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

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?

## Discussions

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 withcontinuousquantities (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.Im looking forward to understand the WHY's instead of the HOW's because I already know the formulas. As you suggested, i have picked up a copy of Calculus for engineers and physicists! Thanks. In the meantime, if you come across a particular book , be sure to mail me!

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

For a point mass, Newton's formula for gravity is F = Gm

_{1}m_{2}/r^{2}, where r is the distance between the two masses m_{1}and m_{2}.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

ignorethe 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 = dm

_{E}dm_{M}/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

integrateover the volumes of the Earth and Moon, adding up the mass elements and all of the 1/r^{2}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.

So very, very true! I have no objection to his question -- in fact, in my opinion it's

exactlythe right thing to ask about math -- I just wasn't sure what he really wanted to know.Understood...seems like 2/10 are illegible, 3/10 are nearly illegible but decypherable, another 4/10 are good ideas but that leave out one or more critical details, and 1/10 that's an easy mark What one of us misses the other usually catches so it's almost all good.

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!

Not only are the teachers boring, but they don't understand the concepts of calculus themselves , so it makes things even more difficult. Any book in particular that you have referred to, and liked?

The book that's REALLY good for understanding what's going in is by Sylvanus P Thompson (and Martyn Gardner)

http://www.amazon.com/Calculus-Made-Easy-Silvanus-Thompson/dp/0312185480

Mathematics for Physics, Thermodynamics, Physical Optics, Digital Control theory, and the list goes on.

Once you get beyond a cursory treatment, calc becomes <coughs> integral ;)

Thanks! I have downloaded Mathematics for Physics. Hopefully it should help me understand calculus better.

sort of. Honestly, it's "practical" only in the sense that it helps prepare you for the practical application of calculus (and other mathematics) in many areas of physical and theoretical sciences, since so many are just

derivativesof Physics anyway:-) You must be a physicist to make a comment (and awful, awful pun) like that :-D

You must have missed the first one... look up above... ty, ty. I'll be at the Holiday Inn on Main Street til Sunday.

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?