# Partial Differential Equations and ODEs in Game Development

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I have read that ODEs are used in game development, particularly in physics engines and programming (I'd like a little elaboration on how), but what I'd really like to know is if PDEs are used in game dev. Has anyone used them, or have they studied them and see that they are or aren't that useful or are or aren't indirectly useful? Thanks.

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I have read that ODEs are used in game development, particularly in physics engines and programming

I've used Newton's 2nd and 3rd Laws of Motion a lot, as well as derived equations - i.e., F = ma. I also use torque in several apps - i.e., torque = dL/dt (L = angular momentum). Both used primarily in simulation of motion for objects - reaction to collisions, calculating position/velocity/rotation, etc.

e.g.,

F = m * a

xt = x0 + v * t

I use partial diff. eq. in shaders to find normals - i.e., float3 normal = normalize(cross(ddx(input.worldPos), ddy(input.worldPos))); Very useful HLSL intrinsic functions.

have they studied them ... ?

Oh, yeah.   Successful completion of several courses in both [EDIT: oridinary??] ordinary and partial diff-e-q were required for my college degree.

Are ordinary and partial diff-e-q useful? Yes.

EDIT: Occasionally it's convenient to remember, in addition to other similar trig relationships, that cosine(angle) = d(sine) / d(angle) when rate-of-change (slope) is needed.

Edited by Buckeye

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