4450/5135 FUNCTIONS OF A COMPLEX VARIABLE
Fall 1999. University of Colorado Denver


Current enrollment 4450.  Current enrollment 5135.

Offered spring of even-numbered years (not really).

PREREQUISITE for 5135: MATH 4320. MATH 5070 is recommended.

PREREQUISITE for 4450: MATH 3200

HOURS: Tuesday Thursday    0200PM-0315PM 
Has been moved to Tramway 105 on Tuesday and to CU/Dravo 656 on Thursday

INSTRUCTOR:
Prof. Andrew Knyazev
Office: CU (Dravo) 644. Phone: 556-8102.
Office hours: Wed 3pm - 6pm (or by appointment)
WWW: http://math.ucdenver.edu/~aknyazev
Email: aknyazev@math.ucdenver.edu

Students are invited to participate in the interactive DISCUSSION

TEXTBOOK: Visual Complex Analysis by Tristan Needham
$45    Paperback - 616 pages (January 1999)
Oxford University Press; ISBN: 0198534469
Other Editions: Hardcover $55 Clarendon Pr; ISBN: 0198534477

Other recommended books and materials on a separate Web page.

SUBJECT: Functions of a Complex Variable.  Complex numbers and complex plane, Cauchy-Reimann equations, complex integration, Cauchy integral theory, infinite series and products, residue theory, conforming, mapping, analytic continuation, singularities, elementary special functions.

CONTENTS:
The class will follow the outline below, touching on each major topic in a depth that will be determined by the pace of the class.

   1.Geometry and Complex Arithmetic, Homework 1
   2.Complex functions as Transformations, Homework 2  Test 1
   3.Mobius Transformations and Inversion
   4.Differentiation: The Amplitwist Concept
   5.Further Geometry of Differentiation, Homework 3   Test 2
  
Optional, if time allows:  
   8.Complex Integration: Cauchy's Theorem
   9.Cauchy's Formula and Its Applications
 

GRADING:

Undergraduate: Homework/Quizzes - 50%, Midterm Test - 25%, Final Test - 25%.

Graduate: Homework/Quizzes - 25%, Midterm Test - 25%, Final Project - 25%, Final Test - 25%.

 
Extra credit will be given for problems solved on board in the class and other extra work.
Preliminary grades will be distributed during the semester.