Complex Variable and Applications (math. 3160) HW.

Instructor:

Class meets: T, Th, 9:40 - 10:30, NS 205
Office Hours: T, 4:00 - 5:00

Text : Churchill and Brown `Complex Variable and Applications', 9-th ed. chapters 1-10.

Exams

Exam	firstst midterm	second midterm	Final
Sections	1 - 29	30 - 64	1 - 92

Policy:

Course outline and homework problems

Section Topic Page [Problems]

1- 2 Complex Numbers 5 [2, 4, 5, 9, 12]

3- 5 Geometric Prop. 11 [3, 10, 14], 17 [1, 4, 5, 8, 13]

6- 8 Roots 22 [1, 4, 6, 7, 8], 25 [1-5]

9-14 Mappings 32 [3, 4, 5, 7]

15-18 Derivatives 42 [2, 4, 9], 47 [1, 3, 8], 54 [1, 2d, 7]

19-22 CR Eqns. 62 [1, 6, 7b, 10, 12]

23-25 Exponentials 68 [3, 6, 8, 10], 71 [2, 7, 9], 74 [2, 5]

26-29 Logs 79 [3, 6, 14], 84 [2, 6, 9, 10, 11]

30-33 Integrals 92 [3, 4, 11], 102 [1, 5, 7, 11, 13, 15]

34-35 Contour Integrals 119 [2, 3, 7]

36-38 Cauchy Goursat 128 [1, 3, 5]

39-40 Liouville's Th. 136 [1, 2, 3, 4, 5, 6]

43-45 Algebra & Series 156 [4, 6, 8]

46-51 Laurent Series 172 [1, 3, 10, 15]

53-55 Residues 188 [1, 2, 4, 7]

56-58 Poles 197 [1, 2, 3, 4, 10]

60-61 Evaluation of integrals 208 [1, 2, 3, 4, 6, 9], 214 [1, 2, 6, 13)]

62-64 Improper Integrals 218 [1, 3, 6], 226

66-67 Other applications [1, 2, 3, 7], 242 [1, 6]

68-72 Linear fractions 250 [2, 8, 11, 17], 258 [2, 5, 6, 13]

79-81 Exp-sin-log-root 266 [4, 5, 6, 9], 275 [3, 4, 8]

82-83 Harmonic Mapping 289 [1, 4, 6], 297 [1, 3, 9]

84-85 Steady Temp. 307 [1, 2, 5, 8]

86-87 Electrost. potential 312 [2, 3, 7, 10]

88-92 Stream Function 322 [3, 4, 5, 7, 11]

Acknowledgement. The selection of the homework problems has been done by Professor Andrejs Treibergs.

Internet sourses

Quadratic, cubic and quartic equations; introduction of complex numbers
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 let me know if you find interesting web sites related to the course
Thank you.

Back to Homepage || Back to Teaching Page

Section	Topic	Page [Problems]
1- 2	Complex Numbers	5 [2, 4, 5, 9, 12]
3- 5	Geometric Prop.	11 [3, 10, 14], 17 [1, 4, 5, 8, 13]
6- 8	Roots	22 [1, 4, 6, 7, 8], 25 [1-5]
9-14	Mappings	32 [3, 4, 5, 7]
15-18	Derivatives	42 [2, 4, 9], 47 [1, 3, 8], 54 [1, 2d, 7]
19-22	CR Eqns.	62 [1, 6, 7b, 10, 12]
23-25	Exponentials	68 [3, 6, 8, 10], 71 [2, 7, 9], 74 [2, 5]
26-29	Logs	79 [3, 6, 14], 84 [2, 6, 9, 10, 11]
30-33	Integrals	92 [3, 4, 11], 102 [1, 5, 7, 11, 13, 15]
34-35	Contour Integrals	119 [2, 3, 7]
36-38	Cauchy Goursat	128 [1, 3, 5]
39-40	Liouville's Th.	136 [1, 2, 3, 4, 5, 6]
43-45	Algebra & Series	156 [4, 6, 8]
46-51	Laurent Series	172 [1, 3, 10, 15]
53-55	Residues	188 [1, 2, 4, 7]
56-58	Poles	197 [1, 2, 3, 4, 10]
60-61	Evaluation of integrals	208 [1, 2, 3, 4, 6, 9], 214 [1, 2, 6, 13)]
62-64	Improper Integrals	218 [1, 3, 6], 226
66-67	Other applications	[1, 2, 3, 7], 242 [1, 6]
68-72	Linear fractions	250 [2, 8, 11, 17], 258 [2, 5, 6, 13]
79-81	Exp-sin-log-root	266 [4, 5, 6, 9], 275 [3, 4, 8]
82-83	Harmonic Mapping	289 [1, 4, 6], 297 [1, 3, 9]
84-85	Steady Temp.	307 [1, 2, 5, 8]
86-87	Electrost. potential	312 [2, 3, 7, 10]
88-92	Stream Function	322 [3, 4, 5, 7, 11]