Complex Variables
General
Prefix
MATH
Course Number
423
Course Level
Undergraduate
Department/Unit(s)
College/School
College of Science and Engineering
Description
The complex field, the theory of analytic functions, power series. Fundamental theorem of algebra.
Prerequisites
Credits
Min
3
Max
3
Repeatable
No
Goals and Diversity
MN Goal Course
No
Cultural Diversity
No
Learning Outcomes
Outcome
Perform basic algebraic operations using various representations of the complex number system.
Outcome
Prove simple facts about the topology of the complex number system and functions of a single complex variable.
Outcome
Compare and contrast functions of a real variable and functions of a complex variable.
Outcome
Identify and differentiate analytic functions.
Outcome
Find harmonic functions that solve classical applied problems in mathematics.
Outcome
Define complex generalizations of the definite integral of a function of a real variable.
Outcome
Compute contour integrals.
Outcome
State the Cauchy Integral Formula and Liouville's Theorem.
Outcome
Compute the Taylor and Laurent expansions of simple functions, determining the nature of the singularities, regions of convergence, and calculating residues
Outcome
Use the Cauchy Residue Theorem to evaluate integrals.
Dependencies
Courses
MATH423
is a
prerequisite
for:
Programs
MATH423
is a
completion requirement
for: