On successful completion of this module, students will be able to:
Use basic theorems on complex sequences and series, with a particular
emphasis on power series. Calculate coefficients and radii of convergence
of power series using these theorems.
Demonstrate a familiarity with the basic properties of analytic
functions. Apply these theorems to simple examples.
State correctly the theorems of Cauchy and Morera.
Calculate, using Cauchy's theorem and its corollaries, the
values of contour integrals.
Prove and apply properties of important examples of analytic
functions, including rational functions, the exponentential and
logarithmic functions, trigonometric and hyperbolic functions.
Aims to introduce complex variable theory and reach the residue theorem, applications of that to integral evaluation.
This module will be examined in a 2-hour examination in Trinity term. Continuous assessment will contribute 15% to the final grade for the module at the annual examination session, with the examination counting for the remaining 85%.