Wronskian of two functions - Revision history

Vipul at 22:54, 5 July 2012

2012-07-05T22:54:08Z

← Older revision		Revision as of 22:54, 5 July 2012
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	defined wherever the right side expression makes sense, which happens at the points where <math>f,g</math> and their [[derivative]]s <math>f',g'</math> exist.		defined wherever the right side expression makes sense, which happens at the points where <math>f,g</math> and their [[derivative]]s <math>f',g'</math> exist.

			Note that the Wronskian is skew-symmetric in <math>f</math> and <math>g</math> rather than symmetric, i.e., the Wronskian of <math>g</math> and <math>f</math> is the negative of the Wronskian of <math>f</math> and <math>g</math>. We are typically concerned, not with the precise Wronskian but with the Wronskian up to scalar multiples, and in particular with whether it is identically zero. These aspects of its behavior ''are'' symmetric.

Vipul: Created page with "==Definition== Suppose $f$ and $g$ are both functions of one variable. The '''Wronskian''' of $f$ and $g$ is defined as the [[..."

2012-06-29T17:05:59Z

Created page with "==Definition== Suppose <math>f</math> and <math>g</math> are both functions of one variable. The '''Wronskian''' of <math>f</math> and <math>g</math> is defined as the [[..."

New page

==Definition==

Suppose <math>f</math> and <math>g</math> are both [[function]]s of one variable. The '''Wronskian''' of <math>f</math> and <math>g</math> is defined as the [[determinant]] of the following matrix:

<math>\begin{pmatrix} f & g \\ f' & g' \\\end{pmatrix}</math>

Explicitly, it is the function:

<math>x \mapsto f(x)g'(x) - f'(x)g(x)</math>

defined wherever the right side expression makes sense, which happens at the points where <math>f,g</math> and their [[derivative]]s <math>f',g'</math> exist.

Wronskian of two functions - Revision history

Vipul at 22:54, 5 July 2012

Vipul: Created page with "==Definition== Suppose f and g are both functions of one variable. The '''Wronskian''' of f and g is defined as the [[..."

Vipul: Created page with "==Definition== Suppose $f$ and $g$ are both functions of one variable. The '''Wronskian''' of $f$ and $g$ is defined as the [[..."