God gave the digits, man made the rest...

My dear friends

I could not post yesterday. Actually last portion on Maths - Calculus is still pending to be discussed. Calculus is developed independently and at the same time by both Newton[1643-1727]  ( at your left)             and     
Leibnitz [1646-1716]  ( down and at your right ) at the end of seventeenth century. Newton applied the same to explain Motion and Gravitation.

Calculus is a latin word meaning stones for counting. Calculus is the branch of Mathematics that deals with the study of changes.
Let us consider that a car be moving along a straight road with constant speed.  If we want to know the distance covered at a given interval of time then we just calculate the product of that speed and time interval. But in general if the car moves with variable speed and along any path, the technique described above cannot solve the problem.

First we must know the speed of that car at each point of its path; we call it instantaneous speed. To determine this we break the path into very small fragments of distances that are travelled in even smaller intervals of time. So speed, in any such small interval, is the ratio of that description of small distance to the very small time interval. This is the speed during that time interval but still not instantaneous. We know that there is no end to reach smallness i.e., whatever small quantity you may think, I can  think even smaller. That is why we call it infinitesimally small. As a matter of fact we approach towards zero but not exactly zero. 

Now if we approach zero for that time interval, we get that ratio as the instantaneous speed. This ratio, subject to the condition of approaching zero, is called the derivative and determination of this derivative is the primary objective of Calculus through its one branch - Differential Calculus. The process to find the derivative is called differentiation. Basically derivative in general is the rate of change of a function (distance) per unit change of the independent variable (time) on which the function is dependent, at a desired value of the variable (time). This is why derivative is also called the rate measurer and Calculus is called study of changes. In every sphere of life we have a dependence to study and is therefore, the importance of the subject.

However, it is not finished yet. We still  need to know the total path described by the car with variable speed during a given finite time interval. For that we need to sum up each product of that ratio  [small distance to the infinitesimally small time interval] and that infinitesimally small time interval all over the path. The summation is called integration and this other branch is called Integral Calculus.

In differentiation you measure the function at each point by breaking whereas in integration you sum up to know the function along a finite interval. Integration is thus reverse process of differentiation.

I hope you now have got some idea about the purpose of this subject. I have seen in many cases the students learn Calculus mechanically without knowing its necessity and purpose.

Please do not learn this branch of Mathematics just for your examination. Be positive. If you love Mathematical Analysis, I am sure that, you will collect enough fuel to go for without looking back.

Wish you all the best