INFINITESIMAL CALCULUS Vol.1

                     
                             Mathematics, a beautiful creation of humans, took us to unknown places of the universe in ship of imagination. It has got various tools to help us explore the unknown, one of them being “INFINITESIMAL CALCULUS”. The origin of the word lies in Latin language, which means “small pebbles”. This seems irrelevant at first. What does a complex branch of maths has to do with small pebbles? But when you dig deeper into the subject you will find the connection.

Leibniz-Newton

The origin of calculus is often debated because it was formulated by two people in different part of world at same time! (Sound like a highly unlikely mathematical probability!). The idea was introduced by Sir Isaac Newton and Gottfried Leibniz in mid 17^th century. Sir Newton explained the idea as rate of change of a function while Gottfried used coordinate geometry. Years of research had been done on this topic before Newton and Leibniz. Both these masterminds put it together, their ideas and gave birth to a beautiful baby, the baby was named “INFINITESIMAL CALCULUS”.

                          We know why the area of a square is x²?  Why the area of rectangle is L*B? But can you tell why are of circle is pi times r² ? To start understanding the simplicity of the supposedly hard calculus let’s begin with a simple question. Imagine you have two bikes, one of them has only a speedometer (a device which measures speed) and another has only odometer (a device which measures the distance travelled). Now when you ride bike 1 you know only your speed and when you ride bike 2 you can only know the distance you covered. So can you find your distance travelled by bike 1 with speed known to you and can you find speed of the bike 2 when distance is known at every single point in time? Yes it’s that simple! The whole calculus is just trying to solve this problem. Now to understand anything further we need to know about a mathematical term called ‘Function’. It can be understood as a machine, we put the raw material inside and we get some finished product. So it’s like defining a set of mathematical rules for a variable. And if the variable is ‘x’ then it’s written as ‘f(x)’. If we put a value of ‘x’ in f(x) we get some value as the answer.

E.g. If f(x) = x², then f (1) =1, f (2) =4, f (3) =9...

                      So whenever we say the words like speed, distance, acceleration, etc. they all are mathematical function of physical quantities. Now these functions are classified into many types. One of the classifications being: Continuous and Discontinuous. The one which are continuous are of our concern in study of calculus. Now you might ask how we will know whether a function is continuous or not? This is the time when GRAPHS come to our rescue. We can plot a graph and check weather the function is continuous or not. And another way is to take ‘limits’ (which is long but efficient). So the first problem, given speed find distance is called ‘The Problem of Tangents’. And second given distance find speed is called ‘The Problem of Areas’.

To find answers to these questions and more in a interesting way, stay with B.R.A.I.N foundation and together we will explore the secrets of mathematics! 

Special Thanks to -- Piyush Suryawanshi6719

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