Jul 05, 2022  
2020-2021 Undergraduate Academic Catalog 
    
2020-2021 Undergraduate Academic Catalog [ARCHIVED CATALOG]

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MA 381 - Complex Variables

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, 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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