Talk:Partial differential equation: Difference between revisions
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==Rewrite needed== |
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Can somebody who understands this article rewrite the following please? "Partial differential equations also occupy a large sector of pure mathematical research, in which the usual questions are, broadly speaking, on the identification of general qualitative features of solutions of various partial differential equations, such as existence, uniqueness, regularity, and stability." As is, it is incomprehensible. Perhaps break it into two or three sentences? <!-- Template:Unsigned IP --><small class="autosigned">— Preceding [[Wikipedia:Signatures|unsigned]] comment added by [[Special:Contributions/2600:1702:170:3B90:252F:91F:542:7612|2600:1702:170:3B90:252F:91F:542:7612]] ([[User talk:2600:1702:170:3B90:252F:91F:542:7612#top|talk]]) 17:59, 26 October 2022 (UTC)</small> <!--Autosigned by SineBot--> |
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:I agree that area is incomprehensible. I find the entire article to be incomprehensible. Start over. Boil it down to exactly what is a PDE. Precisely. Explain each part precisely. Only then go into why PDE's are useful, and solutions and etc.. |
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:[[User:J Mark Morris|J Mark Morris]] ([[User talk:J Mark Morris|talk]]) 01:44, 20 May 2024 (UTC) |
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::Even the first sentence is very confusing: "In mathematics, a partial differential equation (PDE) is an equation which computes a function between various partial derivatives of a multivariable function." I cannot tell what the word "between" is supposed to mean there, and an equation doesn't "compute" anything. [[Special:Contributions/74.96.10.88|74.96.10.88]] ([[User talk:74.96.10.88|talk]]) 15:01, 10 December 2024 (UTC) |
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== Notation and examples == |
== Notation and examples == |
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'''thermal diffusivity'''.<br> |
'''thermal diffusivity'''.<br> |
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[[User:Chentianran|Tianran Chen]] 03:56, 2004 Mar 1 (UTC) |
[[User:Chentianran|Tianran Chen]] 03:56, 2004 Mar 1 (UTC) |
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Tianran, are you still alive? <!-- Template:Unsigned IP --><small class="autosigned">— Preceding [[Wikipedia:Signatures|unsigned]] comment added by [[Special:Contributions/37.232.69.137|37.232.69.137]] ([[User talk:37.232.69.137#top|talk]]) 04:17, 19 April 2022 (UTC)</small> <!--Autosigned by SineBot--> |
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== Conceptual Definition == |
== Conceptual Definition == |
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What i would like to know is if there exists such a nice conceptual definition of a PDE. |
What i would like to know is if there exists such a nice conceptual definition of a PDE. |
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==Wiki Education assignment: 4A Wikipedia assignment== |
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==Assessment comment== |
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{{dashboard.wikiedu.org assignment | course = Wikipedia:Wiki_Ed/Riverside_City_College/4A_Wikipedia_assignment_(spring_2023) | assignments = [[User:Jalenlthomas|Jalenlthomas]] | reviewers = [[User:Ogomzn|Ogomzn]], [[User:Jmorales169|Jmorales169]] | start_date = 2023-02-13 | end_date = 2023-06-12 }} |
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{{Substituted comment|length=291|lastedit=20070609221626|comment=The front-line article on PDEs should cover vector-valued PDEs (aka, systems, which are mentioned briefly). Fundamental concepts such as underdetermined, determined, and overdetermined PDEs need to be discussed more systematically. [[User:Geometry guy|Geometry guy]] 22:16, 9 June 2007 (UTC)}} |
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Substituted at 02:27, 5 May 2016 (UTC) |
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== Can someone please add a section on the unified transform (Fokas) method == |
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We need a section on the [http://unifiedmethod.azurewebsites.net/introduction.html unified transform method], first published by [[Athanassios Fokas]]. The number of [http://unifiedmethod.azurewebsites.net/authors.html mathematicians] researching this area is large, and so is the number of [http://unifiedmethod.azurewebsites.net/applications.html applications]. Perhaps someone who can explain it properly can help us out? [[User:Yoodlepip|Yoodlepip]] ([[User talk:Yoodlepip|talk]]) 20:11, 1 January 2017 (UTC) |
