I started to learn differential equation after learning calculus,self study.After few days,I couldn't get beyond the concept.
I know differential equation have some part in algorithms to construct fluid simulation and other area of computer graphics but that I believe have something to do with simulation stuff ....
But in practice,do you encounter any instance where you need to understand differential equation for use in building games.
Right now,I can't think of anything hence my low motivation right now in learning differential equation.
Differential equations are exceptionally useful in real world simulations.
They're usually encountered at undergraduate level, and are used extensively afterwards, which should give you some indication of their complexity. You could fill (and indeed there are) many tomes on differential equations. It is not surprising you are having difficulty if you are trying to learn them through self study, although don't let me put you off.
I can't say how much they're used in games design, although I did hear that the games design industry is short on maths graduates (good news for me, should I ever choose to pursue a career in that area), perhaps this is one of the reasons. But I'm just guessing at that.
Whilst differential equations are indeed important in all sorts of different maths-related areas, for most purposes (particularly in games), you can usually just use an already existing formula to derive the result where a derivation is needed.
Of course, games programming covers MANY different areas. You can't be expected to be an expert in ALL those areas.
Thanks for your answers :D
I fail my maths in high school :( but now self-studying mathematics after I realize I couldn't get very far in programming especially computer graphics stuff which I'm very passionate...
Btw,This message board is awesome,the replies came not even 1 hour mark after I post my original question.Hell yeah,maybe cboard banner should have the same slogan as pizza deliveries XD
Well I don't want to put you off, but if you failed maths at high school then you're going to struggle.
There is some good news though. DE's are a massive area of maths, it's equivalent to learning "programming", in fact even more so (they've been around a lot longer than computers). You can break it down into so many sub categories. My advice would be to forgo them for now, and if you find you do need them in the future, just learn what you need.
I'm not a games programmer, but I've heard that a good area of maths to study is linear algebra, especially for 3d programming.
In addition, there are also books you can buy which specifically teach you the maths needed for games design and 3d programming. I haven't read them myself, but they would be a good place to start.
I must mention that you do not absolutely have to know everything about differential equations in order to use them and make games. The biggest usage of DEs in game programming would be physics simulation, in which case you can use a physics library.
Thanks for all your replies and encouragement.
I was scouring the bookstore today and after half an hour,I found differential equation for dummies,just one of a few books on differential equation.I was hesistant in buying because of it titles,but the author of the dummies book is Steve Holzner.I remember enjoying his vtc screencasts.
Yeah,so now I'm learning...not giving up yet :D
Well, if you do this:
you are solving a differential equation numerically. :)
pos.x += vel.x * frameTime;
pos.y += vel.y * frameTime;
I didn't get a great maths grade despite having been into coding since I was 8. But I have quite a 'mathematical' mind in the sense that I can solve a fairly simple mathematical problem just by sitting down and reasoning, despite lacking the parlance and tools of traditional maths.
But now I'm finding myself more interested in the concepts I found boring at school so I'm always looking things up on the net and learning more.
Game programming is like any other field that uses applied mathematics. In that, I am simply saying that you are applying rules, and formulas for the most part. You are not usually deriving them, you are not usually reworking them, you are just taking something that is well studied and putting it to use. It is nice to be the guy in the corner of your office who can actually explain how these equations are derived when someone invariably asks though.
I often find complex math formulas and things such as DE's to flesh themselves out much clearer in the realm of computers than on paper. Essentially they are simpler with a computer as long as you understand the basic premise. Actually implementing them is quite simple as Sang-drax has illustrated.
And unless you are someone like Bob I highly doubt you will ever be deriving complex formulas for a game since most of the equations are computed by a third party library or have been derived and figured out long before you ever see the code line. Funny thing is that the hardest part about a physics engine is not really the math for computing mass moment of inertia, impulses, etc., but actually detecting the collision between the objects. So in the end collision detection, at least for me, becomes the most complex and difficult part of game programming.
These days entire books and libraries (that is, as in compiled code libraries, not the ones that contains the books) are devoted to teaching the end result of a lot of the mathematical theories that are used in modern computer science. Some stuff seems trivial enough to figure out on your own, while other stuff may not be so easily derived without doing some reading.
Collision is one of the harder things to get exactly right. Like most game developers, you can probably even see flawed collision detection bugs in almost every game you play (btw, I notice that writing your own code either adds a fun level of constructive critisism to playing games, or an evil level of picking them apart).