Complex Variable and Applications (math. 3160).

The imaginary number is a fine and wonderful recourse of the divine spirit, almost an amphibian between being and not being.
--Gottfried Whilhem Leibniz
The shortest path between two truths in the real domain passes through the complex domain.
-- Jacques Hadamard

The complexity of the complex variable course is more imaginary than real.
-- An encouraging observation
"The number you have dialed is imaginary. Please rotate your phone 90 degrees and try again."
-- A math joke

Instructor:

Andrej V. Cherkaev, professor
Department of Mathematics
Office: JWB 225
Email: cherk@math.utah.edu
Tel : +1 801 - 581 6822
Fax : +1 801 - 581 4148

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', 6-th ed. chapters 1-10.

Exams

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

Policy:

Exercises:

Calculator: A calculator is not required for the course, although it may be useful for some homework problems. Calculators will be forbidden in exams.

Final exam: Half of the final will be devoted to material covered after the second midquarter exam. The rest will be comprehensive. Students must take the final to pass the course.

Grades: The final grade will be based on the following score: Two midquarter exams (50%) + homework(10%) + final score (40%).

ADA: The Americans with Disabilities Act requires that reasonable accommodations be provided for students with physical, sensory, cognitive, systemic, learning and psychiatric disabilities. Please contact me at the beginning of the quarter to discuss any such accommodations for the course.

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]

41 Fundamenal Th. 142 [4], 149 [1, 2, 4, 8]

43-45 Algebra & Series 156 [1, 3, 5]

46-51 Laurent Series 172 [1, 3, 10, 13, 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 Int. 218 [1, 3, 6], 226

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

68-72 Linear frac. 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 in the fifth and sixth edition of the textbook has been done by Professor Andrejs Treibergs.

Internet sourses

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

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The imaginary number is a fine and wonderful recourse of the divine spirit, almost an amphibian between being and not being. --Gottfried Whilhem Leibniz	The shortest path between two truths in the real domain passes through the complex domain. -- Jacques Hadamard
The complexity of the complex variable course is more imaginary than real. -- An encouraging observation	"The number you have dialed is imaginary. Please rotate your phone 90 degrees and try again." -- A math joke

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]
41	Fundamenal Th.	142 [4], 149 [1, 2, 4, 8]
43-45	Algebra & Series	156 [1, 3, 5]
46-51	Laurent Series	172 [1, 3, 10, 13, 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 Int.	218 [1, 3, 6], 226
66-67	Other applications	[1, 2, 3, 7], 242 [1, 6]
68-72	Linear frac.	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]

Complex Variable and Applications (math. 3160).

Andrej V. Cherkaev, professor Department of Mathematics Office: JWB 225 Email: cherk@math.utah.edu Tel : +1 801 - 581 6822 Fax : +1 801 - 581 4148

Andrej V. Cherkaev, professor
Department of Mathematics
Office: JWB 225
Email: cherk@math.utah.edu
Tel : +1 801 - 581 6822
Fax : +1 801 - 581 4148