Notational confusion of multivariable derivatives: Difference between revisions
No edit summary |
No edit summary |
||
| Line 4: | Line 4: | ||
* The thing where if <math>f(x,y) = (x^2,y^2)</math> then <math>\frac{\partial f}{\partial x}(x,x)</math> feels like it might be <math>(2x,2x)</math> even though it's actually <math>(2x,0)</math>. (Example from Tao.) See also [https://issarice.com/mathematics-and-notation] | * The thing where if <math>f(x,y) = (x^2,y^2)</math> then <math>\frac{\partial f}{\partial x}(x,x)</math> feels like it might be <math>(2x,2x)</math> even though it's actually <math>(2x,0)</math>. (Example from Tao.) See also [https://issarice.com/mathematics-and-notation] | ||
* The thing where the total derivative for <math>n=m=1</math> "should" be a function but people treat it as a number. | * The thing where the total derivative for <math>n=m=1</math> "should" be a function but people treat it as a number. | ||
* Total derivative vs derivative matrix | |||
==See also== | ==See also== | ||
* [[Summary table of multivariable derivatives]] | * [[Summary table of multivariable derivatives]] | ||
Revision as of 07:26, 16 July 2018
I think there's several different confusions that arise from multivariable derivative notation:
- The thing where can mean two different things on LHS and RHS when is used as both an initial and intermediate variable. (See Folland for details.)
- The thing where if then feels like it might be even though it's actually . (Example from Tao.) See also [1]
- The thing where the total derivative for "should" be a function but people treat it as a number.
- Total derivative vs derivative matrix