Talk:Partial differential equation: Difference between revisions
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==Rewrite needed== |
==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--> |
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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::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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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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== Definition of the quasi-linear equations == |
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I saw that in the article [[Method of characteristics]] is mentioned a quasi-linear type of equation. But the definition can't be found on Wikipedia and there's a link to wolfram Mathematica language specification. I think this article could be suited for the definition of such equations. What do you think about it? Where should it be written? |
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== Comparison with simple differential equations == |
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:If someone decides to add the definition, I have a book that can be used as a reference. [[User:MaxwellMolecule|MaxwellMolecule]] ([[User talk:MaxwellMolecule|talk]]) 19:13, 19 June 2020 (UTC) |
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:I have made this addition, see semilinear and quasilinear in the page [[User:Nick Mulgan|Nick Mulgan]] ([[User talk:Nick Mulgan|talk]]) 04:25, 27 November 2020 (UTC) |
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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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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)