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Can someone give me ideas for specific examples that might motivate biology/chemistry students to learn basic calculus ( limits, derivatives and basic integrals and theorems such as Lagrange's, Rolle's ,etc... )

Thanks in advance !

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Modelling population dynamics, diffusion (e.g. Fick's law), model of Lotka-Volterra and many more. –  Your Ad Here Oct 16 '12 at 18:41
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Is there a real need to motivate basic calculus for chemistry students? I mean the whole concept of rate and equilibrium is based on calculus. –  EuYu Oct 16 '12 at 18:50
    
Thanks ! Any other examples? –  joshua Oct 16 '12 at 18:58
    
I think that anything from those fields would be an example. Are there any counterexamples (i.e., chemical or biological processes that calculus does not help us understand?) –  Trevor Wilson Oct 16 '12 at 19:27
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@TrevorWilson That's certainly the attitude we should have, although understandably there are subjects which calculus really doesn't contribute much towards. For example, it doesn't take any amount of mathematics to get a rather thorough understanding of DNA translation and transcription. (Although interestingly, knot theory does play a role if you consider for example, the action of Topoisomerase) –  EuYu Oct 16 '12 at 19:35

4 Answers 4

Even the least mathematical areas of biology, a good understanding of basic statistics is essential. Such an understanding is not really possible without some calculus background.

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For example, in Biology:

Let a medical research has shown that over short periods of time, when the valves to the aorta of a normal adult close, the pressure in the aorta is a rule (which we called it in Mathematics, a function) of time and can be modeled by the equation $$P=95e^{-0.49t}$$ wherein $t$ is time in second. Here, one can predict the aortic pressure when the valves are first close. In fact you want to find the $P$ when $t=0$. Indeed, there are many examples about what you wanted.

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Soroh: Sorry if I didn't get something, but where is the calculus in what you just mentioned? Thanks! –  joshua Oct 16 '12 at 18:59
    
I would say that the key point is that it was probably obtained by solving an ODE –  Belgi Oct 16 '12 at 19:00
    
@joshua@Belgi: Yes probably it was. In fact any level of the calculus may be used in these areas. From a simple basic function and manipulating it to higher lever as solving an ODE. –  Babak S. Oct 16 '12 at 19:04
    
@joshua - define $e$ –  Belgi Oct 16 '12 at 20:55
    
Got it...Thanks ! –  joshua Oct 17 '12 at 12:20

How about Nonlinear Mechanics of DNA!

First of all, Calculus is a forming subject, meaning it provides students not only with strong and usefull mathematical tools, but also with the bricks for the kind of abstract thinking needed to understand very complex aspects of mathematics and nature, no matter the discipline.

For me it was a very insightfull experience, like finding jesus sort to speek. There is no turning back. Here is some truth you can share with your students: if you grasp the main concepts of Calculus, Mathematics will reveal themselves to you.

All this are examples of continuum models: Reaction-Difussion Systems, Population Dynamics, Nonlinear Mechanics of DNA, Molecular Dynamics,

You can find more on Mathematical Biology in Wikipedia

The most important thing to learn is that Calculus is a gateway to harder drugs, like Probability, Stochastic Processes, Combinatorics, Topology, Geometry, Differential Equations, and so on and so on and so on.

If you want to motivate your students, tell them to type on their favorite search engine

"mathematic field" + biology/chemistry + applications

and see what comes up.

A certain thing is that more and more problems in biology will be approached from a mathematical point of view.

If chemics students need motivation, they are on the wrong field.

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Great!!! Thanks!!! –  joshua Oct 17 '12 at 12:18

Examples can be found in signal processing in the brain. The nerve cell called "Axon" usually has electric potential of -70 mV; When receiving a signal "depolarization" happens as the positive sodium molecules enter the cell and after reaching the potential of -55 mV the "sodium gate" closes and potassium gates open, which results in "Repolarization" during which the electric potential goes back to -70 mV.

for example; You change the rate of the sodium and potassium gates (the derivative of the amount of molecules to get in) ask when the cell gets to the threshold of -55 mV and when it returns to -70 mV.

For more about the Axon read here.

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Great!!! Thanks!!! –  joshua Oct 17 '12 at 12:18

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