Mixing
Notation Question for “Generalization of L’hopital’s Rule” PDF by V. V. Ivlev and I. A. Shilin
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Within this brief text starting on page 2, the author(s) have a habit of employing a sort of "mixed" notation of differentiation, mixing the "prime marks" of Lagrange's notation for differentiation of a single-variable with the subscript notation commonly used in partial differentiation; that is, something like:
f 'x (x0,y0)
Now, being that this text has had a few errors that I have noticed already, this could simply be an accidental use of the Lagrange notation via force of habit for performing differentiation; however, being that this "error" is repeated throughout the document, I find this unlikely to be the case. Might it be that this is some sort of abuse of notation used to represent a more common mathematical concept? If so, what mathematical concept might that be?
limits multivariable-calculus nonstandard-analysis infinitesimals indeterminate-forms
edited Jan 2 at 14:34
Bernard
119k639112
asked Jan 2 at 14:28
Travis AsherTravis Asher
62
$endgroup$
add a comment |
$begingroup$
Within this brief text starting on page 2, the author(s) have a habit of employing a sort of "mixed" notation of differentiation, mixing the "prime marks" of Lagrange's notation for differentiation of a single-variable with the subscript notation commonly used in partial differentiation; that is, something like:
f 'x (x0,y0)
Now, being that this text has had a few errors that I have noticed already, this could simply be an accidental use of the Lagrange notation via force of habit for performing differentiation; however, being that this "error" is repeated throughout the document, I find this unlikely to be the case. Might it be that this is some sort of abuse of notation used to represent a more common mathematical concept? If so, what mathematical concept might that be?
limits multivariable-calculus nonstandard-analysis infinitesimals indeterminate-forms
edited Jan 2 at 14:34
Bernard
119k639112
asked Jan 2 at 14:28
Travis AsherTravis Asher
62
$endgroup$
$begingroup$
$f'_x(x_0,y_0)$ is a Russian/exUSSR notation for the partial derivative and means just the same as $f_x(x_0,y_0)$.
$endgroup$
– AVK
Jan 2 at 16:38
add a comment |
$begingroup$
Within this brief text starting on page 2, the author(s) have a habit of employing a sort of "mixed" notation of differentiation, mixing the "prime marks" of Lagrange's notation for differentiation of a single-variable with the subscript notation commonly used in partial differentiation; that is, something like:
f 'x (x0,y0)
Now, being that this text has had a few errors that I have noticed already, this could simply be an accidental use of the Lagrange notation via force of habit for performing differentiation; however, being that this "error" is repeated throughout the document, I find this unlikely to be the case. Might it be that this is some sort of abuse of notation used to represent a more common mathematical concept? If so, what mathematical concept might that be?
limits multivariable-calculus nonstandard-analysis infinitesimals indeterminate-forms
edited Jan 2 at 14:34
Bernard
119k639112
asked Jan 2 at 14:28
Travis AsherTravis Asher
62
$endgroup$
Within this brief text starting on page 2, the author(s) have a habit of employing a sort of "mixed" notation of differentiation, mixing the "prime marks" of Lagrange's notation for differentiation of a single-variable with the subscript notation commonly used in partial differentiation; that is, something like:
f 'x (x0,y0)
Now, being that this text has had a few errors that I have noticed already, this could simply be an accidental use of the Lagrange notation via force of habit for performing differentiation; however, being that this "error" is repeated throughout the document, I find this unlikely to be the case. Might it be that this is some sort of abuse of notation used to represent a more common mathematical concept? If so, what mathematical concept might that be?
limits multivariable-calculus nonstandard-analysis infinitesimals indeterminate-forms
limits multivariable-calculus nonstandard-analysis infinitesimals indeterminate-forms
edited Jan 2 at 14:34
Bernard
119k639112
asked Jan 2 at 14:28
Travis AsherTravis Asher
62
edited Jan 2 at 14:34
Bernard
119k639112
asked Jan 2 at 14:28
Travis AsherTravis Asher
62
edited Jan 2 at 14:34
Bernard
119k639112
edited Jan 2 at 14:34
Bernard
119k639112
edited Jan 2 at 14:34
Bernard
119k639112
119k639112
asked Jan 2 at 14:28
Travis AsherTravis Asher
62
asked Jan 2 at 14:28
Travis AsherTravis Asher
62
asked Jan 2 at 14:28
Travis AsherTravis Asher
62
62
$begingroup$
$f'_x(x_0,y_0)$ is a Russian/exUSSR notation for the partial derivative and means just the same as $f_x(x_0,y_0)$.
$endgroup$
– AVK
Jan 2 at 16:38
add a comment |
$begingroup$
$f'_x(x_0,y_0)$ is a Russian/exUSSR notation for the partial derivative and means just the same as $f_x(x_0,y_0)$.
$endgroup$
– AVK
Jan 2 at 16:38
$begingroup$
$f'_x(x_0,y_0)$ is a Russian/exUSSR notation for the partial derivative and means just the same as $f_x(x_0,y_0)$.
$endgroup$
– AVK
Jan 2 at 16:38
$begingroup$
$f'_x(x_0,y_0)$ is a Russian/exUSSR notation for the partial derivative and means just the same as $f_x(x_0,y_0)$.
$endgroup$
– AVK
Jan 2 at 16:38
add a comment |
1 Answer
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$begingroup$
I guess that if you view $f'(x_0, y_0)$ as a row vector and denote its components with $x$ or $y$ subscripts (in physics this is often done for vectors) then $f'_x(x_0, y_0)$ would actually be the partial derivative w.r.t $x$ of $f$ at $(x_0, y_0)$.
