MTH 4130 - Complex Analysis

3 lecture hours 0 lab hours 3 credits

Course Description
This course is an introduction to the theory of analytic functions of a complex variable. Topics covered include algebra of complex numbers, mapping by elementary functions, analytic functions, complex integrals, Cauchy's theorem, Taylor and Laurent series, and residues.
Prereq: MTH 2130, MTH 2140 (quarter system prereq: MA 235, MA 2323)
Note: None
This course meets the following Raider Core CLO Requirement: Think Critically

Course Learning Outcomes
Upon successful completion of this course, the student will be able to:

Represent complex numbers algebraically and geometrically
Analyze limits and continuity for complex functions as well as consequences of continuity
Apply the concept and consequences of analyticity and the Cauchy-Riemann equations and results on harmonic and entire functions including the fundamental theorem of algebra
Analyze sequences and series of analytic functions and types of convergence
Evaluate complex contour integrals directly and by the fundamental theorem
Apply the Cauchy integral theorem in its various versions and the Cauchy integral formulas
Represent functions as Taylor and Laurent series
Classify singularities and poles
Find residues and evaluate complex integrals using the residue theorem

Prerequisites by Topic

Differential and integral calculus
Elementary differential equations

Course Topics

Complex numbers and the complex plane
Complex functions and mappings
Analytic functions
The elementary functions
Elementary transcendental functions over the complex numbers
Integration of analytic functions
Series and residues
Conformal mappings (if time permits)

Coordinator
Dr. Chunping Xie

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