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.
- 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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