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2014 Spring Vince MAA 4402/5404

Complex Analysis

MAA 4402-2838 and 5404-1083
Spring 2014
______________________________________________________
Time: MWF period 6
Place: Little 237
Phone: 392-0281 Ext. 246
Office: 438 Little Hall
Email: avince@ufl.edu
Textbook: Complex Variable and Applications (9th edition)
Office Hours: Monday, Wednesday, Friday period 7
(or by appointment)

Homework

|z w| = |z||w|, (z+w)* = z* + w*, (zw)* = z*w* where z* denotes the conjugate (because I can’t type a bar)

  • Pg 7 #1  Pg 13 #1cd,5  Pg 16 #2,7,10   (due Wednesday, Jan 15).
  • Pg 23 #1,2,5,6  Pg 30 #1,2,4,7*  (due Friday, Jan 17)
  • Pg 34 #1-4
  • Pg 43 #2,4
  • Pg 42 #3,4, Pg 53 #3b,5,10,11, Pg 59 #1,8b, Pg 68 #1ac,3ab,4a
  • Pg 73 #1c,2c,4c,6, Pg 89 #1b,2,6,8ac,10 Pg 103 #2,7a,9
  • Pg 94 #1,2,5,8 Pg 96 #1, Pg 99 #1,2,3,8c, Pg 78 #1b
  • Pg 312 #1,3,4,7a
  • Pg 115 #2,3,4 Pg 128 #1-6,10 Pg 133 #1,2,5, Pg 141 #2,3,5
  • Pg 153 #1,2,3,4,6 Pg 162 #1-4,7 Pg 74 #7b
  • Pg 171 #1,2,4,5,6
  • Pg 181 #1,2 Pg 188 #1-3,6-8,13
  • Pg 198 #1-6
  • Pg 212 #1-4,6,7 Pg 218 #1-3
  • Pg 230 #1-3 Pg 233 #1,2
  • Pg 238 #1-6 Pg 245 #2-6
  • Pg 257 #1,4,6
  • Pg 265 #1,2,4,9
  • Pg 276 #1-3

Topics

  • Complex numbers
  • rectangular and polar form
  • Analytic functions
  • limits and the derivative
  • Cauchy-Riemann equations
  • harmonic functions
  • Examples
  • exponential and log functions
  • complex exponents
  • trig functions
  • linear fractional transformations
  • Integrals
  • contour integral
  • antiderivatives
  • Cauchy-Goursat Theorem (and Morera’s Theorem)
  • Cauchy Integral Formula
  • Liouville’s theorem and the Fundamental Theorem of
  • Algebra
  • maximum modulus principal
  • Series
  • geometric series
  • power series
  • Taylor series
  • Laurent series
  • Residues and poles
  • isolated singularities
  • residue theorem
  • residues at poles
  • behavior of a function near a singularity
  • Evaluating real integrals

Messages

Welcome to Complex Variables
Free tutoring at the Teaching Center, SW Broward Hall. Check www.teachingcenter.ufl.edu for the time schedule.
Students requesting classroom accommodation must first register with the Dean of Students Office. The Dean of Students Office will
provide documentation to the student who must then provide this documentation to the Instructor when requesting accommodation.
The course will be conducted in accordance with the University honor code, academic honesty policy, and policy regarding the use of copyrighted material.

Grades

three exams 30%
homework