Could someone summarize the basic premise of calculus for someone who never got past college algebra?
by 
Freedom00
ANSWERS: 4
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If I had to define it in a short sentence, I'd probably say it's the mathematics of motion and/or change.
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You have a function y = f(x) (Actually THAT'S the most basic concept here.) Differential calculus describes how to calculate the RATE OF CHANGE, called the derivative, of the function. Integral calculus describes how to calculate the AREA UNDER THE CURVE, called the integral, of the function. The fundamental theorem of calculus says that these two descriptions of the function are inverse to one another -- derivative of integral = integral of derivative = original function.
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imagine a sphere. Now paint the sphere. Each layer of paint has the same thickness (we'll assume). As you paint, the size of the sphere increases. The larger the sphere, the more paint is required to cover it. The larger the sphere, the faster the volume changes for each small increase in radius. Calculus describes stuff like this quantitatively, and uses similar techniques to use the properties of a single point to determine surrounding functions (e.g. the value of the point tells you where it is, the rate of change of the point, the rate of change of the rate of change of the point, etc).
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Math good for marking tiny little things in motion and to mark the changes in between their conditions and results.
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