Course Materials 

Back

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
• Dr. Herman's Complex Variable Notes

Handouts

• Midterm: Review Topics
• Final: Review Topics
• Poisson integral formula and fluid flow
• Elliptic Functions

Complex Variable History

• Cardano's Method for Cubic

• From Bombelli to Euler

• van Roomen's Problem, van Roomen pg, Viete response

Visualizing Complex Functions

• Moebius Transformations Revealed - Video

• Domain Coloring

  • Lundmark's Complex Analysis

  • Gandhi Viswanathan's Blog

  • Dr. Herman's Complex Analysis Chapter

• MATLAB code

  • complexplot.m - Plot images of single lines (Minimal version complexplotmin.m)

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

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

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

  • Domain Coloring: domcol2.m

  • Julia and Mandelbrot sets

• Mobius transformations

• Software Collection for Complex Variables

• Visualizing Complex Functions Using Domain Coloring

• Visual Complex Analysis, The Book

Gamma Function

• The Gamma Function - representations

• Who Invented the Gamma Function?

• D. Bernoulli Letter

• Davis paper on history, another history

• Stirling Approximation

Fluid Flow

• Irrotational Flow around objects

• Conformal Mapping Example

• Ideal Flow Machine

Hopf Fibration

• Hopf Fibration - Wikipedia entry

• Niles Johnson page, YouTube Video

• Mathematica page

• Villarceau circles

• MATLAB - hopfmap.m, hopfcircles.m

Other Topics

• Geometry of Riemann Surfaces, Elliptic Function

• Stereographic Projection

• Perimeter Institute Lectures on a variety of topics

• Zipper

• The Chaos Hypertextbook

• Laplace Transform and more

• Methods of Steepest Descent and Stationary Phase

Top