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.