## Spring 2018

 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

Class meets: T, Th, 12:25 - 1:45, AEB 320
Office Hours: T, 3:00-4:00

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

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

Policy:
Exercises: 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 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 midterm exams (50%= 25%+25%) + homework(20%) + final (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.

Homework problems - to be posted (pages and numbers corresponds to 8th edition of the Churchill and Brown text)
The only way to learn mathematics is to do mathematics.
-- Paul Halmos
WH1
Chapter 1.
Due Thursday January 18
p8 -1(a), 1(b),
p12 1(a), 4
p23 5(b), 5(c), 9, 10
p29 1b), 2(b)
p30 6

WH2
Chapter 2.
Due Tuesday, January 23
p 44 3(b), 3(c)
p 55 2(a), 5
p 56 10(a), 10(b), 10(c)
p71 1(c), 4(c)

HW3
Chapter 2
Due Jan 30

p 71- 4(c) , p 77- 1(b), p 78- 6, p 81- 1(c), p 82 -5, 9, 11 (use Maple, Matlab, Matematica, or any other platform to graph the families of level curves).

HW4
Chapter 3
Due Thursday, February 8

p 97: 4(a), 4(b), 9(b)

p 100: 1

p 104: 2(c)

p 108: 2(a), 2(b), 8(a)

p 115: 3

First Midterm exam at Thursday, February 8 - chapters 1, 2, 3. of the textbook

HW5 Chapter 4 Due February 22
p 135 1(b), 2, 6
p 149 1, 2(b), 5
*(more diffucult) p 126, 6

HW6 due March 6
p140: 1, 3
p160: 1(a),1(b)
p170: 1(b). 1(d)
p170: 4

See this video about series that do not converge: 1+2+ 3+ 4 + .. = - 1/12  https://www.youtube.com/watch?v=YuIIjLr6vUA

Second Midterm exam at Thursday, March 15 (before Spring break) - chapters 4, 5, 6.  of the textbook

HW7 due March 15
p 206 4, 5
p 225. 1
p 239. 2(a), 2(c)
p 243  1(a), 1(c) 1(e), 3(a)
p 248 1(a),1(b), 4.

Additional date/time for the Second Midterm exam is
Tuesday, March 27, 4:00-5:30, in LCB 323

HW8 due April 5

p 255  2(a), 4(a),
p 256  6,
p 267 1, 5

HW 9 due April 12

P 286 #3

p. 275 #2

p. 276 #10 (factorize the demoninator)

p. 286 #4.

HW 10 due April 12

p 287 #6

p313 # 5

r 318 #4

p 324 #2

Final exam - Wednesday, May 2, 2018
10:30 am – 12:30 pm

Problems from midterm 1
Problems from midterm 2

Internet sources

History of complex numbers - a short note
Quadrdatic, 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