Recently I have been struggling with Differential Equations in the college, in part with the algebra, but more important, looking for the importance of this topics. I have read about some applications in physics but I feel them so far away in the sense that I don't know if I will ever apply that knowledge in my area(CS).
Now, I love programming and I don't hate mathematics, simply I always try to find the utility of them, otherwise all that theory seems so boring. And the point is, have you ever faced with programming problems involving derivatives, integrals, DE? If so, can you give me some examples? Please.
An example: how many permutations of N distinct numbers have this property: each number is either greater than both of its neighbours or less than both of them?
Actually, that's math problem, not a programming problem. Still, it's somehow related. =)
Some years ago i've faced such a task: given about 100 points in 3D, you should find the mass of the polyhedron built on these points if the mass of every single point if our "world" is equals to it's z coordinate.
An example of integral problem (in the ICPC world finals):
http://livearchive.onlinejudge.org/index.php?option=com_onlinejudge&Itemid=8&category=547&page=show_problem&problem=4038
Indeed, doing these kind of calculation by hand is awful.
But some "abstract" parts in calculus are much more interesting: some awesome "theorem"s, and the definition involving first-order logic(A statement in "first-order logic" correspond to a "game", so when you are finding a proof, it's same to think about how to win the game).
When I was learning calculus, I come up with this problem: PasswordXGrid. My original solutions involved some knowledge in both calculus and something we used in programming contest: conservative vector field, curl, line integral, gradient, Stokes' theorem, Max-flow min-cut Theorem, duality theory and shortest path. (click HERE for more info)
OMFG... Actually, this problem is much easier for those who don't know much than for people such as you, since if you know much, you often overcomplicate many things. I don't criticize you, I just state this fact.
Recently I solved a problem using Lagrange multipliers: http://problemsolvingnotes.wordpress.com/2012/06/10/uva-12407-speed-zones/