Applications of Multivariable Calculus As part of the final for my Multivariable Calculus class, I am to create a project wherein I find an application of some multivariable calculus subject (up to and including Green's Theorem), and create a presentation and model of that topic.
Because of this, I spent a while searching textbooks online for any topic that includes multivariable. However, all the texts I found were either too simple (e.g. integrating polynomials) or too difficult (e.g. Stokes' & Divergence theorems).
Are there any scientific topics that can be explored fully using primarily only the multivariable I know?
Something to do with Econ, CS, or Physics would be great, though other fields would be good as well.
 A: A main use of Stoke's Theorem is in electricity and magnetism. Perhaps you could set up an electromagnet that creates a magnetic field in order to demonstrate that the integral of the curl of a magnetic field is proportional to the flux of the current through a surface?
A: As a suggestion, I'd look up something of Maxwell equations of Electromagnetism. Multivariable Calculus is of critical importance there and you don't need very complicated tools for that. Furthermore, it's a very important application in real world.
A: Work-Energy Theorem:
$W = \int\limits_C {\mathbf{F}}  \bullet d{\mathbf{r}} =  - V$
Newtonian Gravity:
${\mathbf{g}}\left( {\mathbf{r}} \right) =  - \nabla \varphi $
$\nabla  \bullet {\mathbf{g}}\left( {\mathbf{r}} \right) =  - 4\pi G\rho $
${\mathbf{g}}\left( {\mathbf{r}} \right) =  - G\iiint\limits_V {{d^3}x\frac{{\rho \left( {\mathbf{r}} \right)\left( {{\mathbf{r}} - {\mathbf{x}}} \right)}}{{{{\left\| {{\mathbf{r}} - {\mathbf{x}}} \right\|}^3}}}}$
Euler-Lagrange Equation:
$\frac{d}{{dt}}\frac{{\partial \mathcal{L}}}{{\partial \dot x}} = \frac{{\partial \mathcal{L}}}{{\partial x}}$
Schrödinger Equation:
$i\hbar \frac{\partial }{{\partial t}}\Psi \left( {x,t} \right) = \left[ {\frac{{ - {\hbar ^2}}}{{2m}}\frac{{{\partial ^2}}}{{\partial {x^2}}} + V\left( x \right)} \right]\Psi \left( {x,t} \right)$
and so much more...
