# Teaching

#### MATH705 Introduction to Vortex Dynamics

This is a 4th-year Masters degree level course of my design. I will be lecturer for this course in the second semester 2018-2020.

This is an advanced course which will provide an introduction to the mathematics associated with vorticity. Vortices are ubiquitous throughout nature and many fluid dynamical processes arising in physics and engineering make use of different vortex models to facilitate the modelling, and to encapsulate the key features, of their associated flow fields. Three important types of vortex which will be explored in this course are the point vortex, the vortex patch and the hollow vortex.

At the end of the course, students will have an understanding of the introductory concepts in vortex dynamics and will be equipped with the mathematical tools to solve problems involving three types of vortex in different domains.

A basic knowledge of fluid dynamics and complex variable theory is desirable but not essential.

• Euler and vorticity equations
• Biot-Savart law
• Kelvin's circulation theorem
• Helmholtz laws
• Point vortex dynamics
• Equilibria and stability
• Kirchhoff-Routh theory
• Point vortex motion on a sphere
• Distributed vorticity
• Vortex patches
• Hollow vortices.

#### MATH236 Mathematical Methods IIB

I was lecturer for the 'vector calculus' part of this course in semester two 2017.

This course is for second-year mathematics and engineering undergraduates at Macquarie. The course consists of two parts: complex analysis and vector calculus.

The following is an outline of the course:

• complex numbers
• complex functions and analyticity
• Cauchy's Theorem
• singularities
• complex integration
• vector fields
• path integrals
• surface integrals
• integral theorems of vector calculus.

I was lecturer for this course in semester two 2016.

This course is for second-year mathematics and engineering undergraduates at QUT. The course builds on a typical first-year single variable calculus course by extending calculus to several variables, using ‘div grad and curl’ to study vector fields, and applying the key integral theorems of vector calculus. The topics covered lay the foundations for many advanced undergraduate courses at the third and fourth year level (such as asymptotic analysis, partial differential equations, stochastic processes, fluid dynamics, mathematical biology, etc).

The following is an outline of the course:

• partial differentiation
• multiple integrals
• vector fields