Math 4512 - Complex Analysis

Analytic functions, elementary functions and mappings, integrals, Cauchy's integral theorem and formula, power series, residues and poles. Prerequisite: MATH 2511. 3 credits.

General Information

• Syllabus

Resources

• Flatland (the Book)
• Mandelbrot applet
• Some math on Iterations of Functions
• Video: zooming into and zooming out of the Mandelbrot set
• Nova: On Fractals, Benoit Mandelbrot, and StarTrek 2
    
• ZMap
• Wolfram Mathworld
• DyKnow Collaboration software

Exams

• Final Exam (take-home) (pdf)
   
• Practice Exam 1 (pdf) - Answers

Lectures

• 22 - Residue Thm (pdf)
• 21 - Residues (pdf)
• 20 - Laurent Series (pdf)
• 19 - Taylor Series (pdf)
• 18 - Series and Taylor's Thm - no notes
• 17 - Max Modulus Thm (pdf)
• 16 - Cauchy Consequences (pdf)
• 15 - Cauchy Int Formula (pdf)
• 14 - Cauchy_thm (pdf)
• 13 - integration (pdf)
• 12 - spec_funs (pdf)
  12 - addendum i^i^i (pdf)
• 11 - harmonic (pdf)
• 10 - analytic (pdf)
• 09 - diffble (pdf)
• 08 - limits (pdf)
• 07 - topology (pdf)
• 06 - maps (pdf)
• 05 - functions (pdf)
• 04 - more roots (pdf)
• 03 - exp_roots (pdf)
• 02 - alg_exp (pdf)
• 01 - basic alg in C (pdf)

Assignments

• 22 - hw Residue thm (pdf)
• 20 - hw Laurent series (pdf)
• 19 - hw Taylor series (pdf)
• 16 - hw cauchy consequences (pdf)
• 14 - hw cauchy thm (pdf)
• 13 - hw_integration (pdf)
• 12 - hw_spec_funs (pdf)
• 11 - hw harmonic (pdf)
• 10 - hw_analytic (pdf)
• 09 - hw_difble (pdf)
• 08 - hw limits (pdf)
• 07 - hw topology (pdf)
• 05 - hw_functions (pdf)
• 04 - hw_visual algebra (pdf) and
     roots of unity (pdf)
• 03 - hw exp_roots (pdf)
• 02 - hw alg_exp (pdf)
• 01 - hw basic alg (pdf)