Complex Analysis (M3.2)

LECTURER:  J Larena

Description

Building on the first year introduction to complex numbers, this course provides a rigorous introduction to the theory of functions of a complex variable. It introduces and examines complex-valued functions of a complex variable, such as notions of elementary functions, their limits, derivatives and integrals.

Topics

Revision of complex numbers, Cauchy-Riemann equations, analytic and harmonic functions, elementary functions and their properties, branches of logarithmic functions, complex differentiation, integration in the complex plane, Cauchy's Theorem and integral formula, Taylor and Laurent series, Residue theory and applications. Fourier Integrals.

Tutorials

ONE tutorial per week.

Tests/Exams

TWO class tests and ONE final examination.