Functions of Complex Variables

Course Description

This course is a study of functions of complex variables and their applications to other mathematics branches, sciences, and engineering. The following topics will be examined: the complex plane, analytic functions, integration and Cauchy’s Theorem, sequences and series, residue calculus, Fourier and Laplace transforms, and applications.

Learning Outcomes

  • Easily describe domains and compute limits in the complex plane.
  • Verify analyticity of functions.
  • Use line and contour integration to evaluate integrals.
  • Calculate Taylor or Laurent series for functions.
  • Verify convergence or divergence of complex series.
  • Use residues to evaluate integrals.
  • Compute Fourier and Laplace transforms.


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Jackson M., Class of 2021, Military Veteran
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