Where does one start with differential equations?

[superduckdude]

Hi,

So, I'm a programmer with a deep interest in simulations and mechanics and I'm currently trying to delve into a bit of fluid simulation.
To set the scene, I'm completely new to this field and my searches so far have yielded such things as 'Stokes-Navier equations' which no doubt sound familiar to some of you, but flew straight over my head.
Reading a bit and realising I had no idea what PDEs, or even DEs for that matter, were, I backtracked to the point where I got to MIT OCW Lec1 - Differential Equations.
However, I'm still dumbstruck as to what differential equations are, what they do, and how to solve them.

I'd appreciate any advice on where I could start learning about these things to get a solid understanding.

Cheers,

Hamzah

(also, if you're worried about me being 'new to the scene', don't worry, I've had plenty of experience in basic Newtonian mechanics (ballistics, celestial sims etc.) so this shouldn't be a problem)

 

[jedishrfu]

Welcome to PF!

Since you're into simulations checkout the Open Source Physics site. They have a collection Java code that does sims with many examples.

A differential equation describes the rates of change of one or more variables with respect to other variables and their rates of change.

You can read a summary about on Wikipedia.

http://en.m.wikipedia.org/wiki/Differential_equation

The open source physics examples basically integrate some differential equation that describes the simulation rates of change and displays the results numerically or graphically or visually.

 

[superduckdude]

Ah, I've had a look through this stuff and it looks like I'll be having to learn Calculus 1,2,3 + a bunch of other stuff in order to have the world of physics at my fingertips.
Do you know of any place (on here) were I can post about specific mechanics I wish to learn (fluid simulation in particular)?
At the moment I'm trying to come up with something like this and I could do with guiding hand from people versed in the art.

 

[SteamKing]

Ah, I've had a look through this stuff and it looks like I'll be having to learn Calculus 1,2,3 + a bunch of other stuff in order to have the world of physics at my fingertips.
Do you know of any place (on here) were I can post about specific mechanics I wish to learn (fluid simulation in particular)?
At the moment I'm trying to come up with something like this and I could do with guiding hand from people versed in the art.

If you are hoping to do fluid simulations and the like (remember the Navier-Stokes equations?), learning Calc 1, 2, 3 will be the least of your worries, insofar as mathematical preparation is concerned.

Solving ordinary differential equations numerically is relatively basic and well understood. Solving PDEs numerically represents another level of difficulty, especially when these equations are used to describe 2-D and 3-D flows. The numerical techniques used to solve PDEs bear little resemblance to those techniques used to solve ODEs. Often, one can find an analytical solution to an ODE which can be used to check a numerical solution; for most PDEs, analytical solutions often do not exist or are otherwise unknown.

Is there a Royal Road to the knowledge you seek, one which will not present too much difficulty? None that I know of.

 

[SteamKing]

If I haven't scared you straight, you can look at this thread in this forum:

https://www.physicsforums.com/threads/intro-to-differential-equations.6148/

It should give you a look at the basics of what a differential equation is.

 

[davidbenari]

Also, try Khan academy. It's good as an introduction, at least for me, that I'm taking DiffEq right now this semester.