Student: Senthil Kumar

Q. Why we need to study differential calculus? What is it`s practical significance.


Answer :

Hello Senthil, 


Differential calculus is the study of rates of change of functions.

Let`s take an example first.
Suppose you take a trip from Chennai to Hyderabad. That`s over 600 kms, and it will take about 12 hours depending on the traffic.

Now we know distance = rate x time, So we can figure  average velocity during the trip as 50 kms/hour (dividing 600 kms by 12 hours).

But you know that when you`re in the city, you`re driving much slower than 50 kms/h!

On the other hand, when you get to the highways, you would going more than 50 kms/h. Right? 

The calculation we did is just an average, but not the speed at particular instant. Isn`t it?

But your vehicle knows better. It has a speedometer that keeps track of the speed (or velocity) at any given instant. When you look at the speedometer and it shows 65 kmph, that is telling you the instantaneous velocity at the particular instant of time you decided to look at it. 

How does it know? Your vehicle is doing something like differential calculus to figure it out!

Topic: Calculus
Concept: As evident from example above,  Calculus is the study of how things change. It provides a framework for modeling systems in which there is change, and a way to deduce the predictions of such models.
The fundamental idea of calculus is to study change by studying "instantaneous" change, by which we mean changes over tiny intervals of time.

Examples:
You can use calculus in the real world in a lot of ways and applications. Disciplines that utilize calculus include  engineering, physics, economics, statistics and medicine. It is used to create mathematical models in order to arrive into an optimal solution.

For example, in physics, calculus is used in a lot of its concepts. which include motion, electricity, heat, light, harmonics, acoustics, astronomy, and dynamics. 
The most common practical use of calculus is when plotting graphs of certain formulae or functions. 

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