Math 3160, Fall 2006

Mathematics 3160

Applied Complex Variables

Fall 2006

Time and Place: MW 9:40-10:30am, AEB 110
Instructor: Grady Wright, JWB 126, 581-8649, Email:

Office Hours: MTW 10:35-11:45am, or by appointment (email is best).

Please see the syllabus for more information.

Homework

See "How to Present your Work" for instructions on writing up your homework assignments. You may also be interested in this page describing some basic mathematical symbols.

Homework will now be assigned on Mondays and due on the following Monday, unless otherwise stated.

# Due Section(s) Topic Page[Problem Numbers] Additional Problems

1 08-30-2006 1-2
4 Complex Numbers
Geometric Properties 4[2,3,4,5,10], 7[1,5]
11[1,4]

2 09-06-2006 5
6-7 Geometric Properties
Polar Coordinates 13[1,2,7,10]
21[1,2,5,6,7]

3 09-13-2006 6-7
8-10
11 Polar Coordinates
Roots
Functions of a complex variable 21[5,10]
28[3,6,7,8],31[1,5]
35[1b,1d,2,4]

4 ~~09-20-2006~~
New due date:
09-25-2006 12-13
14-17 Mapping
Limits 42[1,3,7],Supplemental
53[1c,2a,2b,3b,5,10]

5 09-25-2006 18-19 Derivatives 59[1b,1d,3,7,8]

6 Monday: 10-02-2006 20-22
23-24
25 Cauchy-Riemann
Analytic functions
Harmonic functions 68[1b,1d,2b,2d,3c,4a]
73[2c,4a,4c]
78[1b,1d,9]

Exam 1 Wednesday: 10-04-2006 1-27 All material up to 10-02-2006 Practice Exam A
Practice Exam B
Solutions Practice A
Solutions Practice B

7 Monday: 10-16-2006 28-30
31-32 Exponential and log
Complex exponents 89[3,6,8a,10],94[1b,3b,4,5]
96[1,4],99[2a,2b,3,6,9]

8 Monday: 10-23-2006 33-35
36-37 Trigonometric functions
Definite integrals 103[13,17],107[1,15],110[3]
115[2a,2c,3]

9 Monday: 10-30-2006 38-41 Contour Integrals 121[5],128[2,3,6,7,10],133[4]

10 Monday: 11-06-2006 42-43
44-48 Antiderivatives
Cauchy Integral Formula 141[2,4]
153[1a,1c,1e,1f,2b,3,4,6], 162[1b,1d,2b,4,7]

11 Monday: 11-13-2006 49-50
51-54
55-56 Max. principle
Power series
Laurent series 171[4,8]
181[4],188[2,3,7,8]
198[1,2,4]

Exam 2 (solutions) Wednesday: 11-15-2006 28-56 All material up to 11-8-2006 Practice Exam A
Practice Exam B Solutions Practice A
Solutions Practice B

12 Monday: 11-27-2006 57-61
62-65 Manipulating power series
Residues and singular points 212[1,3,4,6],218[1,2,4]
230[1a-c,2a,2c,3a],233[1a,1c,1d,2b]

13 Monday: 12-11-2006 66-69
71-72
73-74, 81-82 Residues and poles
Improper integrals
Fourier and Laplace integral 238[2,3,5,6a],245[1,2b,4b,8b]
257[2,4,6]
265[2.3,5,8],296[1,4]

Ex. Credit Monday: 12-11-2006 1-82 Choose any 12 of the following
26 problems. 14[14],28[5],42[6],59[4],68[1c],73[4b],
78[3],89[12],94[7],99[1b],103[11],107[14],
115[7],128[11],153[1d],162[5],188[13],198[6],
212[2],218[8],230[1e],233[2c],238[4],245[5],257[8],265[12]

Review Friday: 12-08-2006, 10:00am - 12:00pm Location: JWB 208 Come with questions!

