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Post by abacus9900 on Dec 30, 2014 9:34:40 GMT 1
Why is calculus such an important tool in science and engineering?
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Post by alancalverd on Dec 31, 2014 1:43:20 GMT 1
Because there are many important phenomena where the effect is proportional to the rate of change of the cause or to the sum of causes.
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Post by abacus9900 on Dec 31, 2014 9:17:16 GMT 1
Because there are many important phenomena where the effect is proportional to the rate of change of the cause or to the sum of causes. For example?
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Post by alancalverd on Jan 3, 2015 1:05:21 GMT 1
Speed is the integral of acceleration over time. Remember F = dp/dt = d(Mv)/dt. Now in the case of a racing car, an airliner, or a rocket, the rate of change of mass (due to burning fuel) is important. We generate an accelerating force by burning fuel, and we need to reach a certain speed (cornering limit, cruising speed, orbital speed...) at a certain time, so we need to solve an integral equation to determine the optimum fuel burn rate if we are goping to hug the hairpin bend, reach New York, or rendezvous with the space station.
V = -Ldi/dt is the equation for the voltage across an inductance L when the current i is varied. This equation turns up whenever you want to generate a high voltage pulse, for instance to start a fluorescent tube or to ignite the fuel in a car engine.
Alan Turing explained how the leopard gets its spots by solving two simultaneous diffusion equations. A diffusion equation relates the second partial derivative of the effect to the cause.
I could go on, but it's late!
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Post by fascinating on Jan 3, 2015 21:09:29 GMT 1
Calculus is a technique used for situations of constant change. For example, if an object is moving at a constant speed, you can easily calculate the distance covered by multiplying the speed with the time elapsed. But suppose the object is accelerating, then it is not a simple matter to work out distance travelled, you need calculus for that. I think Newton first used calculus in studying the motions of objects in the solar system. I believe calculus must be used in most space missions, where you need to precisely determine the path of your spaceship that it must follow to meet the celestial object of interest.
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Post by abacus9900 on Jan 4, 2015 9:20:19 GMT 1
So calculus is to do with rates of change. Thank you both for replying.
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