For Green's theorem, why is the region of integration of the line integral a weird partial derivative character?Meaning of partial differential in limits of integration?Green's theorem for conservative fields - are partials equal?Line Integral of Every Positively Oriented Simple Closed Path - Green's TheoremWhy is $int_partial Dx,dy$ invalid for calculating area of $D$?Green's Theorem and limits on y for fluxGreen's Theorem on Line Integralthe 2-D divergence theorem and Green's TheoremLooking for help understanding the intuition behind 2-D divergence using Green's Theorem.Green's Theorem Derivation and Explanation on the dot product with $mathbfvec F(x,y+Delta y) cdot mathbfvec j,Delta x$Can someone explain to me the jump between steps in the bottom two lines of this proof (not yet totally complete)?What does it mean for a region to be simultaneously a region of type 1 and type 2?
How exploitable/balanced is this homebrew spell: Spell Permanency?
Do creatures with a listed speed of "0 ft., fly 30 ft. (hover)" ever touch the ground?
Is there a hemisphere-neutral way of specifying a season?
The Video Gamers' Double-Duty Crossword
Why didn't Boeing produce its own regional jet?
Why were 5.25" floppy drives cheaper than 8"?
How seriously should I take size and weight limits of hand luggage?
Processor speed limited at 0.4 Ghz
Why was Sir Cadogan fired?
In Bayesian inference, why are some terms dropped from the posterior predictive?
How can saying a song's name be a copyright violation?
Why are UK visa biometrics appointments suspended at USCIS Application Support Centers?
OP Amp not amplifying audio signal
Different meanings of こわい
How does a dynamic QR code work?
Bullying boss launched a smear campaign and made me unemployable
Do Iron Man suits sport waste management systems?
What do you call someone who asks many questions?
files created then deleted at every second in tmp directory
Getting extremely large arrows with tikzcd
How to coordinate airplane tickets?
Why is it a bad idea to hire a hitman to eliminate most corrupt politicians?
Did 'Cinema Songs' exist during Hiranyakshipu's time?
Can I hook these wires up to find the connection to a dead outlet?
For Green's theorem, why is the region of integration of the line integral a weird partial derivative character?
Meaning of partial differential in limits of integration?Green's theorem for conservative fields - are partials equal?Line Integral of Every Positively Oriented Simple Closed Path - Green's TheoremWhy is $int_partial Dx,dy$ invalid for calculating area of $D$?Green's Theorem and limits on y for fluxGreen's Theorem on Line Integralthe 2-D divergence theorem and Green's TheoremLooking for help understanding the intuition behind 2-D divergence using Green's Theorem.Green's Theorem Derivation and Explanation on the dot product with $mathbfvec F(x,y+Delta y) cdot mathbfvec j,Delta x$Can someone explain to me the jump between steps in the bottom two lines of this proof (not yet totally complete)?What does it mean for a region to be simultaneously a region of type 1 and type 2?
$begingroup$
Why the weird $partialQ$ notational for the integral region for Green's Theorm?
$$int_partialQ W cdot ds = iint_Q fracpartialgpartialx - fracpartialfpartialy dx dy$$
Why not just plain "Q" instead:
$$int_Q W cdot ds = iint_Q fracpartialgpartialx - fracpartialfpartialy dx dy$$
If I define Q to be a rectangle region, then what's the difference?
Book says: " The sides Right, Left, Top, and Bottom of Q, with the orientations as indicated... when taken together are referred to as a "boundary". The usual notation for this is a $partialQ$".
I still say, who the heck cares... just call it Q. what hair am i splitting if I remove th the $partial$ character from my notes?
multivariable-calculus line-integrals multiple-integral greens-theorem
asked Mar 28 at 15:15
DiscreteMathDiscreteMath
676
$endgroup$
add a comment |
$begingroup$
Why the weird $partialQ$ notational for the integral region for Green's Theorm?
$$int_partialQ W cdot ds = iint_Q fracpartialgpartialx - fracpartialfpartialy dx dy$$
Why not just plain "Q" instead:
$$int_Q W cdot ds = iint_Q fracpartialgpartialx - fracpartialfpartialy dx dy$$
If I define Q to be a rectangle region, then what's the difference?
Book says: " The sides Right, Left, Top, and Bottom of Q, with the orientations as indicated... when taken together are referred to as a "boundary". The usual notation for this is a $partialQ$".
