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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 $y=mx+b$, $m=\Delta y / \Delta x$
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:
$y' = 2y + x^2$ = $f^'(x)=2*f(x)+x^2)$ = $\frac{dy}{dx}$