This is a list of all courses offered by the Math Department.  Not all courses are offered each year.  What is provided is a general description of the courses and the prerequisites.  The actual content may vary.

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Description

This course is an introduction to complex variables, accessible to juniors and seniors in engineering, physics and mathematics. It covers:  algebra of complex numbers, analytic functions, Cauchy Integral Formula, Taylor and Laurent series, theory of residues (and  application to the evaluation of real integrals), conformal mapping and applications to physical problems.

Prerequisites

1 course with a minimum grade of C- from (MATH241, MATH340).


Level of Rigor

Standard


Sample Textbooks

Complex Variables and Applications, by Churchill/Brown.

Fund. of Complex Analysis for Math. Science & Engineering, by Saff and Snider


Applications

Engineering, physics, astronomy, mathematics


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Additional Notes

Students interested in grad school in MATH should strongly consider this course

Recommended as a foundational course for all math majors.


Topics

Algebra of complex numbers 

Elementary functions of a complex variable (exponential, logarithmic and trigonometric functions)

Analytic functions, Cauchy-Riemann equations

Harmonic functions and harmonic conjugates

Contour Integrals

Cauchy-Goursat theorem

Cauchy integral formulas and application (Liouville's theorem, Fundamental theorem of algebra)

Power series and Taylor series

Laurent series

Residues and applications (evaluation of real integrals)

Mapping properties of some elementary functions

Conformal mappings

Application to the steady state heat flow and electrostatic potential