Does anyone know websites or resources which explains how Diff Eq is used in Computer Science? I know it's used in a variety of areas in CS, but I really like to see or read well-explained tutorials or articles. e.g. what's finding area got to do with the topics in CS? what does 'area' correspond to?
It's essential in computer graphics or in computational geometry and in simulation science, where I can speak from experience - these are more intersectional topics than pure CS I think but I'd say it's applied CS.
E.g. in finding faster ways to do Ray/surface intersections (if we're talking about actually industrially useful geometry like all kinds of splines and not just triangle meshes), differential geometry is essential - even with triangle meshes you can apply it in normal and curvature estimation. Differential equations and integrating them enter the picture if you want to find the shortest way from one surface point to another along the arbitrarily shaped surface.
With simulations differential equations are everywhere because any physical system as a function of space (and time) is a collection of differential equations that you need to solve.
Earth-movers distance and the Wasserstein metric have recently got attention again, its original relevance was in the Monge-Ampere problem, how to distribute a continuous distribution of 'heaps' of some kind into a distribution of 'sinks' with the least amount of total distance moved. Which is a nonlinear partial differential equation to solve in two dimensions.
We need to apply numerical methods, nonlinear optimization to solve such problems and CS is a part of doing that quickly. Because there are no general closed form solutions for most of the systems of differential equations or there we need algorithms to solve them approximately.
Not really Computer Science per se, but practically every engineering field uses numerical solvers. No one reallistically solves nontrivial differential equations by hand these days.
I took DiffEQs (the only 5-credit course offered, which I thought rather odd), of course, on my way to my CP degree at FIT in central Florida, and the one thing I remember was that they turn out to be very useful in biological simulations.
As I remember, population ebb-and-flow based upon available resources is something it was especially good at estimating and tracking over time, so I would imagine that any of the Sims-type games they would be quite useful.
It turns out they are damn good at estimating, over time, many things, so a little bit of research and the right game and it's not hard to see how the two could work well together.
Any type of graph you have, you can use it, just like integrals, to calculate areas etc.
For a lot of things in life we plot graphs. Your software might do it transparently to you, but how it works internally is using mathematical concepts. It is good to know it and I really enjoyed learning it at college, as it opens your mind about how things work. But I don't believe it is a must to know.
