Advanced Calculus Extra Credit Suggestions

[KevinMWHM]

I have an opportunity to present an extra credit project for my advanced calc class. Basically it's calc 4 with a focus on generalizing everything calc 1-3 to R^n. I've never been presented with this kind of opportunity so I'm clueless as to possibilities. I'm not looking to stun or dazzle the professor but I am a bit behind and could use a project that bumps me up.

Any idea of a direction or what kind of projects I should be looking at?Thanks...
-Kevin

 

[RUber]

Hi Kevin,
That sounds like an interesting area for a project. If I were going to generalize methods into n-dimensional space, I would expect to be looking at partial differential equations. Maybe consider the Inverse Function Theorem and Implicit Function Theorem. These have interesting n-dimensional expansions.