Home Page for David B. Damiano

College of the Holy Cross
Department of Mathematics and Computer Science

Mandelbrot and Julia set images created using the Mandelbrot and Julia Set Explorer
written by David E. Joyce of Clark University.

MATH 305 - Spring 2008
Complex Analysis
Prof. David Damiano

Syllabus (pdf version)
Assignments:
- #1 Due Friday, January 25. Read Sections 1.1 and 1.2.
  - Section 1.1: 2ace, 3defg, 5di, 7, 10, 12a.
  - Section 1.2: 11-14, 23-26, 28, 29.
- #2 Due Friday, February 1. Read Sections 1.3 and 1.4.
  - Section 1.3: 2, 4, 5, 6, 10, 11 (for 2, 4, 5, 6), 14, 15, 17, 18, and 19.
- #3 Due Friday, February 8. Read Sections 1.4 and 1.5.
  - Section 1.4: 2, 3, 6, 11, 14-16, 22, 23, 31, 33.
  - Section 1.5: 2-12 even, 15b, 16 (sine only), 18 (sine only), 20, 22 (sine only), 25.
- #4 Due Friday, February 15. Read Sections 1.6 and 2.1.
  - Section 1.6: 2-4, 6, 8, 9, 12, 16.
- Hour Exam Thursday, February 21, 7-8:30 PM. Covers Chapter 1 of the text.
- #5 Due Friday, February 29. Read Sections 2.1 and 2.2.
  - Section 2.1: 1acefg, 2-11, 14, 16, 17, 20.
- #6 Due Friday, March 14. Read Sections 2.2 and 2.3.
  - Section 2.2: 2, 4, 5, 8, 11, 12, 14, 18, 22.
  - Section 2.3: 1-4.
- #7 Due Friday, March 28. Read Sections 2.3 and 2.4.
  - Section 2.3: 1-6, 9, 10.
  - Section 2.4: 1, 3, 4, 6, 8, 9, 12, 14, 24a,c, 28.
- #8 Due Friday, April 4. Read Section 2.5.
  - Section 2.5: 1, 2, 6-9, 14, 22ab, 23a.
- Hour Exam Thursday, April 10, 7-8:30 PM. Covers Sections 2.1-1.5 of the text.
- #9 Due Friday, April 18. Read Sections 2.6, 3.1, and 3.2.
  - Section 2.6: 1, 2, 4, 26a.
  - Section 3.1: 6, 8.
  - Section 3.2: 1, 2, 6, 7.
- #10 Due Tuesday, April 28. Read Sections 3.3 and 3.4.
  - Section 3.3: 4a, 5a, 7a, 11, 12, 16, 17.

Links of interest:

Resources on definitions, terminology, and concepts:
- Complex Numbers, from David E. Joyce of Clark University. This is a nice concise on-line introduction to complex numbers.
- Complex Analysis--Maple Powertools, from Maplesoft, which produces the software package Maple. This is a complete web course on complex analsys. It contains downloadable Maple worksheets on a variety of topics.
- Complex Analysis--Mathworld, from Wolfram Research, which produces the software package Mathematica. A good on-line source with short entries on a wide range of mathematical topics. This link is to the main page for complex analysis.
Complex analysis software and demos:
- Bombelli, a java complex function viewer from Prof. Sérgio Santa Cruz, Paulo Soares Fonseca Departamento de Matemática Universidade Federal de Pernambuco Brazil.
Resources on Fractals and dynamics:
- Fractals--Mathworld, from Wolfram Research. This link is to the main page for complex analysis.
- Dynamical Systems--Mathworld, from Wolfram Research. This link is to the main page for dynamical systems.
Fractals and dynamics software and demos:
- Mandelbrot and Julia Set Explorer, from David E. Joyce of Clark University. A terrific, easy to use interactive web page for exploring these sets.
- The Mandelbrot Set, from Peter Alfeld of the University of Utah. A more involved interactive page.
- The Dynamical Systems and Techonology Project, from Robert L. Devaney of Boston University. Check out the Mandelbrot Set Explorer link.
- Mandelbrot/Julia Set Browser, from Michael G. Henderson of Los Alamos National Laboratory.
Minimal Surfaces (an application of harmonic functions):
- Minimal Surfaces--Mathworld., from Wolfram Research. This link is to the page for minimal surfaces and contains a basic introduction.
- Minimal Surfaces, from Matthias Weber of the Indiana University, Bloomington. This contains a dazzling gallery of ray-traced images of minimal surfaces.
- GANG. Home page of the Geometry, Analysis, Numerics Graphics group at the University of Massachusetss, Amherst.
- Minimal Surface Library, from Martin Steffens and Christian Teitzel of GRAPE, University of Bonn.

Office: Swords 341
Phone: (508) 793-2476
Fax: (508) 793-3530
P.O. Box: 120A
email address: dbd@mathcs.holycross.edu

Prof. Damiano's Homepage
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