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Nov 21, 2024
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MA 381 - Complex Variables3 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, power series, Laurent series, residues, and poles. (prereq: MA 235 , and MA 232 or MA 2323 )
Course Learning Outcomes
Upon successful completion of this course, the student will be able to:
- Determine if a complex-valued function is analytic
- Apply the Cauchy-Riemann equations, Cauchy’s theorem, Cauchy’s integral formula, Cauchy’s inequality, Liouville’s theorem, and the maximum modulus principle to complex valued functions
- Apply Taylor’s theorem, Laurent’s theorem, and residue theorem
Prerequisites by Topic
- Differential and integral calculus
- Elementary differential equations
Course Topics
- Complex numbers and the complex plane
- Analytic functions
- The elementary functions
- Elementary transcendental functions over the complex numbers
- Integration of analytic functions
- Infinite series expansions, residues, and poles
Coordinator
Edward Griggs
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