Final Exam Monday: 12-11-2006 Comprehensive exam Practice Exam A
Practice Exam B Solutions Practice A
Solutions Practice B

Miscellaneous

Irrotational flows by conformal mappings: Interactive page, a lot of pictures.
Lectures on Advanced Topics in Theory of Functions of a Complex Variable by Norm Bleistein
COMPLEX ANALYSIS: Mathematica 4.0 Notebooks by John H. Mathews, and Russell W. Howell. Lecture notes and Mathematica-based examples, including Julia & Mandelbrot sets, conformal mappings, etc.
68 lessons by Dr. John H. Mathews. A part of the book, Complex Analysis for Mathematics & Engineering, 4th Ed, 2001, by John H. Mathews and Russell W. Howell

Please e-mail me regarding any problems with the links on this page.

#	Due	Section(s)	Topic	Page[Problem Numbers]	Additional Problems
1	08-30-2006	1-2 4	Complex Numbers Geometric Properties	4[2,3,4,5,10], 7[1,5] 11[1,4]
2	09-06-2006	5 6-7	Geometric Properties Polar Coordinates	13[1,2,7,10] 21[1,2,5,6,7]
3	09-13-2006	6-7 8-10 11	Polar Coordinates Roots Functions of a complex variable	21[5,10] 28[3,6,7,8],31[1,5] 35[1b,1d,2,4]
4	~~09-20-2006~~ New due date: 09-25-2006	12-13 14-17	Mapping Limits	42[1,3,7],Supplemental 53[1c,2a,2b,3b,5,10]
5	09-25-2006	18-19	Derivatives	59[1b,1d,3,7,8]
6	Monday: 10-02-2006	20-22 23-24 25	Cauchy-Riemann Analytic functions Harmonic functions	68[1b,1d,2b,2d,3c,4a] 73[2c,4a,4c] 78[1b,1d,9]
Exam 1	Wednesday: 10-04-2006	1-27	All material up to 10-02-2006	Practice Exam A Practice Exam B	Solutions Practice A Solutions Practice B
7	Monday: 10-16-2006	28-30 31-32	Exponential and log Complex exponents	89[3,6,8a,10],94[1b,3b,4,5] 96[1,4],99[2a,2b,3,6,9]
8	Monday: 10-23-2006	33-35 36-37	Trigonometric functions Definite integrals	103[13,17],107[1,15],110[3] 115[2a,2c,3]
9	Monday: 10-30-2006	38-41	Contour Integrals	121[5],128[2,3,6,7,10],133[4]
10	Monday: 11-06-2006	42-43 44-48	Antiderivatives Cauchy Integral Formula	141[2,4] 153[1a,1c,1e,1f,2b,3,4,6], 162[1b,1d,2b,4,7]
11	Monday: 11-13-2006	49-50 51-54 55-56	Max. principle Power series Laurent series	171[4,8] 181[4],188[2,3,7,8] 198[1,2,4]
Exam 2 (solutions)	Wednesday: 11-15-2006	28-56	All material up to 11-8-2006	Practice Exam A Practice Exam B	Solutions Practice A Solutions Practice B
12	Monday: 11-27-2006	57-61 62-65	Manipulating power series Residues and singular points	212[1,3,4,6],218[1,2,4] 230[1a-c,2a,2c,3a],233[1a,1c,1d,2b]
13	Monday: 12-11-2006	66-69 71-72 73-74, 81-82	Residues and poles Improper integrals Fourier and Laplace integral	238[2,3,5,6a],245[1,2b,4b,8b] 257[2,4,6] 265[2.3,5,8],296[1,4]
Ex. Credit	Monday: 12-11-2006	1-82	Choose any 12 of the following 26 problems.	14[14],28[5],42[6],59[4],68[1c],73[4b], 78[3],89[12],94[7],99[1b],103[11],107[14], 115[7],128[11],153[1d],162[5],188[13],198[6], 212[2],218[8],230[1e],233[2c],238[4],245[5],257[8],265[12]
Review	Friday: 12-08-2006, 10:00am - 12:00pm	Location: JWB 208	Come with questions!
Final Exam	Monday: 12-11-2006		Comprehensive exam	Practice Exam A Practice Exam B	Solutions Practice A Solutions Practice B