Introduction to Calculus
Previously, we learnt about the Basic Algebra in the three part series of
In this post, let’s learn about the most important and fascinating concepts of Calculus. It is said that without Calculus and some of the concepts of differential calculus such as derivatives, Deep Learning would never be possible and there is definitely some truth in it.
As we go along, you will realize it when we learn derivatives and in that, single, double and partial derivatives.
I know you may already be feeling a bit jittery with the names of derivatives and partial derivatives. But have the trust in me and little bit of patience and you will master some of the most advanced mathematical concepts required for machine learning algorithms.
So let’s begin by understanding in the most fundamental way?
What is Calculus?
Calculus simply means small pebbles and they were being used in the old counting method of abacus.
Calculus also means, a continuous but small change and that’s one of the fundamental principles of the Calculus. As I mentioned earlier, its the most widely used concept in machine learning. In fact in today’s world, there is no algorithm that does not use calculus. Let’s see, what this small continuous change can do.
Let me ask you what is the formula for area of the circle? Well, most of you would remember it as,
Let’s try to derive it. Give me couple of minutes and you will understand where I am heading and why the small but continuous change is so important.
Let’s say we have this circle and if we cut this circle at the gap and drag it down to the surface, what we may have is a straight line.
Now imagine, there are multiple such circles inside this circle and they are very very close to each other. So close that there is actually no gap between these lines. Then it would look like this triangle that has got two sides equal.
Now if these lines are so close, all we need to do is get the area of the triangle to get the area of the circle, because all these lines are nothing but the circumferences of all these circles.
Also, the base of this triangle is nothing but the circumference of the outermost circle. The height of this triangle will now be the radius of the circle.
We also know that the area of a triangle whose two sides are equal, is
Area = Base * Height/2.
and that basically means,
In case you wonder what you have done just now is nothing but the integration of the circumference of the circle with a small change of “dr” in radius.
Remember, those circles became smaller and smaller which basically means changing with smaller radius. It is all about the small step.
So lets learn about this small step or also known as Rate of Change in the next post.
This article is part of my course on Data Science and Machine Learning Using Python. Do check out the course by clicking on the link, Complete Data Science and Machine Learning using Python where we not only go through all such mathematical concepts but also implement the Machine Learning Algorithms Using Python in depth.
Thanks for reading….
