Calculus – A little Personal Background
Calculus was introduced to us in India in Plus 1 is the CBSE curriculum (we have a 10 +2 system, where one spends 12 years in School + 3 years in Nursery, KG1/2 before getting to school). I am an engineer and have taken many courses in mathematics but unfortunately my interest started waning down quite a bit and I missed the fun in doing mathematics and it became a very dry subject for me during my engineering days. Probably the college has very low incentives to study well once you get into them and almost every one was more smarter than you are.
Calculus was introduced in a way that one always asked what’s the use of learning all these. Will we ever use them in our normal lives.
A recent stumbling
Recently started to pick few things up again for no reason as such. And here is book that is available online called Caculus Made Easy which was written by Silvanus P Thompson. This book was originally published in 1910 and claims to introduce the subject in a easy way. I haven’t read it all but this write-up is inspired by the book.
The books starts with the proverb that “What One Fool Can Do, Another Can” and why many students fear the subject.
I was also reading couple of books by Steven Strogatz’s “Joy of X” and “Infinite powers”, Charles Seife’s Zero (another post that I wrote). The world is analog but we human perceive things in a digital way. The music in MP3 or Picture in JPEG are decoding of analog data in digital and the more close we go analog the better the clarity but for after some point of time human ears or eyes fails to recognize the difference.
Anyways here I want to focus on easy interpretation of the Differential Calculus and it has to deal with some approximation and degree of smallness.
Lets start with the most basic differentiation example. I could not find a good tool to enter mathematical formulas so I just wrote them down in a notebook.
It seems like there is some approximation being done here but Newton found that all his formulas aligned pretty well with this. This is the language of nature and it took some time for the mathematicians to get along.
Calculus has two sides differentiation where one breaks things into small slices and integration where slices are combined into a whole.
It has come a long way from days of Newton’s and Leibniz’s in 17th and 18th Century and it will continue to drive the future.