# Thread: Extended essay on Mathematics

1. ## Extended essay on Mathematics

Hey all,

First post on this forum, so.. hi

Anyway, to get to the point.. I live in Ireland, and i'm doing a program called the IB. It more or less covers the last two years of American High School, i think.. One of the requirements is that we write an extended (4000 word) essay on an academic topic. I've been considering writing it on Maths, but not quite sure where to start. It has to be a fairly specific title, and as I'm hoping to study engineering in college, i was thinking of a title along the lines of "Applications of Differential Calculus in Engineering".

I was wondering whether you guys would know a good place to start on this topic. We cover diff. Calculus fairly well, although it'll probably be next year before we get to the "Applications of Diff. Calc." section. If you have any suggestions on the best place to start looking, or even a better, more specific title, then it'd be welcome..

Oh, also, apologies if this isn't the correct topic for this board, or even the forum. And while I'm in 'high school', i figured this is a slightly more university-scale question, though i could be wrong.

Thanks a lot,
_Kar.

2. Seeing as no one else is responding, I will give it a whack. I don't think many (if any) people on a maths forum know about engineering. You may have better luck asking engineers and asking specific maths questions here.

Calculus has many applications in physics that I know of. Newtons laws, Schrodinger equation etc. all involve some sort of a differential equation.

Best place to start (as with any research) is google and wikipedia. Don't ever reference wikipedia but the idea is to get a basic understanding, and to check out their references. Try to get hold of a university level engineering book of some sort and look at what they do.

Good luck.

3. (1) something theoretical, let's say pi. just descriptive will do.
(2) investigative - like modeling?
(3) discrete mathematics.

4. ## Suggestion

If you like number theory, you can try exploring multigrades.

5. Perhaps the most interesting applications of mathematics in engineering are when things go wrong.

E.g. the Space shuttle Challenger disaster happened largely because of an error in the use of statistics.

A good topic would be resonance. Resonance occurs in Civil, mechanical, electrical engineering (and others) and it is responsible for some good things (e.g. radio) and responsible for many failures of electrical equipment, bridges, dams, mechanical parts etc.

The Three Mile island or Chernoble disasters could be interesting topics?

6. DEs are obviously pervasive... which you've noticed by now. I think you'll have plenty to write about with that.

Typical engineering things are fluid dynamics(how fluid flows over an airplane wing or a car, for example, but also more unstandard things--I found an article once on a toilet maker hiring fluid dynamics people to improve flushes), electronics analysis, any kinds of chemical reactions, any kind of trajectories(bullets, spacecraft).

If you were willing to make the concession from 'Engineering' to 'Science and Engineering', you'd have even more. I've previously done research in brain simulations, all of which are differential equations. There's a great book called 'Nonlinear Dynamics and Chaos' by Strogatz that has a ton of applications of differential equations, from fireflys to love to disease outbreak to lasers.

Best of luck with it!