I’ve always been a fan of calculus. It is impressive how this field of math has been used in everything from electromagnetism to economics. So my natural instinct to calculus has always been that it is a very useful field of math to learn and remember. Over the years, I’ve heard a constant stream of complaints from parents and students on how calculus is difficult to grasp. In fact, some students are even put off by math and engineering because they find calculus so difficult.
Flipping through a few pages on calculus, I could see pages and pages of equations. There was little emphasis on applications. In fact, even in book titled “Applications of Calculus”, the applications were abstract. My gut feel is that this emphasis on abstract concepts in calculus is the culprit behind why the topic is so difficult.
The type of applications I’m most used to – optimization, finding the minima / maxima, area under the curve, solving the Poisson’s equation – might be too complex to explain to a high schooler. So I started looking around for some solid examples on this topic. A few in economics were interesting – like trying to find the optimum number of widgets to produce given a cost curve. But this example is contrived. The cost curve is not known in advance but we have to come up with it based on various fixed and variable cost elements. The example that I felt hit close to home is this:
A ball is let go from a building 1000 ft above ground. How fast will the ball hit the ground?
There are multiple ways to solve this – we don’t even need calculus for this in one of the methods. Though our life is made easier if we know the concepts. I decided to choose a method that can be easily explained to different age groups, from elementary school to adults. That will be the topic of a future post
What other examples do you think bring out the beauty of calculus?