Department of Mathematics  

Duke University




    

Contour
    Integral

Complex Analysis
(Math 333)


Fall 2020

Instructor: Paul Aspinwall

Credits: 3.0

Time: TuTh 1:45 - 3:00pm

Location: Tuesdays Physics 154, Thursdays online.

Homework

  • will be given weekly.

Prerequisites

  • (Math 221 or Math 218) and (Math 212 or Math 222)) or consent of instructor.

Evaluations

  • Homework. There will be some longer homework assigmments occasionally which will give credit towards the final grade
  • Take-home Final. Due: Sunday Nov 22, 5:00PM

Office Hours

  • Mondays 10:00-11:00
  • Wednesday 2:00-3:00

Synopsis

  • Basic algebra of complex numbers
  • Exponential form
  • Analytic Functions
  • Cauchy-Riemann equations
  • Branches and derivatives of logarithms
  • Integrals
    • Contours
    • Branch Cuts
    • Cauchy's Theorem
    • Fundamental Theorem of Algebra
  • Series
  • Residues and Poles
  • The Gamma Function and the Zeta Function
  • Conformal Mappings

Textbooks

The course will be based on the text:
  1. J.W. Brown and R.V. Churchill, Complex Variables and Applications, published by McGraw-Hill, eighth or ninth edition.
See also
  1. L. Ahlfors, Complex Analysis, McGraw Hill.

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Durham, NC 27708-0318