Course Materials 

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Other Texts

• Applied Complex Variables, John W. Dettman,  Dover 1984. 
• Complex Variables, Murray R. Spiegel, Shaum's, McGraw Hill, 1999.
• Complex Variables and Applications, James W. Brown and Ruel V. Churchill, McGraw Hill, 2004.
• Complex Variables, Francis Flannigan, Dover, 1983

Midterm: Review Topics, Sample Problems
Final: Review Topics, Sample Problems
Poisson integral formula and fluid flow
Summation of Series Using Residues

Complex Numbers

• History of Complex Numbers
• Dr Herman's Complex Analysis Chapter
• Dave's Short Course on Complex Numbers
• Stereographic Projection

• Wikipedia with Worked Problems

• Class Notes - from previous course

• Lectures

  • Perimeter Institute

Plotting Complex Functions

• Complex Functions

• f(z) Demo

• Complex Function Viewer - Java

• Moebius Transformations Revealed - Video

• Domain Coloring

  • Lundmark's Complex Analysis

  • Gandhi Viswanathan's Blog

• Mappings

• MATLAB code

  • plotcompc.m - Plot tangets to curves and their images

  • complexcurves.m - Plots curves in xy plane and their images in the uv plane

  • complexplot.m - Plot images of single lines

  • complexgrid.m - Plot images of grids under f(z) - complexgrid2.m for images only

  • mapstrip.m - Plot image of strip under f(z)=z+exp(z).

  • Domain Coloring: domcol2.m

  • Julia and Mandelbrot sets

Differentiation

• Complex Differentiation

• Harmonic Conjugate Function

Series

• Laurent Series

• Handbook of Complex Variables - Google Books Result - Great for everything!

Contour Integration

• Wikipedia

• Cauchy's Integral Theorem vs Cauchy's Integral Formula

Other Topics

• Irrotational Flow around objects

• Conformal Mapping Example

• Ideal Flow Machine

• Visual Complex Analysis, The Book

• Zipper

• Software Collection for Complex Variables

• Visualizing Complex Functions Using Domain Coloring

• The Chaos Hypertextbook

• Laplace Transform and more

• The Gamma Function - representations

• Stirling's Approximation

• Methods of Steepest Descent and Stationary Phase

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