# 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?

active| newest | oldestWhat 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.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.

exactlythe right thing to ask about math -- I just wasn't sure what he really wanted to know.http://www.amazon.com/Calculus-Made-Easy-Silvanus-Thompson/dp/0312185480

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

derivativesof Physics anyway