Differential

Syntax

differential ( expression )

Implemented in iMath since version 2.2.0 or earlier.

Explanation

Create a differential, e.g. dx. Please keep in mind that though you can handle this object like a symbol, it does not always make mathematical sense!

If you want iMath to be able to match differentials, as in d²f = y dx², then you must specify them as differential(f,2) = y differential(x, 2), not as differential(f,2) = y differential(x)^2.

If you want to create a complete differential of a function f (i.e. df/dx), use DIFFERENTIATE(f,x,1) instead. iMath will automatically separate this into two differentials df and dx^{-1}, but will mark them as being connected, so that on printing they can be displayed correctly.

In other words, you should only use differential when it is really necessary.

Example

FUNCTION { {none}, T, x}

@eq1@ EQDEF q = -k A DIFFERENTIATE( T,x,1 )

@eq2@ EQDEF @eq1@ * differential(x)

This defines the equation for heat conduction and prepares it for integration by separation of the variables.

See also

PARTIAL DIFFERENTIATE PDIFFERENTIATE