In November '18, I decided to join the London Mathematical Society (LMS). Last month I attended a meeting there in Russell Square in Central London which involved a couple of lectures and a "swearing in" of new members.
As a part of the swearing in, new members have the opportunity to sign the LMS Member's Book. Interesting thing about this is it dates back to 1865(!). So after signing it, I flicked back the pages to find the signatures of both Arthur Cayley on June 19th 1865:
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:
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?)
Matrices and determinants.
Eigenvalues and eigenvectors.
Systems of linear differential equations. (solving simultaneous differential equations).
Functions of several variables. (
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).
Systems of differential equations. (Equilibrium points of two differential equations and use of the Jacobian matrix).
Partial differential equations.
Vector calculus. (Scalar fields and gradients).
Further vector calculus. (Conservative vector fields, curl, and divergence).
Multiple integrals. (Area and volume integrals).
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.
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.