# Differential equations in computer science

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Kartoffl    10

I haven't searched thoroughly, so I apologize if I missed an existing thread...

Can anyone give me an example of a differential equation used in computer science with a brief explanation? I'm working on a project that needs a specific example, but I don't know any yet, and a Google search failed to yield anything I could understand (I'm working with somewhat patchy first-year knowledge).

Any help is appreciated. Thanks!

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timo    539

Not sure if I really understand what you say/want. Are you looking for an example where diff.eqs. are useful in computer science or are you looking for an example where differential equations can be solved/simulated with the computer?

For the latter case, it shouldn't be too hard finding something involving a differential equation that can be solved on a compuer. Simplemost case probably is movement in a jump&run game where, as soon as you're in the air and not on the floor, the movement would -in first approximation- follow $\frac{ d^2 P }{dt^2} = \vec g$ with P being position and g being the gravitational field. The computer implementation is pretty simple: Each frame you alter the position according to the current velocity (P += v*dt) and the velocity by the gravitational field (v += g*dt).

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I'm also looking on how can I find a way to apply Differential equation to Computer Science field...

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bascule    731
Can anyone give me an example of a differential equation used in computer science with a brief explanation? I'm working on a project that needs a specific example, but I don't know any yet, and a Google search failed to yield anything I could understand (I'm working with somewhat patchy first-year knowledge).

Any help is appreciated. Thanks!

Calculus and differential equations are used extensively in signal processing and perceptual media which are heavily based on Fourier transforms.

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mooeypoo    1603

When modeling physical movement (lagrangians and hamiltonians are equations of motion, and are also differential equations) you use diff equations quite a lot. From movement of planets around stars to movement of various objects in various conditions.

Actually, I'm going to soon open a "help me!" thread about those, soon, probably, to figure out how to solve and model these in Mathematica.

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bascule    731
When modeling physical movement (lagrangians and hamiltonians are equations of motion, and are also differential equations) you use diff equations quite a lot. From movement of planets around stars to movement of various objects in various conditions.

Actually, I'm going to soon open a "help me!" thread about those, soon, probably, to figure out how to solve and model these in Mathematica.

Yes the climate models I worked with certainly used calculus up the wazoo, as I expect any physical modeling program would