why do we need to study calculus
When I was younger (a little less than a year ago! ), the very mention of calculus made my friends and I groan. To us, the subject seemed impossibly difficult, and we were dreading having to study it in our senior year of high school. Still, even though we were so freaked out by the
idea of calculus, I doubt that any of us really had a solid understanding of what it actually was. Calculus' reputation blinded us to seeing the beauty of it or the potential benefits of its study. Rest assured, calculus is not a fancy word for the slow torture of high school students. Rather, it can be simply defined as the study of change. According to author Jennifer Oullette, there are fundamental concepts in calculus: 1) The Derivative (Differential Calculus) --- A way of measuring instantaneous change, speed of a car when all you know is its position. 2) The Integral (Integral Calculus) --- Describes the accumulation of an infinite number of tiny pieces that add up to a whole and can be used, for instance, to determine the distance a car has traveling when only the speed is known.
Sounds pretty easy, huh? Well, if you've been paying attention in algebra and geometry, calculus can be a fairly painless way of solving complex problems. Just don't let all those weird symbols paralyze you with fear! The fact that calculus is the study of change actually makes it wonderfully applicable to our everyday lives; we live in a dynamic world that always moving an d always changing.
On a large scale, we can use calculus figure out how global temperatures are changing or we can examine the expansion of space. However, we can also use calculus to do small things, like find the speed of our cars or how much interest we should have in our savings account. o further show that calculus isn't the frightening and foreign concept that many think it is, here's a short video that will give you an introduction to the subject. After you know about the basic nature of calculus, we can begin to discuss all the awesome things you can do with it! Calculus divides naturally into two parts, differential calculus and integral calculus. Differential calculus is concerned with finding the instantaneous rate at which one quantity changes with respect to another, called the derivative of the first quantity with respect to the second.
For example, determining the speed of a falling body at a particular instant of time, say that of a skydiver or bungi jumper, is equivalent to calculating the instantaneous rate of change in his or her position with respect to time. In general, evaluating the derivative of a function, f(x), involves finding another function, f (x), such that f (x) is equal to the slope of the tangent to the graph of f(x) at each x. This is accomplished, for each 2, by determining the slope of an approximating line segment in the limit that its length approaches zero.
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