- #1
Teclis
- 25
- 2
- Homework Statement
- What does the subscript mean
- Relevant Equations
- $$\frac{\partial( x_{1}, x_{2})}{\partial (y_{1}, y_{2})} =
\begin{vmatrix}
\left (\frac{\partial x_{1}}{\partial y_{1}} \right )_{y_{2}}& \left ( \frac{\partial x_{1}}{\partial y_{2}} \right )_{y_{1}}\\
\left (\frac{\partial x_{2}}{\partial y_{1}} \right )_{y_{2}}& \left ( \frac{\partial x_{2}}{\partial y_{2}} \right )_{y_{1}}
\end{vmatrix}$$
On Page 406 of Nolting Theoretical Physics 1 he has the following notation for the Jacobian determinant
$$\frac{\partial( x_{1}, x_{2})}{\partial (y_{1}, y_{2})} =
\begin{vmatrix}
\left (\frac{\partial x_{1}}{\partial y_{1}} \right )_{y_{2}}& \left ( \frac{\partial x_{1}}{\partial y_{2}} \right )_{y_{1}}\\
\left (\frac{\partial x_{2}}{\partial y_{1}} \right )_{y_{2}}& \left ( \frac{\partial x_{2}}{\partial y_{2}} \right )_{y_{1}}
\end{vmatrix}$$
I am unfamiliar with this notation and can not find an explanation in any textbooks .
What does the bracket subscript mean? In ##\left(\frac{\partial x_{1}}{\partial y_{1}} \right )_{y_{2}}## what does the ## y_{2}## mean?
$$\frac{\partial( x_{1}, x_{2})}{\partial (y_{1}, y_{2})} =
\begin{vmatrix}
\left (\frac{\partial x_{1}}{\partial y_{1}} \right )_{y_{2}}& \left ( \frac{\partial x_{1}}{\partial y_{2}} \right )_{y_{1}}\\
\left (\frac{\partial x_{2}}{\partial y_{1}} \right )_{y_{2}}& \left ( \frac{\partial x_{2}}{\partial y_{2}} \right )_{y_{1}}
\end{vmatrix}$$
I am unfamiliar with this notation and can not find an explanation in any textbooks .
What does the bracket subscript mean? In ##\left(\frac{\partial x_{1}}{\partial y_{1}} \right )_{y_{2}}## what does the ## y_{2}## mean?