Syllabus
Instructor: André Wehner, Olin 111, Ph. 238-5919, e-mail wehner@centre.edu,
Office Hours: Mo-Tu-We-Th 4-6, Tu-Th 10:20-11:20, or by appointment.
Class Time:
Text: Complex Analysis, 5th edition, Mathews&Howell
Grading: 3 tests @ 15% each = 45%
Final 25%
Homework 30%
Tentative grading scale: 90 = A-, 80 = B-, 70 = C-, 60 = D
Course Description
In this course, we study the beautiful theory of functions
of one complex variable. The prerequisite course for this class is
We begin by introducing complex numbers (Ch. 1) and functions (Ch. 2), and proceed by developing the calculus of such functions in a way that formally resembles the development of ordinary calculus of one real variable (notions of limits, continuity, differentiability, and integrability), but in fact uses the concepts of multivariate calculus, such as partial derivatives and line integrals (Ch. 2-7). That’s because complex-valued functions of one complex variable are, in a sense, equivalent to pairs of real-valued functions of two real variables. As such, they transform regions in the plane to other regions in the plane. However, the notion of differentiability of a complex function is far more restrictive than that of real functions, a fact that gives rise to a series of remarkable and elegant integral theorems with no equivalent in real analysis. These theorems may be used to compute real integrals, solve boundary value problems, or even prove the fundamental theorem of algebra. As time permits, we will conclude the class with applications of complex analysis to physics and engineering (Ch. 8-11).
There will be three one-hour tests during the course of the semester, closed everything. If you have to miss class for a valid reason (proof required!), you will be allowed to make up a test. Homework is an essential part of this class. You are encouraged to cooperate on the assignments, but you should only turn in your own work. Late homework will be marked down (of course, exceptions can be made for emergencies). The solutions you present in both the homework and the tests must be complete, coherent, and well-organized.
We will make repeated use of the computer algebra system Maple. I will pass out worksheets on the relevant Maple commands in class. Right next to my office, in Olin 110, you will find a Maple computer lab with four desktops and a long study table. Most of the time, I’ll be right next door waiting to help you!
There is an accompanying website for our textbook at http://www.jbpub.com/catalog/9780763737481/ .
This syllabus can be found at http://web.centre.edu/wehner/courses/m340f08.htm .
Schedule
|
Day |
Section covered |
Homework (due dates will be announced in class) |
|
|
|
|
|
9/1 |
1 |
1.2: 1-5, 8, 9 |
|
9/3 |
1 |
1.3: 1, 4, 6, 9, 22, 24 |
|
9/5 |
1 |
1.4: 1-3, 5, 7-12; 1.5: 2-5,
7-9, 15 |
|
9/8 |
1 |
1.6: 1-3, 5, 9 |
|
9/10 |
2 |
2.1: 1, 3-5, 7, 8 |
|
9/12 |
2 |
2.2: 1-5, 7-9; 2.3: 1, 2, 7,
8, 15, 19, 22 |
|
9/15 |
2 |
2.4: 1, 5; 2.5: 1-5, 9, 11,
15, 18 |
|
9/17 |
3 |
3.1: 1-4, 7, 13 |
|
9/19 |
3 |
3.2: 1-3, 6, 7, 9, 11, 16 |
|
9/22 |
3 |
3.3: 1-5, 8-10, 12, 13 |
|
9/24 |
Test 1 |
|
|
9/26 |
4 |
4.1: 1, 5-7, 10, 12 |
|
9/29 |
4 |
4.3: 1-5, 12; 4.4: 3-6 |
|
10/1 |
4 |
4.2: 1, 4, 7 |
|
10/3 |
5 |
5.1: 4, 5, 8, 11, 17, 18 |
|
10/6 |
5 |
5.2: 1, 3, 5, 12, 13; 5.3:
1-4, 7 |
|
10/8 |
5 |
5.4: 5-7, 10, 16, 18; 5.5: 1 |
|
10/10 |
6 |
6.1: 1, 2; 6.2: 1, 2, 5, 7, 9 |
|
10/13 |
6 |
6.3: 1-4, 6, 7, 10 |
|
10/15 |
6 |
6.4: 1-5, 17, 18 |
|
10/20 |
6 |
6.5: 1-10, 19; 6.6: 1-4 |
|
10/22 |
Test 2 |
|
|
10/24 |
7 |
7.1: 1, 2, 4; 7.2: 1-5, 7, 12,
17, 19 |
|
10/27 |
7 |
7.3: 1-3, 9, 10, 15, 16 |
|
10/29 |
7 |
7.4: 1-3; 7.5: 1, 3,
6 |
|
10/31 |
8 |
8.1: 1-3, 5-9 |
|
11/3 |
8 |
8.2: 1, 3, 5 |
|
11/5 |
8 |
8.3: 1, 3, 5, 7, 9 |
|
11/7 |
8 |
8.4: 1, 3, 5, 7, 9 |
|
11/10 |
8 |
8.5: 1, 3, 5, 7, 9 |
|
11/12 |
10 |
10.1: 1-7 |
|
11/14 |
10 |
|
|
11/17 |
10 |
10.2: 2, 3, 5-8, 11, 16-18 |
|
11/19 |
10 |
|
|
11/21 |
Test 3 |
|
|
11/24 |
11 |
11.2: 1-5, 8, 10 |
|
12/1 |
11 |
11.3: 2-5 |
|
12/3 |
11 |
11.5: 1-6 |
|
12/5 |
11 |
11.6: 1-4 |
|
|
|
|
|
12/11,
8:30 |
Final (comprehensive) |
|