I still say, who the heck cares... just call it Q. what hair am i splitting if I remove th the $partial$ character from my notes?
multivariable-calculus line-integrals multiple-integral greens-theorem
asked Mar 28 at 15:15
DiscreteMathDiscreteMath
676
$endgroup$
add a comment |
$begingroup$
Why the weird $partialQ$ notational for the integral region for Green's Theorm?
$$int_partialQ W cdot ds = iint_Q fracpartialgpartialx - fracpartialfpartialy dx dy$$
Why not just plain "Q" instead:
$$int_Q W cdot ds = iint_Q fracpartialgpartialx - fracpartialfpartialy dx dy$$
If I define Q to be a rectangle region, then what's the difference?
Book says: " The sides Right, Left, Top, and Bottom of Q, with the orientations as indicated... when taken together are referred to as a "boundary". The usual notation for this is a $partialQ$".
I still say, who the heck cares... just call it Q. what hair am i splitting if I remove th the $partial$ character from my notes?
multivariable-calculus line-integrals multiple-integral greens-theorem
asked Mar 28 at 15:15
DiscreteMathDiscreteMath
676
$endgroup$
Why the weird $partialQ$ notational for the integral region for Green's Theorm?
$$int_partialQ W cdot ds = iint_Q fracpartialgpartialx - fracpartialfpartialy dx dy$$
Why not just plain "Q" instead:
$$int_Q W cdot ds = iint_Q fracpartialgpartialx - fracpartialfpartialy dx dy$$
If I define Q to be a rectangle region, then what's the difference?
Book says: " The sides Right, Left, Top, and Bottom of Q, with the orientations as indicated... when taken together are referred to as a "boundary". The usual notation for this is a $partialQ$".
I still say, who the heck cares... just call it Q. what hair am i splitting if I remove th the $partial$ character from my notes?
multivariable-calculus line-integrals multiple-integral greens-theorem
multivariable-calculus line-integrals multiple-integral greens-theorem
asked Mar 28 at 15:15
DiscreteMathDiscreteMath
676
asked Mar 28 at 15:15
DiscreteMathDiscreteMath
676
edited Mar 28 at 15:18
DiscreteMath
asked Mar 28 at 15:15
DiscreteMathDiscreteMath
676
asked Mar 28 at 15:15
DiscreteMathDiscreteMath
676
asked Mar 28 at 15:15
DiscreteMathDiscreteMath
676
676
add a comment |
add a comment |
1 Answer
1
active
oldest
votes
$begingroup$
Because the double integral is over some region $Q$ (e.g. a disc), while the line integral is over the boundary of $Q$ (e.g. the circle bounding that disc): they're not the same.
You can give it another name if you like, such as "$C$, the boundary of $Q$", but I wouldn't call it $Q$ again since $Q$ is already used for the entire region!
For this boundary of $Q$, the notation $partial Q$ is common.
Referring to my example above, you could have the unit disc $Q$:
$$Q=leftleft(x,yright)inmathbbR^2 ;vert; x^2+y^2 le 1right$$
and its boundary, the unit circle $partial Q$ (possibly with a chosen orientation):
$$partial Q=leftleft(x,yright)inmathbbR^2 ;vert; x^2+y^2 = 1right$$
Related: Meaning of partial differential in limits of integration?
answered Mar 28 at 15:16
StackTDStackTD
24.3k2254
$endgroup$
add a comment |
Your Answer
StackExchange.ifUsing("editor", function ()
return StackExchange.using("mathjaxEditing", function ()
StackExchange.MarkdownEditor.creationCallbacks.add(function (editor, postfix)
StackExchange.mathjaxEditing.prepareWmdForMathJax(editor, postfix, [["$", "$"], ["\\(","\\)"]]);
);
);
, "mathjax-editing");
StackExchange.ready(function()
var channelOptions =
tags: "".split(" "),
id: "69"
;
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: true,
noModals: true,
showLowRepImageUploadWarning: true,
reputationToPostImages: 10,
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/3.0/"u003ecc by-sa 3.0 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
);
);
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
Required, but never shown
StackExchange.ready(
function ()
StackExchange.openid.initPostLogin('.new-post-login', 'https%3a%2f%2fmath.stackexchange.com%2fquestions%2f3166016%2ffor-greens-theorem-why-is-the-region-of-integration-of-the-line-integral-a-wei%23new-answer', 'question_page');
);
Post as a guest
Required, but never shown
1 Answer
1
active
oldest
votes
1 Answer
1
active
oldest
votes
active
oldest
votes
active
oldest
votes
$begingroup$
Because the double integral is over some region $Q$ (e.g. a disc), while the line integral is over the boundary of $Q$ (e.g. the circle bounding that disc): they're not the same.
