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Should I use “with” or “as” in place of X in “The derivative can be approximated X a finite-difference scheme”?
help on / with somethingWhat should be the correct preposition after “out of keeping”Rolled down/off/onWhat is the preposition that I should put after the verb “recommend” and before object pronoun?Which preposition to use with injury nouns?What's the difference in using prepositions of place?Difference between “ The vase was sold at 300 dollars.” vs “ The vase was sold for 300 dollars.”The usage of “of” or “for” with “forecast”kind to vs gentle withWhat is the correct preposition to use with “corporation”
.everyoneloves__top-leaderboard:empty,.everyoneloves__mid-leaderboard:empty,.everyoneloves__bot-mid-leaderboard:empty margin-bottom:0;
Which of the two examples is more appropriate?
The derivative can be approximated with a finite-difference scheme.
The derivative can be approximated as a finite-difference scheme.
I believe that the most appropriate preposition to use is "with", given that "as" should intuitively be followed by a formula (at least, this sounds better to me).
For example
The derivative can be approximated as
f(x+1) - f(x).
prepositions
asked 8 hours ago
nbronbro
7114 gold badges14 silver badges36 bronze badges
add a comment |
Which of the two examples is more appropriate?
The derivative can be approximated with a finite-difference scheme.
The derivative can be approximated as a finite-difference scheme.
I believe that the most appropriate preposition to use is "with", given that "as" should intuitively be followed by a formula (at least, this sounds better to me).
For example
The derivative can be approximated as
f(x+1) - f(x).
prepositions
asked 8 hours ago
nbronbro
7114 gold badges14 silver badges36 bronze badges
add a comment |
Which of the two examples is more appropriate?
The derivative can be approximated with a finite-difference scheme.
The derivative can be approximated as a finite-difference scheme.
I believe that the most appropriate preposition to use is "with", given that "as" should intuitively be followed by a formula (at least, this sounds better to me).
For example
The derivative can be approximated as
f(x+1) - f(x).
prepositions
asked 8 hours ago
nbronbro
7114 gold badges14 silver badges36 bronze badges
Which of the two examples is more appropriate?
The derivative can be approximated with a finite-difference scheme.
The derivative can be approximated as a finite-difference scheme.
I believe that the most appropriate preposition to use is "with", given that "as" should intuitively be followed by a formula (at least, this sounds better to me).
For example
The derivative can be approximated as
f(x+1) - f(x).
prepositions
prepositions
asked 8 hours ago
nbronbro
7114 gold badges14 silver badges36 bronze badges
asked 8 hours ago
nbronbro
7114 gold badges14 silver badges36 bronze badges
edited 7 hours ago
nbro
asked 8 hours ago
nbronbro
7114 gold badges14 silver badges36 bronze badges
asked 8 hours ago
nbronbro
7114 gold badges14 silver badges36 bronze badges
asked 8 hours ago
nbronbro
7114 gold badges14 silver badges36 bronze badges
7114 gold badges14 silver badges36 bronze badges
add a comment |
add a comment |
3 Answers
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The Wikipedia page for Finite difference method has
In mathematics, finite-difference methods (FDM) are numerical methods for solving differential equations by approximating them with difference equations.
In your second example, I think "by" would be better.
The derivative can be approximated by f(x+1) - f(x).
answered 7 hours ago
Weather VaneWeather Vane
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add a comment |
If you are using a finite-difference scheme to create the approximation, but the finite-difference scheme is not itself the actual approximation, use "with".
If some particular finite-difference scheme is the approximation, use "as".
answered 7 hours ago
Edward BarnardEdward Barnard
1,4991 silver badge9 bronze badges
add a comment |
I think you understand this issue well. Both of these are frequently and interchangebly used in this case, but using with is a little more vague/general. The writer is saying that there exists a finite difference scheme that reasonably approximates the derivative, but may not actually specify which one, presumably because that's not the point.
On the other hand, it would be more likely to say as if you were about to actually insert the finite difference scheme in place of the derivative in your formula, or if you were about to put a comma and the formula itself.
answered 4 hours ago
farnsyfarnsy
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3 Answers
3
active
oldest
votes
3 Answers
3
active
oldest
votes
active
oldest
votes
active
oldest
votes
The Wikipedia page for Finite difference method has
In mathematics, finite-difference methods (FDM) are numerical methods for solving differential equations by approximating them with difference equations.
In your second example, I think "by" would be better.
The derivative can be approximated by f(x+1) - f(x).
answered 7 hours ago
Weather VaneWeather Vane
9,7712 gold badges14 silver badges28 bronze badges
add a comment |
The Wikipedia page for Finite difference method has
In mathematics, finite-difference methods (FDM) are numerical methods for solving differential equations by approximating them with difference equations.
In your second example, I think "by" would be better.
The derivative can be approximated by f(x+1) - f(x).
answered 7 hours ago
Weather VaneWeather Vane
9,7712 gold badges14 silver badges28 bronze badges
add a comment |
The Wikipedia page for Finite difference method has
In mathematics, finite-difference methods (FDM) are numerical methods for solving differential equations by approximating them with difference equations.
