Wronskian of two functions

Definition

Suppose $f$ and $g$ are both functions of one variable. The Wronskian of $f$ and $g$ is defined as the determinant of the following matrix:

$\left(\begin{array}{cc}f& g\\ f\text{'}& g\text{'}\\ \end{array}\right)$

Explicitly, it is the function:

$x\mapsto f(x)g^{\prime }(x)-f^{\prime }(x)g(x)$

defined wherever the right side expression makes sense, which happens at the points where $f,g$ and their derivatives $f^{\prime },g^{\prime }$ exist.