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.
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