Complex Variable and Applications (math. 3160).

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. 12:25 PM-01:45PM, AEB 320 Office Hours: T, 4:00 - 5:00 Text : Churchill and Brown `Complex Variable and Applications', 6-th ed. chapters 1-10.

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

Exercises: HW problems are typical of what you'll be asked on exams.

Calculator: A calculator is not required for the course, although it may be useful for some homework problems. Calculators and phones are 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 midterm exams (25% each) + homework(20%) + final score (30%).

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.

The course discusses the algebra of complex numbers, elementary functions of complex arguments, theory of analytical functions with applications, especially the conformal mappings, complex integration.

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.

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