Autonomous
A differential equation or system of Ordinary Differential Equations is said tobe autonomous if it does not explicitly contain the independent variable (usually denoted 
). A second-orderautonomous differential equation is of the form 
, where 
. By the ChainRule, 
can be expressed as
For an autonomous ODE, the solution is independent of the time at which theinitial conditions are applied. This means that all particles pass through a given point in phase space. Anonautonomous system of
first-order ODEs can be written as an autonomous system of 
ODEs by letting 
and increasing the dimension of the system by 1 by adding the equation
- Fourier Matrix
- Fourier-Mellin Integral
- Fourier Series
- Fourier Series--Power Series
- Fourier Series--Right Triangle
- Fourier Series--Square Wave
- Fourier Series--Triangle
- Fourier Series--Triangle Wave
- Fourier Sine Series
- Fourier Sine Transform
- Fourier-Stieltjes Transform
- Fourier Transform
- Fourier Transform--1
- Fourier Transform--Cosine
- Fourier Transform--Delta Function
- Fourier Transform--Exponential Function
- Fourier Transform--Gaussian
- Fourier Transform--Heaviside Step Function
- Fourier Transform Inverse Function
- Fourier Transform--Lorentzian Function
- Fourier Transform--Ramp Function
- Fourier Transform--Rectangle Function
- Fourier Transform--Sine
- Four Travelers Problem
- Four-Vector