Calculus

“calculus of infinitesimals”, study of continous change

study of rates ath which quantities change.

Example of a straigth line $y=mx+b$, $m=\Delta y / \Delta x$

Differential quotient:

$m = \lim_{x_1 -> x_0} \frac{f(x_1) - f(x_0)}{x_1 - x_0}$

Geometrically, derivative of f at point x=a is slope of tangent line.

Relation between collection of functions and their derivatives.

Ordinary differential equation:

Differential operator

$y' = 2y + x^2$ ⇒ $f'(x)=2*f(x)+x^2$ ⇒ $\frac{dy}{dx} = 2y + x^2$