Editing Differential calculus (section)

=== Differential equations ===
{{Main|Differential equation}}

A differential equation is a relation between a collection of functions and their derivatives. An [[ordinary differential equation]] is a differential equation that relates functions of one variable to their derivatives with respect to that variable. A [[partial differential equation]] is a differential equation that relates functions of more than one variable to their [[partial derivative]]s. Differential equations arise naturally in the physical sciences, in mathematical modelling, and within mathematics itself. For example, [[Newton's second law]], which describes the relationship between acceleration and force, can be stated as the ordinary differential equation
:<math>F(t) = m\frac{d^2x}{dt^2}.</math>
The [[heat equation]] in one space variable, which describes how heat diffuses through a straight rod, is the partial differential equation
:<math>\frac{\partial u}{\partial t} = \alpha\frac{\partial^2 u}{\partial x^2}.</math>
Here {{math|''u''(''x'',''t'')}} is the temperature of the rod at position {{math|''x''}} and time {{math|''t''}} and {{math|''α''}} is a constant that depends on how fast heat diffuses through the rod.