What is calculus?

Friday, December 19, 2014

I am in the beginning part of the Electronics Associate Degree. I know that I will study calculus later on in the course. Just what is calculus, anyway?

A. There are two kinds of calculus: integral and differential. Basically, in differential calculus you find the slope of a curve. In integral calculus you find the area under a curve.

In electronics, differential calculus is usually concerned with finding a rate of change. For example, you might want to find out how fast the voltage in a particular signal changes. With integral calculus, we are usually concerned about accumulated values. An example of this would be the charge accumulated on a capacitor by a signal over a given period of time.

In most situations, you start with an equation. You then apply a set of rules to get a second equation out of the first. In electronics we mostly work with certain kinds of equations, so in the course we just concentrate on the rules for those kinds of equations.

Using one set of rules, we work on the original equation to get a second equation called the derivative. The derivative is an equation for the rate of change of the original equation. We use another set of rules to find the integralfor the original equation. The integral is an equation for the area under the curve that represents the original equation. In either case, in studying calculus you mainly learn these rules.

Of course, we build this up in stages as you go along. We teach you how to understand the curves that correspond to different kinds of equations. For example, there is an equation for a sine wave. There is another kind of equation that represents a square wave.

CIE teaches you how to write equations for important signals like these. Then we teach you how to use calculus to analyze circuit action involving these signals.

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