In your second example, I think "by" would be better.
The derivative can be approximated by f(x+1) - f(x).
answered 7 hours ago
Weather VaneWeather Vane
9,7712 gold badges14 silver badges28 bronze badges
The Wikipedia page for Finite difference method has
In mathematics, finite-difference methods (FDM) are numerical methods for solving differential equations by approximating them with difference equations.
In your second example, I think "by" would be better.
The derivative can be approximated by f(x+1) - f(x).
answered 7 hours ago
Weather VaneWeather Vane
9,7712 gold badges14 silver badges28 bronze badges
answered 7 hours ago
Weather VaneWeather Vane
9,7712 gold badges14 silver badges28 bronze badges
answered 7 hours ago
Weather VaneWeather Vane
9,7712 gold badges14 silver badges28 bronze badges
answered 7 hours ago
Weather VaneWeather Vane
9,7712 gold badges14 silver badges28 bronze badges
9,7712 gold badges14 silver badges28 bronze badges
add a comment |
add a comment |
If you are using a finite-difference scheme to create the approximation, but the finite-difference scheme is not itself the actual approximation, use "with".
If some particular finite-difference scheme is the approximation, use "as".
answered 7 hours ago
Edward BarnardEdward Barnard
1,4991 silver badge9 bronze badges
add a comment |
If you are using a finite-difference scheme to create the approximation, but the finite-difference scheme is not itself the actual approximation, use "with".
If some particular finite-difference scheme is the approximation, use "as".
answered 7 hours ago
Edward BarnardEdward Barnard
1,4991 silver badge9 bronze badges
add a comment |
If you are using a finite-difference scheme to create the approximation, but the finite-difference scheme is not itself the actual approximation, use "with".
If some particular finite-difference scheme is the approximation, use "as".
answered 7 hours ago
Edward BarnardEdward Barnard
1,4991 silver badge9 bronze badges
If you are using a finite-difference scheme to create the approximation, but the finite-difference scheme is not itself the actual approximation, use "with".
If some particular finite-difference scheme is the approximation, use "as".
answered 7 hours ago
Edward BarnardEdward Barnard
1,4991 silver badge9 bronze badges
answered 7 hours ago
Edward BarnardEdward Barnard
1,4991 silver badge9 bronze badges
answered 7 hours ago
Edward BarnardEdward Barnard
1,4991 silver badge9 bronze badges
answered 7 hours ago
Edward BarnardEdward Barnard
1,4991 silver badge9 bronze badges
1,4991 silver badge9 bronze badges
add a comment |
add a comment |
I think you understand this issue well. Both of these are frequently and interchangebly used in this case, but using with is a little more vague/general. The writer is saying that there exists a finite difference scheme that reasonably approximates the derivative, but may not actually specify which one, presumably because that's not the point.
On the other hand, it would be more likely to say as if you were about to actually insert the finite difference scheme in place of the derivative in your formula, or if you were about to put a comma and the formula itself.
answered 4 hours ago
farnsyfarnsy
3,1611 gold badge3 silver badges6 bronze badges
add a comment |
I think you understand this issue well. Both of these are frequently and interchangebly used in this case, but using with is a little more vague/general. The writer is saying that there exists a finite difference scheme that reasonably approximates the derivative, but may not actually specify which one, presumably because that's not the point.
On the other hand, it would be more likely to say as if you were about to actually insert the finite difference scheme in place of the derivative in your formula, or if you were about to put a comma and the formula itself.
answered 4 hours ago
farnsyfarnsy
3,1611 gold badge3 silver badges6 bronze badges
add a comment |
I think you understand this issue well. Both of these are frequently and interchangebly used in this case, but using with is a little more vague/general. The writer is saying that there exists a finite difference scheme that reasonably approximates the derivative, but may not actually specify which one, presumably because that's not the point.
On the other hand, it would be more likely to say as if you were about to actually insert the finite difference scheme in place of the derivative in your formula, or if you were about to put a comma and the formula itself.
answered 4 hours ago
farnsyfarnsy
3,1611 gold badge3 silver badges6 bronze badges
I think you understand this issue well. Both of these are frequently and interchangebly used in this case, but using with is a little more vague/general. The writer is saying that there exists a finite difference scheme that reasonably approximates the derivative, but may not actually specify which one, presumably because that's not the point.
On the other hand, it would be more likely to say as if you were about to actually insert the finite difference scheme in place of the derivative in your formula, or if you were about to put a comma and the formula itself.
answered 4 hours ago
farnsyfarnsy
3,1611 gold badge3 silver badges6 bronze badges
answered 4 hours ago
farnsyfarnsy
3,1611 gold badge3 silver badges6 bronze badges
answered 4 hours ago
farnsyfarnsy
3,1611 gold badge3 silver badges6 bronze badges
answered 4 hours ago
farnsyfarnsy
3,1611 gold badge3 silver badges6 bronze badges
3,1611 gold badge3 silver badges6 bronze badges
add a comment |
add a comment |
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