You can give it another name if you like, such as "$C$, the boundary of $Q$", but I wouldn't call it $Q$ again since $Q$ is already used for the entire region!
For this boundary of $Q$, the notation $partial Q$ is common.
Referring to my example above, you could have the unit disc $Q$:
$$Q=leftleft(x,yright)inmathbbR^2 ;vert; x^2+y^2 le 1right$$
and its boundary, the unit circle $partial Q$ (possibly with a chosen orientation):
$$partial Q=leftleft(x,yright)inmathbbR^2 ;vert; x^2+y^2 = 1right$$
Related: Meaning of partial differential in limits of integration?
answered Mar 28 at 15:16
StackTDStackTD
24.3k2254
$endgroup$
add a comment |
$begingroup$
Because the double integral is over some region $Q$ (e.g. a disc), while the line integral is over the boundary of $Q$ (e.g. the circle bounding that disc): they're not the same.
You can give it another name if you like, such as "$C$, the boundary of $Q$", but I wouldn't call it $Q$ again since $Q$ is already used for the entire region!
For this boundary of $Q$, the notation $partial Q$ is common.
Referring to my example above, you could have the unit disc $Q$:
$$Q=leftleft(x,yright)inmathbbR^2 ;vert; x^2+y^2 le 1right$$
and its boundary, the unit circle $partial Q$ (possibly with a chosen orientation):
$$partial Q=leftleft(x,yright)inmathbbR^2 ;vert; x^2+y^2 = 1right$$
Related: Meaning of partial differential in limits of integration?
answered Mar 28 at 15:16
StackTDStackTD
24.3k2254
$endgroup$
add a comment |
$begingroup$
Because the double integral is over some region $Q$ (e.g. a disc), while the line integral is over the boundary of $Q$ (e.g. the circle bounding that disc): they're not the same.
You can give it another name if you like, such as "$C$, the boundary of $Q$", but I wouldn't call it $Q$ again since $Q$ is already used for the entire region!
For this boundary of $Q$, the notation $partial Q$ is common.
Referring to my example above, you could have the unit disc $Q$:
$$Q=leftleft(x,yright)inmathbbR^2 ;vert; x^2+y^2 le 1right$$
and its boundary, the unit circle $partial Q$ (possibly with a chosen orientation):
$$partial Q=leftleft(x,yright)inmathbbR^2 ;vert; x^2+y^2 = 1right$$
Related: Meaning of partial differential in limits of integration?
answered Mar 28 at 15:16
StackTDStackTD
24.3k2254
$endgroup$
Because the double integral is over some region $Q$ (e.g. a disc), while the line integral is over the boundary of $Q$ (e.g. the circle bounding that disc): they're not the same.
You can give it another name if you like, such as "$C$, the boundary of $Q$", but I wouldn't call it $Q$ again since $Q$ is already used for the entire region!
For this boundary of $Q$, the notation $partial Q$ is common.
Referring to my example above, you could have the unit disc $Q$:
$$Q=leftleft(x,yright)inmathbbR^2 ;vert; x^2+y^2 le 1right$$
and its boundary, the unit circle $partial Q$ (possibly with a chosen orientation):
$$partial Q=leftleft(x,yright)inmathbbR^2 ;vert; x^2+y^2 = 1right$$
Related: Meaning of partial differential in limits of integration?
answered Mar 28 at 15:16
StackTDStackTD
24.3k2254
edited Mar 28 at 15:26
answered Mar 28 at 15:16
StackTDStackTD
24.3k2254
answered Mar 28 at 15:16
StackTDStackTD
24.3k2254
answered Mar 28 at 15:16
StackTDStackTD
24.3k2254
24.3k2254
add a comment |
add a comment |
Thanks for contributing an answer to Mathematics Stack Exchange!
- Please be sure to answer the question. Provide details and share your research!
But avoid …
- Asking for help, clarification, or responding to other answers.
- Making statements based on opinion; back them up with references or personal experience.
Use MathJax to format equations. MathJax reference.
To learn more, see our tips on writing great answers.
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
Required, but never shown
StackExchange.ready(
function ()
StackExchange.openid.initPostLogin('.new-post-login', 'https%3a%2f%2fmath.stackexchange.com%2fquestions%2f3166016%2ffor-greens-theorem-why-is-the-region-of-integration-of-the-line-integral-a-wei%23new-answer', 'question_page');
);
Post as a guest
Required, but never shown
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
Required, but never shown
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
Required, but never shown
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
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
