Problems for
Intermediate Methods in Theoretical Physics

Edward F. Redish

Analytic Functions

(a) Explain what is meant by a function of two variables x and y being analytic and discuss why we might want to work with such functions.

(b) Consider the following three functions of the two variables x and y and determine which of them are analytic when considered as functions of z = x + iy.

Demonstrate your conclusions in two ways: by using the Cauchy-Riemann equations and by rewriting them as a function of z and z*.

(c) Are these three functions all analytic everywhere in the x-y plane? If not, specify where they are and where they are not.


RETURNS

University of MarylandPhysics DepartmentPhysics 374 Home


This page prepared by

Edward F. Redish
Department of Physics
University of Maryland
College Park, MD 20742
Phone: (301) 405-6120
Email: redish@umd.edu

Last revision 7. December, 2005.