Calculus not important?

Depends upon your context.

Assuming you are talking about maths and physics in the computer games industry - well, I don't work there (yet) - but for an example of some of the things calculus underpins:

Differentiation and integration - for example, what is the volume of a sphere? Of a cylinder? Of an arbitrary object expressed as a function of (x, y, z)?
Differential equations (and all that that entails, particularly in relation to physics)
All kinds of splines (what is the definition of continuity - or, in laymans terms, how do you make sure your splines look smooth).

As an aside - having worked as a professional mathematician, I have found that plenty of people can do things when they come in standard form - for example, I did a lot of statistical analysis, and there are loads of people who can use excel, SAS, Splus (etc, etc) to do a standard t-test or whatever. The problem is - the minute you try and do something that isn't standard (assuming you know and understand the assumptions behind what you are trying to do in the first place), there's no more hand-holding - and that's when you need to have a firm basis in the fundamentals of mathematics - which definately includes calculus (amongst other things).

So - in short - yeah, I would say calculus is pretty important.

Regards,
Jim.

decode yourself. w/o calculus you can't do physics. Almost at all. (calculus was invented partially for physics)
So if you want to do something slightly more advanced than before-yesterday game with no physics, you need calculus.
And splines, of course.
And optimal actions for AI (differenciation to find extremum)
And so-on.
<sub>Wow."decide"->"decode" That was my funniest English typo of the year!

[Edited by - Dmytry on October 19, 2004 10:38:04 AM]</sub>

In terms of the 'real world', the calculus taught in school isn't directly relevant. However, the calculus taught in school lays down all of the theory you need to be able to work with real world problems, whether as a game developer or say, a mechanical engineer for example.

Here's some anecdotal evidence...

I spent 4 years at college making games, and I have put about 1 year in as a professional game developer at this point. I have never, ever used calculus for any of my programs.

Take that for what it's worth, but I also happen to believe you probably won't need much of a calculus background to make games unless you are an intermediate to high-end physics programmer. As processors become more powerful, more calculus approaches in physics (or to a lesser extent, other disciplines) may become feasible, and thus expected.

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Original post by Geronimo2000 Here's some anecdotal evidence... I spent 4 years at college making games, and I have put about 1 year in as a professional game developer at this point. I have never, ever used calculus for any of my programs. Take that for what it's worth, but I also happen to believe you probably won't need much of a calculus background to make games unless you are an intermediate to high-end physics programmer. As processors become more powerful, more calculus approaches in physics (or to a lesser extent, other disciplines) may become feasible, and thus expected.

Your programs had forces and masses? Had a bumpmap? Even needed to multiply something on per-frame basis and make it be time-driven? Maybe my translation of "calculus" is incorrect, but... every 4th thread in that forum now is somehow related to calculus.(not counting this thread)
That is, there's currently 5 threads(except this) somehow related to calculus as i understand:

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Buoyancy Problem Best type of curve -continuity,etc Random vector in cone -statistics need differenciation to produce desired distribution a pendulum problem Implementing Runge Kutta integrators in existing engine

I've done most of the things you listed, and still haven't used an Integrate() function. I assumed we were talking about having to use something like that, but I'm not sure...

I also don't claim calculus isn't used in games, just that it hasn't been in MY experience so far, and in the experiences of many people I talk to. Like I said, it was just anecdotal evidence.

1. My experience has been most game developers don't use it, if for no other reason, they aren't the physics programmer.
2. Often times, the theoretical gives way to the practical - the physics guy will often choose a less accurate technique rather than using true calculus for something.

My opinion is that currently you actually should learn a little about calculus (mainly so you math concepts won't confuse you in books), but focus more on linear algebra/vector math. In the future, I predict calculus will become more relevant in all of our disciplines, but I can't predict when.

The calculus concepts are absolutely necessary to be able to code a robust physics engine that uses numerical techniques. The calculus in school (except for the chapters on numerical techniques) almost always assumes continuity of functions, where this is not the case in a computer application where the positions, velocities, and accelerations are only known at discrete time steps.

In real world problems, even in engineering, numerical techniques are employed more than the type of problem you'd do in a calculus book, but the theory in the calculus book is important to understand what is going on with the numerical side of things.

Geronimo, my guess is that you are in the minority of game developers at this site who haven't used calculus concepts.

Well - I am originally from England, school in Devon and Warwick and Leicester Universities. And I certainly had an introduction to calculus.

Firstly - and I think this is a common point - do you know what calculus actually is? Do you know the range of topics it covers?