I haven't seen that notation ever before however. Maybe it's a Russian thing...
answered Jan 2 at 14:56
0x5390x539
1,117317
$endgroup$
$begingroup$
You know, that seems to make sense, as this notation is first used to make use of the requirement that [ f'_x (x_0,y_0) ]^2 + [ f '_y (x_0,y_0) ]^2 be nonzero; this would be synonymous to requiring the magnitude of the gradient of f to be nonzero using your notation assumption, which certainly seems reasonable. I appreciate this response, thanks! *Edited because mini-markdown does not support the "<>" formatting notations.
$endgroup$
– Travis Asher
Jan 2 at 15:13
add a comment |
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1 Answer
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active
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1 Answer
1
active
oldest
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active
oldest
votes
$begingroup$
I guess that if you view $f'(x_0, y_0)$ as a row vector and denote its components with $x$ or $y$ subscripts (in physics this is often done for vectors) then $f'_x(x_0, y_0)$ would actually be the partial derivative w.r.t $x$ of $f$ at $(x_0, y_0)$.
I haven't seen that notation ever before however. Maybe it's a Russian thing...
answered Jan 2 at 14:56
0x5390x539
1,117317
$endgroup$
$begingroup$
You know, that seems to make sense, as this notation is first used to make use of the requirement that [ f'_x (x_0,y_0) ]^2 + [ f '_y (x_0,y_0) ]^2 be nonzero; this would be synonymous to requiring the magnitude of the gradient of f to be nonzero using your notation assumption, which certainly seems reasonable. I appreciate this response, thanks! *Edited because mini-markdown does not support the "<>" formatting notations.
$endgroup$
– Travis Asher
Jan 2 at 15:13
add a comment |
$begingroup$
I guess that if you view $f'(x_0, y_0)$ as a row vector and denote its components with $x$ or $y$ subscripts (in physics this is often done for vectors) then $f'_x(x_0, y_0)$ would actually be the partial derivative w.r.t $x$ of $f$ at $(x_0, y_0)$.
I haven't seen that notation ever before however. Maybe it's a Russian thing...
answered Jan 2 at 14:56
0x5390x539
1,117317
$endgroup$
$begingroup$
You know, that seems to make sense, as this notation is first used to make use of the requirement that [ f'_x (x_0,y_0) ]^2 + [ f '_y (x_0,y_0) ]^2 be nonzero; this would be synonymous to requiring the magnitude of the gradient of f to be nonzero using your notation assumption, which certainly seems reasonable. I appreciate this response, thanks! *Edited because mini-markdown does not support the "<>" formatting notations.
$endgroup$
– Travis Asher
Jan 2 at 15:13
add a comment |
$begingroup$
I guess that if you view $f'(x_0, y_0)$ as a row vector and denote its components with $x$ or $y$ subscripts (in physics this is often done for vectors) then $f'_x(x_0, y_0)$ would actually be the partial derivative w.r.t $x$ of $f$ at $(x_0, y_0)$.
I haven't seen that notation ever before however. Maybe it's a Russian thing...
answered Jan 2 at 14:56
0x5390x539
1,117317
$endgroup$
I guess that if you view $f'(x_0, y_0)$ as a row vector and denote its components with $x$ or $y$ subscripts (in physics this is often done for vectors) then $f'_x(x_0, y_0)$ would actually be the partial derivative w.r.t $x$ of $f$ at $(x_0, y_0)$.
I haven't seen that notation ever before however. Maybe it's a Russian thing...
answered Jan 2 at 14:56
0x5390x539
1,117317
answered Jan 2 at 14:56
0x5390x539
1,117317
answered Jan 2 at 14:56
0x5390x539
1,117317
answered Jan 2 at 14:56
0x5390x539
1,117317
1,117317
$begingroup$
You know, that seems to make sense, as this notation is first used to make use of the requirement that [ f'_x (x_0,y_0) ]^2 + [ f '_y (x_0,y_0) ]^2 be nonzero; this would be synonymous to requiring the magnitude of the gradient of f to be nonzero using your notation assumption, which certainly seems reasonable. I appreciate this response, thanks! *Edited because mini-markdown does not support the "<>" formatting notations.
$endgroup$
– Travis Asher
Jan 2 at 15:13
add a comment |
$begingroup$
You know, that seems to make sense, as this notation is first used to make use of the requirement that [ f'_x (x_0,y_0) ]^2 + [ f '_y (x_0,y_0) ]^2 be nonzero; this would be synonymous to requiring the magnitude of the gradient of f to be nonzero using your notation assumption, which certainly seems reasonable. I appreciate this response, thanks! *Edited because mini-markdown does not support the "<>" formatting notations.
$endgroup$
– Travis Asher
Jan 2 at 15:13
$begingroup$
You know, that seems to make sense, as this notation is first used to make use of the requirement that [ f'_x (x_0,y_0) ]^2 + [ f '_y (x_0,y_0) ]^2 be nonzero; this would be synonymous to requiring the magnitude of the gradient of f to be nonzero using your notation assumption, which certainly seems reasonable. I appreciate this response, thanks! *Edited because mini-markdown does not support the "<>" formatting notations.
$endgroup$
– Travis Asher
Jan 2 at 15:13
$begingroup$
You know, that seems to make sense, as this notation is first used to make use of the requirement that [ f'_x (x_0,y_0) ]^2 + [ f '_y (x_0,y_0) ]^2 be nonzero; this would be synonymous to requiring the magnitude of the gradient of f to be nonzero using your notation assumption, which certainly seems reasonable. I appreciate this response, thanks! *Edited because mini-markdown does not support the "<>" formatting notations.
$endgroup$
– Travis Asher
Jan 2 at 15:13
add a comment |
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$begingroup$
$f'_x(x_0,y_0)$ is a Russian/exUSSR notation for the partial derivative and means just the same as $f_x(x_0,y_0)$.
$endgroup$
– AVK
Jan 2 at 16:38