Mixed boundary condition for the heat equation
$begingroup$
Would someone help me understand the way the solution obtained in this question:
Heat Equation Mixed Boundaries Case: Fourier Coefficients
I did not understand why in the final solution, he took $b_m$ and not $b_{2m-1}$. I am confused not just because of the rank of the coefficients, this is because according to this rank $$b_m= frac{1}{L} int_{0}^{2L} f(x) sinBig(frac{m pi x}{2L}Big)$$ or
$$b_{2m-1}= frac{1}{L} int_{0}^{2L} f(x) sinBig(frac{(2m-1) pi x}{2L}Big)$$
Sorry if I appear much confused, but I really want to understand it.
Thanks in adavnce.
pde boundary-value-problem heat-equation linear-pde
asked Dec 8 '18 at 13:10
NizarNizar
2,39921023
$endgroup$
add a comment |
$begingroup$
Would someone help me understand the way the solution obtained in this question:
Heat Equation Mixed Boundaries Case: Fourier Coefficients
I did not understand why in the final solution, he took $b_m$ and not $b_{2m-1}$. I am confused not just because of the rank of the coefficients, this is because according to this rank $$b_m= frac{1}{L} int_{0}^{2L} f(x) sinBig(frac{m pi x}{2L}Big)$$ or
$$b_{2m-1}= frac{1}{L} int_{0}^{2L} f(x) sinBig(frac{(2m-1) pi x}{2L}Big)$$
Sorry if I appear much confused, but I really want to understand it.
Thanks in adavnce.
pde boundary-value-problem heat-equation linear-pde
asked Dec 8 '18 at 13:10
NizarNizar
2,39921023
$endgroup$
1
$begingroup$
Use$sin$for $sin$ (instead of$sin$for $sin$).
$endgroup$
– Shaun
Dec 8 '18 at 13:22
$begingroup$
Both formulas are equivalent. The first one restricts the subscript $m$ to odd integers; the second one doesn't.
$endgroup$
– Dylan
Dec 13 '18 at 4:28
add a comment |
$begingroup$
Would someone help me understand the way the solution obtained in this question:
Heat Equation Mixed Boundaries Case: Fourier Coefficients
I did not understand why in the final solution, he took $b_m$ and not $b_{2m-1}$. I am confused not just because of the rank of the coefficients, this is because according to this rank $$b_m= frac{1}{L} int_{0}^{2L} f(x) sinBig(frac{m pi x}{2L}Big)$$ or
$$b_{2m-1}= frac{1}{L} int_{0}^{2L} f(x) sinBig(frac{(2m-1) pi x}{2L}Big)$$
Sorry if I appear much confused, but I really want to understand it.
Thanks in adavnce.
pde boundary-value-problem heat-equation linear-pde
asked Dec 8 '18 at 13:10
NizarNizar
2,39921023
$endgroup$
Would someone help me understand the way the solution obtained in this question:
Heat Equation Mixed Boundaries Case: Fourier Coefficients
I did not understand why in the final solution, he took $b_m$ and not $b_{2m-1}$. I am confused not just because of the rank of the coefficients, this is because according to this rank $$b_m= frac{1}{L} int_{0}^{2L} f(x) sinBig(frac{m pi x}{2L}Big)$$ or
$$b_{2m-1}= frac{1}{L} int_{0}^{2L} f(x) sinBig(frac{(2m-1) pi x}{2L}Big)$$
Sorry if I appear much confused, but I really want to understand it.
Thanks in adavnce.
pde boundary-value-problem heat-equation linear-pde
pde boundary-value-problem heat-equation linear-pde
asked Dec 8 '18 at 13:10
NizarNizar
2,39921023
asked Dec 8 '18 at 13:10
NizarNizar
2,39921023
edited Dec 8 '18 at 14:11
Nizar
asked Dec 8 '18 at 13:10
NizarNizar
2,39921023
asked Dec 8 '18 at 13:10
NizarNizar
2,39921023
asked Dec 8 '18 at 13:10
NizarNizar
2,39921023
2,39921023
1
$begingroup$
Use$sin$for $sin$ (instead of$sin$for $sin$).
$endgroup$
– Shaun
Dec 8 '18 at 13:22
$begingroup$
Both formulas are equivalent. The first one restricts the subscript $m$ to odd integers; the second one doesn't.
$endgroup$
– Dylan
Dec 13 '18 at 4:28
add a comment |
1
$begingroup$
Use$sin$for $sin$ (instead of$sin$for $sin$).
$endgroup$
– Shaun
Dec 8 '18 at 13:22
$begingroup$
Both formulas are equivalent. The first one restricts the subscript $m$ to odd integers; the second one doesn't.
$endgroup$
– Dylan
Dec 13 '18 at 4:28
1
1
$begingroup$
Use
$sin$ for $sin$ (instead of $sin$ for $sin$).$endgroup$
– Shaun
Dec 8 '18 at 13:22
$begingroup$
Use
$sin$ for $sin$ (instead of $sin$ for $sin$).$endgroup$
– Shaun
Dec 8 '18 at 13:22
$begingroup$
Both formulas are equivalent. The first one restricts the subscript $m$ to odd integers; the second one doesn't.
$endgroup$
– Dylan
Dec 13 '18 at 4:28
$begingroup$
Both formulas are equivalent. The first one restricts the subscript $m$ to odd integers; the second one doesn't.
$endgroup$
– Dylan
Dec 13 '18 at 4:28
add a comment |
0
active
oldest
votes
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%2f3031090%2fmixed-boundary-condition-for-the-heat-equation%23new-answer', 'question_page');
}
);
Post as a guest
Required, but never shown
0
active
oldest
votes
0
active
oldest
votes
active
oldest
votes
active
oldest
votes
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%2f3031090%2fmixed-boundary-condition-for-the-heat-equation%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
1
$begingroup$
Use
$sin$for $sin$ (instead of$sin$for $sin$).$endgroup$
– Shaun
Dec 8 '18 at 13:22
$begingroup$
Both formulas are equivalent. The first one restricts the subscript $m$ to odd integers; the second one doesn't.
$endgroup$
– Dylan
Dec 13 '18 at 4:28