Question

What is a differential???

Answer 1

It depends on what field of study, there are multiple meanings depending on the context of the word. In calculus, it is often associated with the change in the slope of the tangent lines of a function....sometimes referred to as slope fields.

There are also differential equations that can be solved using an initial condition.

There is also a calculus course that is devoted to primarily differential equations...(Cal IV)...

This is just a start....again, it depends on the context of the word....

Answer 2

In AP Calculus, we often solve differential equations with an initial condition.
This can be accomplished easily by a seperation of variables and integrating both sides of the equation.

Answer 3

yes, thank you. But what dx, for example, means in calculus?

Answer 4

Leibniz used the s symbol for the sum and the dx to represent infinitely small increments of x or y...called infinitesimals.
Think of the slicing a vertical cylinder into discs that have a width very near to zero, the sum of the discs would still represent the volume of the cylinder, therefore, think of the smallest width imaginable to represent dx and the s to represent the sum of these widths and you get the general idea. I hope this made some sense.

Answer 5

dx for infinitely small increments of x.
dy for infinitely small increments of y.

Answer 6

Let's say you want to find the gradient of a curved line at a particular point. On a straight line it would be easy because you just divide the change in y by the change in x. On a curve however, this is not possible, or at least only gives you an approximate answer.

We can make delta x smaller and smaller, and this will improve our answer, the gradient will be closer that at the very point we are interested in. As PROSS said, in differential calculus we make delta x tend toward zero.

\[\Delta x \rightarrow 0 = dx\]

I can recommend "Calculus Made Easy" by Silvanus P. Thompson, hope you can find it in your library.