Study has been so busy this year, I've failed in keeping an up-to-date account of how it's been going. Here's a very quick run-though:

Assignment 2:

- First and second-order differential equations.
- Vector algebra and statics. (There are two blocks connected with taut string on a ramp and nothing is moving, what are the forces?)
- Dynamics. (A block is sliding down a ramp with a certain friction, what are the forces?)

Assignment 3:

- Matrices and determinants.
- Eigenvalues and eigenvectors.
- Systems of linear differential equations. (solving simultaneous differential equations).
- Functions of several variables. (

and

instead of

and

).

Assignment 4:

- Mathematical modelling. (Introduction to writing a mathematical modelling paper).
- Oscillations and energy. (Forces in a spring system, and potential energy).
- Forcing, damping an resonance. (Forces in a system of springs and dampers).
- Normal modes. (Oscillations of particles in a spring system).

Assignment 5:

- Systems of differential equations. (Equilibrium points of two differential equations and use of the Jacobian matrix).
- Fourier series.
- Partial differential equations.

Assignment 6:

- Vector calculus. (Scalar fields and gradients).
- Further vector calculus. (Conservative vector fields, curl, and divergence).
- Multiple integrals. (Area and volume integrals).

Assignment 7:

- Writing a 3000-word mathematical modelling paper.

All the above are now complete, and I'm currently working through the last few units. Namely:

- Systems of particles.
- Circular motion.
- Rotating bodies and angular momentum.

There's a requirement for me to submit one assignment per month, from October to May. These double-credit modules are hectic...

Out of all of the above, Assignment 7 had to be the most nerve-racking. Most assignments normally read like exam papers, though for Assignment 7 I had to write a report. So not only had I never written a report like this on this course before, I'd never written a report like this ever! Results are due in a couple of weeks, so based on the outcome I'll be keen to break down where I went wrong.

Favourite bits from the above have to include my first ever hand-calculation of a Fourier series in Assignment 5, and a question where I had to prove a result of Archimedes (287-212 BCE) regarding relative volumes, using modern calculus in Assignment 6. I'd also always wanted to know more about the construction of a Jacobian, so Assignment 5 was good for applying my new knowledge.