Curious about Calculus

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Calculus means small pebbles in Latin.  A quick search would tell you that calculus is the study of change.  That definition does not help us understand it much.  So beGalileo, put forth a simpler explanation for all who have been curious about what calculus is all about.

First a few questions to ponder.

img_1

To measure this straight line, you would use a refrence of  img_2 .  So, how many of such img_2 fit on this line.  But, what if you have img_10 ?

You would have learnt the Area of a rectangle img_3 ? 

The base is l. Imagine the l dragged through a width of b. We get the region – its area would be l x b.

What about the area of yZgGX ?

Again, area of img_3 is l x b.

If I stack similar rectangles to a height ‘h’, I get a cuboid of Volume h x Area.img_4

Similarly, if I stack up circles of the same size,  I get a cylinderimg_5.   So the Volume of the cylinder is π r 2 h.

But what if, the circles are not of all the same size, I would get img_6 (1).

Now, let us look at each of the problems again.  

img_10 Recall that calculus means tiny pebbles.  Instead of using img_2 , if we were to use really really small pebbles – small parts – to measure.  Then it wouldn’t matter that it is curve.

Similarly for the hemisphere, if we were to have circles that differs tiny weeny bit in area and then we have some way to add them up.  Now that is what the calculus is all about – about splitting change in to the tiniest possible slices.  So as to make it possible to work on non-uniform change and also to know what happens at one particular point during the change.

There is also another way to look at it.  

Remember the symbol sigma img_8, that you might have learnt when learning about averages. It is a symbol to add up.  So, if you say img_7 (1) it means you add up 10 separate things named x1, x2, x3.  For example,it may add up your marks in ten subjects. Each mark is a separate, discrete** value. img_8 sums up discrete values.

If we want to sigma up stuff that are continuous** that’s when we have calculus.  

You would start learning Calculus in school in Grade XI . You would mainly learn two aspects of Calculus.img_9

Soon you would start using it in different subjects especially Physics and Economics.

As in most topics of Math, lack of familiarity and a preconceived notion of difficulty has given Calculus the image of a complex and difficult topic, which is not so. Hope this article made Calculus less of a stranger, a possible friend.

**discrete vs continuous : discrete quantities can be “counted” while continuous quantities are “measured”.

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