Math 130 (Administration)

Complex Analysis

1. Complex Numbers
   1. Real and imaginary parts, polar form, conjugates
   2. Operations: addition, subtraction, multiplication, division
   3. The geometry of the complex numbers
   4. Euler's formula

2. Complex Functions
   1. Powers
   2. Polynomials
   3. Roots
   4. Trig functions
   5. Exponential
   6. Logarithm
   7. Hyperbolic trigonometric functions
   8. Branches of functions
   9. Means of understanding graphs of functions

3. Differentiation
   1. Derivatives
   2. Analytic functions
   3. Cauchy-Rieman Equations
   4. Harmonic functions

4. Singularities
   1. Isolated singularities
   2. Poles
   3. Removable singularities

5. Contour integrals
   1. Definitions and examples
   2. Cauchy's Theorem
   3. Path independence
   4. Generalizations
   5. Morera's Theorem and Liouville's Theorem

6. Residue Theorem
   1. Calculating residues
   2. The Argument Principle
   3. Applications

7. Conformal Maps

See the course calendar for details concerning exams and quizzes.

Math 130 (Spring 2002) web pages Created: 27 Mar 2002 Last modified: May 31, 2002 11:14:10 AM Comments to: dpvc@union.edu

Course Calendar Home Page