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<span class="wikied-assignment" style="font-size:85%;">— Assignment last updated by [[User:Lzepeda12|Lzepeda12]] ([[User talk:Lzepeda12|talk]]) 21:08, 26 April 2023 (UTC)</span> |
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== Comparison with simple differential equations == |
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== Classification section == |
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It would be nice to have an explanation of the difference between simple differential equations in one variable and partial differential equations in multiple variables, with worked examples. |
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It doesn't seem to me that the classification of PDEs needs so much coverage compared to other things. Should we create a separate article for the classification, going into full detail and implications, while adding a word on terminology like "order" and say simply that PDEs can be classified according to their behaviour, with a link to that separate article? [[User:Direwolf202|Direwolf202]] ([[User talk:Direwolf202|talk]]) 14:20, 22 April 2019 (UTC) |
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The current article tells us how they are used but not the very basic step of what happens to the other variables, an explanation of which would let people take the step between the two more easily. [[User:Robin Murison|Robin Murison]] ([[User talk:Robin Murison|talk]]) 10:58, 20 April 2023 (UTC) |
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Rewrite needed
[edit]Can somebody who understands this article rewrite the following please? "Partial differential equations also occupy a large sector of pure mathematical research, in which the usual questions are, broadly speaking, on the identification of general qualitative features of solutions of various partial differential equations, such as existence, uniqueness, regularity, and stability." As is, it is incomprehensible. Perhaps break it into two or three sentences? — Preceding unsigned comment added by 2600:1702:170:3B90:252F:91F:542:7612 (talk) 17:59, 26 October 2022 (UTC)
- I agree that area is incomprehensible. I find the entire article to be incomprehensible. Start over. Boil it down to exactly what is a PDE. Precisely. Explain each part precisely. Only then go into why PDE's are useful, and solutions and etc..
- J Mark Morris (talk) 01:44, 20 May 2024 (UTC)
- Even the first sentence is very confusing: "In mathematics, a partial differential equation (PDE) is an equation which computes a function between various partial derivatives of a multivariable function." I cannot tell what the word "between" is supposed to mean there, and an equation doesn't "compute" anything. 74.96.10.88 (talk) 15:01, 10 December 2024 (UTC)
Notation and examples
[edit]Heat equation
[edit]In the section Heat equation,
the constant k is usually referred to as
thermal diffusivity.
Tianran Chen 03:56, 2004 Mar 1 (UTC)
Tianran, are you still alive? — Preceding unsigned comment added by 37.232.69.137 (talk) 04:17, 19 April 2022 (UTC)
Conceptual Definition
[edit]Arnold defines an ODE in his book as a system evolving in time having the following properties: (1) determinancy (2) finite dimensionality (3) smoothness
where by determinancy he means that the initial data of the problem completely specifies the future and the past of the system. By a finite dim. system he means one whose phase space can be localy parametrized by finite many real numbers. The smoothness property means that the system has a smooth phase space (ie. the phase space is a differentiable manifold, eg. The plane, the real line) and smooth evolution function.
What i would like to know is if there exists such a nice conceptual definition of a PDE.
Wiki Education assignment: 4A Wikipedia assignment
[edit]
This article was the subject of a Wiki Education Foundation-supported course assignment, between 13 February 2023 and 12 June 2023. Further details are available on the course page. Student editor(s): Jalenlthomas (article contribs). Peer reviewers: Ogomzn, Jmorales169.
— Assignment last updated by Lzepeda12 (talk) 21:08, 26 April 2023 (UTC)
Comparison with simple differential equations
[edit]It would be nice to have an explanation of the difference between simple differential equations in one variable and partial differential equations in multiple variables, with worked examples. The current article tells us how they are used but not the very basic step of what happens to the other variables, an explanation of which would let people take the step between the two more easily. Robin Murison (talk) 10:58, 20 April 2023 (UTC)