What is calculus?
Stated as simply as possible, calculus is a type of math used to solve problems that can’t be done if you are limited to using the older forms of math (like algebra, geometry and trigonometry) due to continuously changing factors, such as degree of curvature or rate of speed.
It does so by breaking the problem into tiny sections and then “zooming in” until all the itsy-bitsy parts are so infinitesimally small that each is, for all practical purposes, unchanging.
(To see this concept demonstrated, watch how the curved lavender line appears to straighten out as you “zoom in” when you watch the animation at the URL below.)
Calculus then applies regular math rules to solve each individual part, finishing the problem off by adding up all the little sections (if and when appropriate) to solve the overall problem.
The catch is that you can never break the problem into small enough fragments to be 100% accurate. Calculus handles this dilemma by zooming in infinitely. And since anything changing from one infinitesimal moment to the next is changing infinitely…everything you do in calculus involves infinity in some way.
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Of course, you could drive to a given destination, and then divide the distance covered by the amount of time it took to get there. But if you did that, you would only end up with the vehicle’s average speed. Here is the formula you would be using:
If we were to graph (in yards) the distance covered after 10 seconds, we might get something like this…
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TWO BRANCHES OF CALCULUS
Calculus is divided into two closely related disciplines:
Integral calculus is concerned with calculating the area or volume of figures with curves that change at constantly varying degrees, such as ellipses, parabolas or domes.
Differential calculus is concerned with calculating a moving object’s varying rate of speed at a specific point along its path, based on the time it was there.
DIFFERENTIAL CALCULUS
In simplest terms, differential calculus is used to find the velocity of an object with changing position, or to put it more precisely: to calculate a moving objects varying rate of speed at a specific point along its path, based on the time it was there. It can also be used to find the total distance traveled by an object with changing velocity.
To better understand what differential calculus is all about, let’s look at how is actually applied in a real-life situation…
Let’s say that you have designed a new solar vehicle and you wish to test its performance, or more specifically, to determine its rate of acceleration.
Average speed =
total distance
time elapsed
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