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Calculus
“calculus of infinitesimals”, study of continous change
Differential calculus
study of rates ath which quantities change.
Derivative
Example of a straigth line $y=mx+b$, $m=\Delta y / \Delta x$
Differential quotient:
$m = \limit_{x_1 -> x_0} \frac{f(x_1) - f(x_0)}{x_1 - x_0}$
Geometrically, derivative of f at point x=a is slope of tangent line.
Differential equations
Relation between collection of functions and their derivatives.
Ordinary differential equation:
Differential operator
$y' = 2y + x^2$ ⇒ $f'(x)=2*f(x)+x^2$ ⇒ $\frac{dy}{dx} = 2y + x^2$