OBJECTIVE

The first objective of this course will be to develop in a rigorous and self-contained manner the theory of complex variables prominent in applications. The second objective is to furnish an introduction to applications of residues and conformal mapping. To these ends the course will help students learn modeling problems that can be solved using methods of complex variables and will help them develop problem solving proficiency in complex variables. Another objective of this course is of course to show, in a non-technical way, the excitement, charm, and liveliness of complex analysis and its relation to the physical sciences and other fields of the applied world. As much as possible the software MAPLE will be used for home works as well as class demonstrations.

"A MATHEMATICIAN, like a painter or a poet, is a maker of patterns. If his patterns are more permanent than theirs, it is because they are made with ideas. ... The mathematician's patterns, like the painter's or the poet's, must be beautiful; the ideas, like the colours or the words, must fit together in a harmonious way. Beauty is the first test: there is no permanent place in the world for ugly mathematics." -- G.H. Hardy