MATH 4320

Fall 2006

TTH 12-1:30, Weber SST 1

PROFESSOR GERONIMO

Office Hours: TTH 2:00-3:00,

The course will discuss the properties of complex functions.
We will consider in depth series, contour integrals, and conformal mappings.
The techniques developed will be used to solve certain problems in PDE's

The text that will be used is

Complex Variables and Applications  Seventh Edition  by R. V. Churchill and J. W. Brown

Fundamentals of Complex Anaysis  Third Edition  by E. B. Saff and A. D. Snider
 
A good source for additional problems is

Fundamentals of Complex Anaysis  Third Edition  by E. B. Saff and A. D. Snider

The following is a tentative syllabus

Chapter 1 Complex numbers, complex exponential, powers and roots, planar
sets - 1-2 lecture

Chapter 2 Functions of a complex variable, limits, continuity,
differentiability, Cauchy-Riemann equation  1-2 lectures

Chapter 3 Elementary functions Polynomials, exponential function Log
function trignometric functions, complex powers 1-2 lectures

Chapter 4 Contour integration, Cauchy's Theorem, Cauchy's Integral formula
and its consequences 3-4 lectures

Chapter 5 Series Taylor and Power series, convergence of series, Laurent
series zeros and singularities, Analytic continuation 4-5 lectures

Chapter 6-7 Residue Theorem  Computation of integrals  Argument principle 3-4 
lectures

Chapter 8-10 Conformal mapping Mobius transformations, preservation of
 angles, local inverses, applications 2-3 lectures 

Chapter 11 Schwarz-Christoffel transformation 1-2 lectures 

For more information and
prerequisitessee

• Tests dates and Homework

PRACTICE TESTS

• Partial Practice Test 1

  Curve

  86 or greater                                 A
  less than 86 but greater than or equal 72     B
  less than 72 but greater than or equal 49     C
  less than 49                                  D