Math 4512 - Complex Analysis
This is an introductory course
in Complex Analysis at an
undergraduate level. Complex Analysis, in a nutshell, is the theory of
differentiation and integration of functions with complex-valued
arguments z = x +i y, where i = (-1)1/2.
While the course will try to include rigorous proofs for many - but not
all - of the material covered, emphasize will be placed on applications
and examples. Complex Analysis is a topic that is extremely useful in
many applied topics such as numerical analysis, electrical engineering,
physics, chaos theory, and much more, and you will see some of these
applications throughout the course. In addition, complex analysis is a
subject that is, in a sense, very complete. The concept of complex
differentiation is much more restrictive than that of real
differentiation and as a result the corresponding theory of complex
differentiable functions is a particularly nice one - as you will
hopefully agree at the end of the course.
Catalog Description: Analytic functions, elementary functions and mappings, integrals, Cauchy's integral theorem and formula, power series, residues and poles. Prerequisite: MATH 2511/2411. 3 credits.
General Information
Resources
- Wolfram Mathworld
- DyKnow Collaboration software
- Flatland - the movie (need Blackboard account)
- Flatland - the book
- Lecture Notes for Complex Analysis
-
zMap
applet (add the site "http://mathcs.org"
to the
"site list" of the security settings for Java - search
computer for "Java" to find the Java config panel)
Exams
Lectures
- 23: Residue Theorem (pdf)
- 22: More Laurent series (pdf)
- 21: Laurent series (pdf)
- 20: Power and Taylor series (pdf)
-
Flatland - the movie (need
Blackboard
account)
Flatland - the book - 19: Max Mod Principle (pdf)
- 18: Appl. of Cauchy Int Formula (pdf)
- 17: (General) Cauchy Int. Formula (pdf)
- 16: Cauchy's Theorem (pdf)
- 15: Fund Thm of Complex Contour Int (pdf)
- 14: Review and Integration (pdf)
- 13:
Integration (pdf)
Lecture Notes in Complex: Chap. 4.1-4.3 - 12: Exp, Log, Sin, and Cos (pdf)
- 11: Review; harm conjugate (pdf)
- 10: Analytic functions (pdf)
- 09: CR Equations (pdf)
- 08: Limits and C-differentiability (pdf)
- 06: Mappings (pdf)
- 05: Complex functions (pdf)
- 04: Roots (pdf)
- 03: arg, De Moivre, etc (pdf)
- 02: Algebra, Euler's Theorem & Formula (pdf)
- 01: Complex numbers and basic Algebra (pdf)
Assignments
- 22: Taylor & Laurent series (pdf)
- 20: Power and Taylor series (pdf)
-
Flatland - the movie (need
Blackboard
account)
Flatland - the book - 18: Appl. of Cauchy Int Formula (pdf)
- 17: (General) Cauchy Int. Formula (pdf)
- 16: Cauchy's Theorem & Formula (pdf)
- 14: Practice Exam 1
- 13: Integration (pdf)
Lecture Notes in Complex: Chap. 4:
#1, 2, 3, 4, 6 - 12: Exp, Log, Sin, and Cos (pdf)
- 11: Review; harm conjugate (pdf)
- 10: Analytic functions (pdf)
- 09: CR Equations (pdf)
- 08: Limits and C-differentiability (pdf)
- 06: zMap questions 1, 2 (hint: f'(z) = 0), 3, 4, 5, and 9
- 05: Complex functions (pdf)
- 04: Roots (pdf)
- 03: arg, De Moivre, etc (pdf)
- 02: Algebra, Euler's stuff (pdf)
- 01: Intro (pdf)