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Dec 13, 2025
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MTH 4130 - Complex Analysis3 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. This course meets the following Raider Core CLO requirement: Think Critically. (prereq: MTH 2130 , MTH 2140 ) (quarter system prereq: MA 235, MA 2323)
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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