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Which book can teach me the practical significance of calculus? Answered

Hi. I've learnt calculus in my high school in a very perfunctory manner, not having really understood the concepts behind why we actually do a particular calculus operation. It has always been reading the question, putting in the formulas and grinding out an answer. The books also were'nt very helpful in making me understand calculus. Is there any book which teaches this branch of mathematics from the application point of view?

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I'm not completely sure which question you're asking.

What is the practical significance of calculus? Or, "what is calculus good for?" All of physics, most of chemistry, and a lot of biology, economics, engineering, finance (compound interest, for example) require calculus to understand and apply them. Calculus allows you to deal with continuous quantities (like a weirdly shaped blob of material, or flowing water, or time), in the same way that algebra lets you deal with discrete quantities.

Is there a book which will help me to understand calculus? A few of the posts below give you good examples. I don't have a concrete suggestion (it's been too long for me), but I would definitely recommend something along the lines of "calculus for engineers" rather than a math department textbook.

Okay. Here's one simple example of "why" calculus is useful.

For a point mass, Newton's formula for gravity is F = Gm1m2/r2, where r is the distance between the two masses m1 and m2.

Now, what if your masses are actually big extended blobs, like the Earth and Moon? Each little piece of Earth and little piece of Moon have a gravitational force between them (I'm going to ignore the self-gravitation of each body!), and those pieces are all at significantly different distances. But what is the "net" force between the two big bodies? It is constant, or is it changing as, e.g., the Earth rotates and different little pieces get closer to or farther from the Moon?

The way to solve that problem is with calculus. You write down Newton's gravity for the bit of force between two little pieces: dF = dmEdmM/r(E,M)2. Here I'm taking r to be the distance between the two particular little pieces, as a function of the coordinates of those pieces.

To get the total force, you integrate over the volumes of the Earth and Moon, adding up the mass elements and all of the 1/r2 terms to get the total force. Obviously you have to rewrite the dm's in terms of coordinate elements (density times volume element), so you can actually do the integration.

That's one example, just off the top of my head.

that's a good suggestion Kelsey. I don't personally know of a book with that title (closed I could come is the one I suggested) but the idea is exactly (I think) what he's looking for... practical application of the math. A reason "WHY" he's doing it in the first place...math teachers (and my dad IS one, albeit retired) can be awfully dry on the WhyTheHellAmIDoingThisAnyway question "Why?" ...."because Math is beautiful!"...."erm...um...uh....dad...?" Even if he was right.

Yes, there are many books that do just that. As much as I hate to say it, those books are as easily available as mp3's from your favourite bittorrent client. Look for Practical Calculus. There's even a Dummies book on Calculus. It's so ridiculously prevalent I can only think you must have had a poor and lack-lustre teacher. Here's to learning!

Books are like people; no two are the same and will appeal to different people. So as much as I'd love to suggest some books, I'd say have a look at your library/bookstore/bitttorrent depending on your ethics. I get a strong feeling you'd be a very good teacher; have you thought of it?