On one hand you're right - you won't learn formal definitions of sequence and series convergance, or what Reiman integration is, or how to solve a system of differential equations (Etc.) when you are at school - frankly you're not prepared for it. However - one of the first courses you are likely to do on any maths based degree is going to be Analysis - which lays down the fundamentals of calculus (plus it's cool to learn to write a new language - you'll be surprised how few words / symbols the phrase 'for any epsilon greater than 0 there exists an n such that for any m greater than n etc. etc.' (blimey, that brings back memories!!). Accept that fact that while at school you are learning fundamentals that will prepare you for real mathematics.

Secondarily, I certainly did do some things that would fall under the heading of calculus whilst at school. For example, Taylors and Maclaurins expansions, complex numbers, simple differentiation and integration.

So the difference between school and university is (for example) that at school you learn the chain rule for differentiation; at university you prove it from first principles.


The other point is that, to some degree your assertion is correct (as is the original posters). Calculus is not important to 99% of the worlds population. You'll never need to use it whilst out shopping for groceries. You'll never need it whilst down t' pub having a wee dram of beer.

But - if you are serious about getting into a mathematically based discipline (which includes more things than you might expect) - you're going to come up against it at some point.


On a lighter note - I didn't realise that Englands schooling system was so good that half the worlds schools were there!!!

Regards,
Jim.

I remember seeing a thread in here before about something like this. The best quotation from it said something like: "I've used calculus once in 5 years of game programming. But in that instance, the non-calculus solution would have taken signifigantly more effort and not worked as well."

Basically, you may never use it, but it's certainly a good thing to know. And you may be doing elementary calculus without realising it. Ever done a line like position = velocity * timestep? That's really simple calculus in a way, and if you ever wanted to make it more rigorous/stable, you'll use calculus. Also, rotations in games are often done using quaternions, and angular velocity is added to a quaternion with a differential equation ( http://www.gamasutra.com/features/19980703/quaternions_01.htm ).

Basically, it's not useful for alot of people, but more knowlege can't be a bad thing and it can be very powerful.

thanks guys. I'm glad to know i will have a use for calculus since i am also interested in physics.

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Here in England, we dont study calculus at all. How can it be important if half the worlds schools choose not to teach it?

England isn't half of the world, and Calculus is taught in England

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Firstly - and I think this is a common point - do you know what calculus actually is? Do you know the range of topics it covers?

The easiest definition for calculus: an abstract form of algebra that deals with infinity...quantities either get infinitely small or infinitely large...that's *all calculus really is*...then of course it branches out into lots of concepts and techniques, but at its heart that's all it is

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You don't need to know calculus. The world will not end if you don't know calculus. You are not doomed to be homeless and surviving only by the charity of others because you failed to learn calculus. You are not going to die at an early age because you failed to learn calculus. If you found yourself stranded on a deserted island you would be far more likely to kick yourself because you never learned to start a fire without matchs than because you didn't learn calculus. Rather all that is going to happen is that there will be some things you simply can't understand.

Actually that's exactly what would happen if you are an aspiring physics coder


It bothers me that people can make broad generalizations on whether or not calculus is important...it depends on what you are doing. Plus, I have a friend in mechanical engineering who is struggling, and he keeps asking why calculus is required if a lot of it isn't used. My answer is: I don't want an engineer who can't do easy book calculus where all of the problems are setup nice and neat for you, working on hard realworld problems such as ship or bridge building or construction management where people's lives are at stake based on what you build.

Are you people forgetting that calculus is just plain cool?

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Original post by UbErBeAsT Hello all. I have a friend that told me calculus is not important. Is this true? What do you think about calculus? thanks for your time.

I have an undergrad degree in mathematics; the first math class I took in college was calculus II. Every single math class has been directly applicable to writing a video game.

Um, that would be a bit of a stretch to say someone that wanted to be a "physics coder" is going to end up homeless because they never learned calculus. Many that thought they would like to do this or that have successful careers doing something else.

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Original post by Anonymous Poster Here in England, we dont study calculus at all. How can it be important if half the worlds schools choose not to teach it?

Calculus is in the A-Level Mathematics syllabus. You are wrong.

It depends what you think calculus is.
x+=v*dt is a specific forumula derived from calculus. To me then it IS calculus. v^2 = u^2 + 2as also, in fact all the GCSE physics equations of motion which you derive in A-level maths. Kinda cool I think, calculus is where you really start creating equations rather than plugging values into equations you're given.

I haven't read all posts but I just wanted to add from what i saw...

The Calculus is more than just being able to get an equation for something you need. it's like a foundation math. Even if you don't directly get functions you need from it, it gives you a whole new way of looking at things and working with things. the help it brings is more than just calculating something.