Complex Variable and Applications (math. 3160)

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:
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.

Complex Logo
Exams
Policy: 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

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