly Homework, 12% total.

### Midterm 1:

Tuesday February 20 in class.
Closed-book exam, no calculators, no formula sheet.
Covered sections: 1.1-1.6, 2.1-2.3.
No questions about Cauchy's Formula; however, the rest of section 2.3 is covered, including Cauchy's Theorem.
You may be asked to do calculations, state theorems and definitions, prove statements, and anything else that is relevant for this subject.
Solutions
Average 76/120, Median 82/120, Max 112/120.
F < 60 ≤ D < 80 ≤ C < B < 100 ≤ A

### Midterm 2:

Tuesday April 3 in class.
Closed-book exam, no calculators, no formula sheet.
Covered sections: 1.1-1.6, 2.1-2.6, 3.1-3.2.
While this exam is officially cumulative, I am mostly interested in testing the material covered since MT1.
You may be asked to do calculations, state theorems and definitions, prove statements, and anything else that is relevant for this subject.
Solutions
Average 57/100, Median 58/100, Max 83/100.
F < 34 ≤ D < 53 ≤ C < B < 80 ≤ A

### Final exam:

Friday May 4, 8-11 AM.
Closed-book exam, no calculators, no formula sheet.
Covered sections: 1.1-1.6, 2.1-2.6, 3.1-3.5, 4.1.
This exam is cumulative. There will be no questions about the Gamma or Zeta functions.
You may be asked to do calculations, state theorems and definitions, prove statements, and anything else that is relevant for this subject.

### Homework Policy:

(1) Late homework is not accepted.

(2) It is fine to discuss the problems with others, but write-ups must be individual. If you have received help for solving a problem, then cite your source(s).

(3) Regard a homework problem as an essay with rigorous mathematical content. Explain what you do without making your explanation longer than necessary. Write neatly. It is your responsibility that whoever reads your work will understand and enjoy it!

Assigned homework sets will show up on this course web site.

### Assigned homework:

Homework 0:
Homework 1: Due Thursday January 25 in class.
1.1: 1, 3, 5, 9, 11, 13, 19
1.2: 1, 3, 7, 9, 11, 21, 23, 29
Homework 2: Due Thursday February 1 in class.
1.3: 1, 3, 5, 7, 9, 13, 25
1.4: 1, 3, 5, 15, 19
Homework 3: Due Thursday February 8 in class.
1.4: 31, 35, 39
1.5: 1, 3, 7, 9, 13, 17, 21
1.6: 1, 3, 5
Homework 4: Due Thursday February 15 in class.
1.6: 7, 9, 13, 16
2.1: 2, 5, 9, 15, 23
Homework 5: Due Thursday February 22 in class.
2.2: 1, 3, 5, 9, 15, 19
2.3: 1, 3, 9, 11, 14, 15
Homework 6: Due Thursday March 8 in class.
2.4: 1, 3, 5, 7, 11, 15, 17, 18, 19
2.5: 1, 3, 7, 13, 15
Homework 7: Due Thursday March 22 in class.
2.5: 17, 19, 21, 23, 25, 27
2.6: 1, 2, 3
Homework 8: Due Thursday March 29 in class.
2.6: 5, 7, 8, 9
3.1: 1, 3, 5, 7, 13, 15
Homework 9: Due Thursday April 5 in class.
2.6: 11, 17
3.1: 9, 11
3.2: 1, 3, 5, 9
Homework 10: Due Thursday April 12 in class.
3.1: 16, 17, 23
3.2: 15, 17
3.3: 3, 5, 7, 11, 16, 17
Homework 11: Due Thursday April 19 in class.
3.4: 1, 2, 3, 5, 15
3.5: 1, 3, 5, 9
Practice problems. Do not turn in.
4.1: 1, 2, 4, 5, 9