The East Tennessee State University Department of Mathematics will offer a graduate level class in Complex Analysis (MATH 5510) Fall 2003. The class will be held in Brooks Gym, Room 306A at 10:25-11:20 Monday, Wednesday and Friday. The class will be a standard introduction to classical complex analysis, followed by applications to conformal mapping with a special emphasis on ideal-fluid aerodynamics. The class will use as a text "Functions of One Complex Variable," Second Edition, by John Conway, Graduate Texts in Mathematics, Volume 11, copyright 1978 by Springer-Verlag (ISBN 0-387-90328). The prerequisite for the class is an introductory real analysis class (such as ETSU's Analysis 1, MATH 4217/5217). Students will be evaluated based on their performance on homework assignments, a midterm, and a final. The tentative outline of the class is:
The Complex Number System
absolute value (modulus), conjugate, inequalities, argument, de Moivres
formula, roots, lines, half-planes, extended plane, Riemann sphere,
stereographic projection.
Elementary Properties and Examples of Analytic Functions
convergence and absolute convergence of series, radius of convergence and
its determination for a given series, derivative, analytic function, cos z, sin z, branch of the logarithm, Cauchy-Riemann equations, necessary
and sufficient conditions for a function to be analytic, harmonic
conjugates, path, smooth path, conformal map, Mobius transformations
and properties, cross ratio, symmetric points, orientations of a circle.
Complex Integration
variation, bounded variation, Riemann-Stieltjes integral, line integrals,
analogue of Fundamental Theorem of Calculus.
Conformal Mapping and Ideal-Fluid Aerodynamics
preservation of angles, harmonic conjugates, transformations of harmonic functions and boundary conditions, two-dimensional fluid flow, airfoils (Joukowski, Karman-Trefftz), angle of attack, lift.
For more information, contact Dr. Robert Gardner at (423)439-6977, gardnerr@etsu.edu, or see the class website at http://www.etsu.edu/math/gardner/5510/5510sil.htm.
Return to Robert Gardner's webpage .