**Fundamentals of calculus**

**Chapter 3: differential equations of functions involving one independent variable.**

“Everything big is built out
of smaller units; and if the smaller units fail to cooperate the bigger ones
ultimately fall”

“A good learner never
accepts the educative information he comes across unless he knows for sure,
that there is no practical and logical way to contradict it”

Calculus as a whole evolved
to support something new, a differential equation. One marvellous fact about
differential equations are they don’t have any constants to describe the
graphical structure they represent. In the previous article ‘chapter 2’, we saw how
differentiation eliminates a constant. This fact can be taken advantage of to
frame differential equations that elaborate the actual rate of change of
different quantities. For example if, $z = ax^2 + bx +c$ then $\frac{dz}{dx} =
2ax + b$ and $\frac{d^2z}{dx^2} = 2a$ and $\frac{d^3z}{dx^3} = 0$.