Hi, I've finished "Teach Yourself Calculus" (in only 11 months!) and I feel like I've got a good foundation (Equivalent to Calculus 2, I think) for what's next. So...what's next? I'd like to get to Stochastic Calculus for Finance and Game Theory. I'm tempted to get a book on differential equations and/or partial derivatives. I think I'm lacking a big picture outlook of what's out there, how it's related, and where to go next. Thank you in advance for any advice.

Partial derivatives are fun because they allow you to do lots of funky stuff like fluid dynamics and work with planes/surfaces. It basically involves holding one (or more) variable constant whilst differentiating the other one. so :pdif:/:pdif:x (xy) = y. This is useful for surfaces (e.g. z = sin(xy)) because you can find normals/tangents etc. Also, if you're interested in this then you might want to look at something like double/triple integrals which can be used to find volumes under surfaces (which aren't really all that hard really).

 

Other than that, if you're interested in statistical work, a lot of calculus is used for pdf's and suchforth. There's a wide variety of calculus applications in mechanics. If you're masochistic you can look at something like general relativity which has some big maths in it.

 

In general, calculus can be applied in a wide range of fields, so you're better to find something you're interested in or you like the look of and see if you can get a book on it.