Mdthbs

How to apply a register to a command

Constant integers and constant evaluation

How can I know what hashing algorithm SQL Server used to decrypt the encrypted data when using the function DECRYPTBYPASSPHRASE?

Is it right to use the ideas of non-winning designers in a design contest?

Relationship between speed and cadence?

What's this inadvertent thing?

What is the extent of the commands a Cambion can issue through Fiendish Charm?

Poor management handling of recent sickness and how to approach my return?

Let A,B,C be sets. If A△B=A△C, does this imply that B=C?

Why has Marx's "Das Kapital" been translated to "Capital" in English and not "The Capital"

Did "Dirty Harry" feel lucky?

Professor refuses to write a recommendation letter to students who haven't written a research paper with him

How do draw effects during the discard phase work?

Are fast interviews red flags?

How to best explain that you are taking pictures in a space for practice reasons?

Dynamic Picklist Value Retrieval

Is there some sort of French saying for "a person's signature move"?

Compiler optimization of bitwise not operation

How do English-speaking kids loudly request something?

Do aarakocra have arms as well as wings?

At what point does a land become controlled?

Statistical closeness implies computational indistinguishability

I won a car in a poker game. How is that taxed in Canada?

How should Thaumaturgy's "three times as loud as normal" be interpreted?

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;
}

1

Which of the two examples is more appropriate?

1. The derivative can be approximated with a finite-difference scheme.




2. 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

share|improve this question

edited 8 hours ago

nbro

asked 9 hours ago

nbronbro

71144 gold badges1414 silver badges3636 bronze badges

add a comment | 

1

Which of the two examples is more appropriate?

1. The derivative can be approximated with a finite-difference scheme.




2. 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

share|improve this question

edited 8 hours ago

nbro

asked 9 hours ago

nbronbro

71144 gold badges1414 silver badges3636 bronze badges

add a comment | 

Which of the two examples is more appropriate?

1. The derivative can be approximated with a finite-difference scheme.




2. 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

share|improve this question

edited 8 hours ago

nbro

asked 9 hours ago

nbronbro

71144 gold badges1414 silver badges3636 bronze badges

share|improve this question

edited 8 hours ago

nbro

asked 9 hours ago

nbronbro

71144 gold badges1414 silver badges3636 bronze badges

share|improve this question

edited 8 hours ago

nbro

asked 9 hours ago

nbronbro

71144 gold badges1414 silver badges3636 bronze badges

asked 9 hours ago

nbronbro

71144 gold badges1414 silver badges3636 bronze badges

asked 9 hours ago

nbronbro

71144 gold badges1414 silver badges3636 bronze badges

3 Answers
3

active

oldest

votes

3

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).

share|improve this answer

answered 8 hours ago

Weather VaneWeather Vane

9,78122 gold badges1414 silver badges2828 bronze badges

add a comment | 

2

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".

share|improve this answer

answered 8 hours ago

Edward BarnardEdward Barnard

1,49911 silver badge99 bronze badges

add a comment | 

0

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.

share|improve this answer

answered 5 hours ago

farnsyfarnsy

3,16111 gold badge33 silver badges66 bronze badges

add a comment | 

Your Answer

StackExchange.ready(function() {
var channelOptions = {
tags: "".split(" "),
id: "481"
};
initTagRenderer("".split(" "), "".split(" "), channelOptions);

StackExchange.using("externalEditor", function() {
// Have to fire editor after snippets, if snippets enabled
if (StackExchange.settings.snippets.snippetsEnabled) {
StackExchange.using("snippets", function() {
createEditor();
});
}
else {
createEditor();
}
});

function createEditor() {
StackExchange.prepareEditor({
heartbeatType: 'answer',
autoActivateHeartbeat: false,
convertImagesToLinks: false,
noModals: true,
showLowRepImageUploadWarning: true,
reputationToPostImages: null,
bindNavPrevention: true,
postfix: "",
imageUploader: {
brandingHtml: "Powered by u003ca class="icon-imgur-white" href="https://imgur.com/"u003eu003c/au003e",
contentPolicyHtml: "User contributions licensed under u003ca href="https://creativecommons.org/licenses/by-sa/4.0/"u003ecc by-sa 4.0 with attribution requiredu003c/au003e u003ca href="https://stackoverflow.com/legal/content-policy"u003e(content policy)u003c/au003e",
allowUrls: true
},
noCode: true, onDemand: true,
discardSelector: ".discard-answer"
,immediatelyShowMarkdownHelp:true
});


}
});

draft saved

draft discarded

Sign up or log in

StackExchange.ready(function () {
StackExchange.helpers.onClickDraftSave('#login-link');
});

Sign up using Google

Sign up using Facebook

Sign up using Email and Password

Post as a guest

Name

Email

Required, but never shown

StackExchange.ready(
function () {
StackExchange.openid.initPostLogin('.new-post-login', 'https%3a%2f%2fell.stackexchange.com%2fquestions%2f223255%2fshould-i-use-with-or-as-in-place-of-x-in-the-derivative-can-be-approximated%23new-answer', 'question_page');
}
);

Post as a guest

Name

Email

Required, but never shown

3

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).

share|improve this answer

answered 8 hours ago

Weather VaneWeather Vane

9,78122 gold badges1414 silver badges2828 bronze badges

add a comment | 

3

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).

share|improve this answer

answered 8 hours ago

Weather VaneWeather Vane

9,78122 gold badges1414 silver badges2828 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).

share|improve this answer

answered 8 hours ago

Weather VaneWeather Vane

9,78122 gold badges1414 silver badges2828 bronze badges

share|improve this answer

answered 8 hours ago

Weather VaneWeather Vane

9,78122 gold badges1414 silver badges2828 bronze badges

answered 8 hours ago

Weather VaneWeather Vane

9,78122 gold badges1414 silver badges2828 bronze badges

answered 8 hours ago

Weather VaneWeather Vane

9,78122 gold badges1414 silver badges2828 bronze badges

2

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".

share|improve this answer

answered 8 hours ago

Edward BarnardEdward Barnard

1,49911 silver badge99 bronze badges

add a comment | 

2

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".

share|improve this answer

answered 8 hours ago

Edward BarnardEdward Barnard

1,49911 silver badge99 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".

share|improve this answer

answered 8 hours ago

Edward BarnardEdward Barnard

1,49911 silver badge99 bronze badges

share|improve this answer

answered 8 hours ago

Edward BarnardEdward Barnard

1,49911 silver badge99 bronze badges

answered 8 hours ago

Edward BarnardEdward Barnard

1,49911 silver badge99 bronze badges

answered 8 hours ago

Edward BarnardEdward Barnard

1,49911 silver badge99 bronze badges

0

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.

share|improve this answer

answered 5 hours ago

farnsyfarnsy

3,16111 gold badge33 silver badges66 bronze badges

add a comment | 

0

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.

share|improve this answer

answered 5 hours ago

farnsyfarnsy

3,16111 gold badge33 silver badges66 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.

share|improve this answer

answered 5 hours ago

farnsyfarnsy

3,16111 gold badge33 silver badges66 bronze badges

share|improve this answer

answered 5 hours ago

farnsyfarnsy

3,16111 gold badge33 silver badges66 bronze badges

answered 5 hours ago

farnsyfarnsy

3,16111 gold badge33 silver badges66 bronze badges

answered 5 hours ago

farnsyfarnsy

3,16111 gold badge33 silver badges66 bronze badges