Calculus
dy/dx Differential Equations
From derivatives to equations that model change — the mathematics of everything that moves, grows, or decays.
4 concepts— start at the top and work your way down
- 1→
Derivatives
The instantaneous rate of change of a function — defined as the limit of the difference quotient and interpreted as the slope of a tangent line.
- 2→
Gradient
The vector of all partial derivatives — pointing in the direction of steepest ascent and encoding how a multivariable function changes locally.
- 3→
Partial Derivatives
The rate of change of a multivariable function with respect to one variable, holding all others fixed — the building block of multivariable calculus.
- 4→
Differential Equations
Equations that relate a function to its own derivatives — the mathematical language of physics, biology, finance, and engineering.