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Apr 19, 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 232 , MA 235 )
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 (5 classes)
- Analytic functions (7 classes)
- The elementary functions (4 classes)
- Elementary transcendental functions over the complex numbers (4 classes)
- Integration of analytic functions (6 classes)
- Infinite series expansions, residues and poles (4 classes)
- Review (2 classes)
- Exams (2 classes)
Coordinator
Chunping Xie
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