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
- Cauchy-Rieman 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.
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