Question

Why is differentiation and integration used???
What is the sole purpose of using it ??

Answer 1

Mathematics is great tool to understand the nature. In terms of mathematical equations, we can model any physical system. You would be knowing about Trigonometry. In early days of scientific discoveries, Greeks used this feature to explore nature. They even calculated the very accurate radius of earth by using "Trigonometry". As per my view, calculus (differentiation and integration ) is a way of trigonometry (although it is much more powerful tool that trigonometry).
If mathematical equation is contains relation between dependent variable and independent ones. These variable can have linear relationship between them, or quadratic relationship, similarly these could be related differentially with each other.
Where these are used : Consider case of velocity of your car. To find distance s, traveled in time s, having velocity u\[s=u*t\] . Now U is time change of distance\[u=S2-S1/T2-T1\]. In another form \[u=ds/dt\].
\[s=(ds/dt)*t\] this is example of differentiation
Now integration is total change obtained along the unit with which you have differentiated. For example in case of velocity distance is differentiated with time. So in return s (distance) is integration so \[s=\int\limits_{?}^{?}ds/dt*\delta t\].
I hope u won't get more confused after reading this big story.

Answer 2

Seeing this is an electronics course, electronic differentiation and integration used to be done in analog computers. They were used to model a real world process and eventually used in control circuitry for doing many processes. Today, with greater speeds in digital computing, digital differentiation and integration are used to do the same as analog computers did in the past, and due to larger bandwidths they do a great job. In all engineering and science mathematics is applied to real world problems and solutions.