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Old 10-21-2004, 22:40   #1 (permalink)
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Maths question:

Anyone here familiar with antiderivatives? I should get a kick up the arse for asking whether I've done the following example correctly, as I have been familiar with these for years, but hardly ever use them :-/

It's for a uni assignment (Environmental Modelling: Overshoot and Collapse models for population vs resource)

Here's the derivative:

dx/dt = r.x.(x/k).(1-x/k)-e+m.k

Now, to get from dx/dt to x, do I do the following? (a bit of shuffling and substituting)

dx/dt = rx^2/k - rx^3/k^2 - e + mk (rearranging equation)

dx/dt = "a"x^2 - "b"x^3 - "c" + "d" (substituting)

x(t) = ax^3/3 - bx^4/4 -cx + dx + "k" (k = added constant due to antiderivation)

x(t) = rx^3/3k - rx^4/4k - ex + mkx + k (subsitution removed)

I is confused can anyone help?

-Dave-

PS, I will be offline for a couple of hours before rechecking, just in case anyone is wondering "well, I gave the bastard an answer and he says nothing back! Ingrate! I know what I'll do, I'll send him that new worm virus I've been working on for years now, that'll fix him, lousy rotten..." (trails off)
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Old 10-21-2004, 23:13   #2 (permalink)
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Re: Maths question:

wowzer that looks like fun, i had a quick check i got nfi wether your rearrangement is correct but the rest of it is ok, im only doing yr 12 math studies and that is hard enough, i wanna do mechanical engineering so i think im gunna have to do specialist math in yr 13 :(
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Old 10-21-2004, 23:31   #3 (permalink)
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Re: Maths question:

Don't ask me about derivitives. But shouldn't that just be standard diffrentiation to get that in the form of x?
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Old 10-21-2004, 23:41   #4 (permalink)
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Re: Maths question:

FordFan86: Mech Eng is a wonderful world of maths, and lots of it! Expect to learn shitloads on First Principles, various Calculus stuff, plus equations that take a minimum of three pages to work out... and they're just for the single line equations!!!

ford.boy: due to the LHS of the eqn being wrt x, I figured that all non-x values (r, k, e and m) could be treated as constants. To be honest I don't really care how long and complicated the equation turns out to be (ie simplification doesn't matter), I just need to antiderive (aka antidifferentiate) it so that I can graph it using Excel.

-Dave0
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Old 10-21-2004, 23:48   #5 (permalink)
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Re: Maths question:

Quote:
Originally Posted by Ghia5L
FordFan86: Mech Eng is a wonderful world of maths, and lots of it! Expect to learn shitloads on First Principles, various Calculus stuff, plus equations that take a minimum of three pages to work out... and they're just for the single line equations!!!

-Dave0
i know about first principles, and calculus but screw 3 pages for one equation i get messed up with the lines of equation :( but i love mechanical things eg cars , i suppose there is always some sort of mechanical thing i could do.

and ford.boy there is differentiation then anti differentiation, to differentiate power goes down by one and you times by the power, to antidifferentiate power goes up by one and you divide by the power. simple explanation but basically they are the opposites
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Old 10-21-2004, 23:55   #6 (permalink)
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Re: Maths question:

I think you've got it right Ghia5L, but it would be better to introduce a new constant for the last value rather than using "k" again. It's been a while since I've touched an equation like that but it's surprising how it comes back especially when you laid out all the working in steps!
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Old 10-22-2004, 00:01   #7 (permalink)
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Re: Maths question:

well the first coupla years of mech eng didn't really include cars at all for me, it was mostly on statics/dynamics. You'll do work on wonderful things like swinging pendulums, or getting shown a complex levering system where if you press on one lever with a certain rotational velocity (or it's yukky derivative, acceleration), what does the lever at the end of the system rotate at? <-- gyroscopics & stuff like that :p

The closest you'll get to cars in early mech eng I'm assuming will be pistons, where linear velocity/acceleration gets turned into rotational velocity/acceleration. Or stuff on springs (ie dampening)

Asin(wt) + Bcos(wt)
Awcos(wt) - Bwsin(wt)

I think those equations are major players in early mech eng
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AU thermofans
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Custom cupholders
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Old 10-22-2004, 00:04   #8 (permalink)
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Re: Maths question:

Quote:
Originally Posted by outback_ute
it would be better to introduce a new constant for the last value rather than using "k" again.
oops! I forgot about the original k! I used "k" as a constant on purpose because I'd used "c" in substitution already! I shoulda just written "constant".

Ta mate, you've filled me with confidence, now I'll attack this question!

/me will be offline for a *little* bit now...

-Dave-
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AU thermofans
Explorer intake manifold
Contra 16x9 rims, rubber: 225(f)/245(r)
Custom cupholders
Chiptorque HP2 chip
illegal tint

ET: 14.78 @ 91.48mph, 137rwkw!
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Old 10-22-2004, 00:27   #9 (permalink)
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Re: Maths question:

I just looked at the first post and nearly got a migrane! How can you do that?
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Old 10-22-2004, 00:31   #10 (permalink)
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Re: Maths question:

Anti-differentiation is the same as Integration, right?
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