The course will give a rigorous treatment of
analytic functions of one variable. Topics
include complex differentiation and integration, residues, harmonic
functions, the Riemann
Mapping Theorem, analytic continuation. Particular emphasis will be
placed
the study of special functions and their asymptotics by the contour
integral method.
A detailed exposition of Lobachevsky’s geometry is also planned. If
time permits,
we’ll briefly discuss Riemann surfaces in the end of the term.
Office: HB 444
Email: aib1-at-rice-dot-edu
Telephone: ext 3965
Complex Analysis,
L. Ahlfors, 3d ed., McGraw-Hill, and
Special Functions and Their Applications, N.N. Lebedev, Dover
Publications.