Department of Mathematics
MATH236 - Mathematics
IIB
Unit Syllabus
Complex Analysis:
- Revision of complex numbers.
- Foundations of complex analysis, point
sets in the complex plane, limits and continuity.
- Complex differentiation, Cauchy-Riemann
equations, Laplace's equations and harmonic conjugates.
- Complex integration, contour integrals,
equivalent curves.
- Cauchy's integral theorem.
- Cauchy's integral formula.
- Taylor series, uniqueness and the maximum
principle.
- Isolated singularities and Laurent series.
- Introduction to residue theory.
Vector Analysis:
- Paths, differentiable paths, arc length.
- Vector fields, divergence, curl, basic
identities of vector analysis.
- Integrals over paths, equivalent paths,
simple curves.
- Parametrized surfaces, surface area.
- Integrals over surfaces, equivalent
parametrized surfaces, parametrization of surfaces.
- Integration theorems of Green, Stokes
and Gauss.
