Complex Analysis
 Complex Numbers
 Real and imaginary parts, polar form, conjugates
 Operations: addition, subtraction, multiplication, division
 The geometry of the complex numbers
 Euler's formula
 Complex Functions
 Powers
 Polynomials
 Roots
 Trig functions
 Exponential
 Logarithm
 Hyperbolic trigonometric functions
 Branches of functions
 Means of understanding graphs of functions
 Differentiation
 Derivatives
 Analytic functions
 CauchyRieman Equations
 Harmonic functions
 Singularities
 Isolated singularities
 Poles
 Removable singularities
 Contour integrals
 Definitions and examples
 Cauchy's Theorem
 Path independence
 Generalizations
 Morera's Theorem and Liouville's Theorem
 Residue Theorem
 Calculating residues
 The Argument Principle
 Applications
 Conformal Maps
See the course calendar for details concerning exams and quizzes.

