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Talk:Differential equation

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713:"In the mathematical treatment of the exact sciences, mathematical quantities are assigned symbolic variables, such as 't' for time, 'x, y, z' for position coordinates, 'm' for mass, and so on. Calculus is the study of the rates at which some of these variables change relative to the others. In the course of expressing a law, equations arise which contain both the variables themselves, and their rates of change, and it is these that are called 'differential equations.' The task that the subject of Differential Equations sets itself is broadly to understand the meaning of a differential equation in terms of the geometry that underlies it, and to discover, if possible, simpler equations with fewer of those rates of change (or 'derivatives', as they are called). In particular, if it possible, it is desired to obtain an equation with no rates of change (derivatives) at all." 117: 107: 86: 53: 228: 1399: 44: 195: 1340:, only the ODE case is considered. Moreover, the theory of linear ODE is well developed and widely taught, while the theory of linear PDE is must less known. It could be said in the section on PDE's that linear PDE's have been considered, but this should require an article to be linked to. Apparently such an article does exists ( 619:
air resistance. Gravity is considered constant, and air resistance may be modeled as proportional to the ball's velocity. This means that the ball's acceleration, which is a derivative of its velocity, depends on the velocity. Finding the velocity as a function of time involves solving a differential equation.
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A differential equation is, quite frankly, a technical thing, and a non-specialist can't seriously hope to understand the whole business by reading a Knowledge article. If one of you folks is a good writer (but might not know the mathematics, but is on board with the objective of making a stab at an
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This article flows poorly. Obstructive clauses abound. There is also a decent amount of unnecessary language. I am going to attempt to fix it in a series of small edits so they can be reviewed. Would someone please double check what I do? I don't want to delete something important or add any mistakes
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I respectfully disagree based on how an introductory class on differential equation is often taught. Usually one starts by talking about ODEs and PDEs, Linear and Non-linear, Homogeneous and Non-homogeneous (which could be added). Also, linear PDEs like the diffusion equation, the wave equation, and
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Not sure how you fixed the first example. It still does not fit the definition given. Since the formal definition you quote says "although at least one derivative must be present", just use that in a simplified definition: an equation where at least one derivative of an unknown function is present.
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The example that you cite was incorrectly stated. I have fixed it. This is true that a formal definition, should be "a mathematical equation that relates some function with its derivatives and its variable(s); the unknown function, the variables or and the derivatives need not to appear all in the
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The current definition of Differential Equation "a mathematical equation that relates some function with its derivatives" is technically not correct. For instance, the very first example provided in the page, dy/dx=f(x), is not a differential equation according to this definition since it does not
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An example of modelling a real world problem using differential equations is the determination of the velocity of a ball falling through the air, considering only gravity and air resistance. The ball's acceleration towards the ground is the acceleration due to gravity minus the deceleration due to
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The unreadability of the article arises not for want of effort, but by the nature of the material. The general suggestion to keep only the most qualitative descriptions of the problems and the approaches here, and move all procedural and specific material to other specialized pages is the only
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Seconded. As the it currently stands, the casual reader (such as myself) ends up with 42 browser tabs open with all the fancy math nerd terms used. Since those pages then reference other terms, the cycle is endless. An article this high on the list of frequently referenced math subjects should
555:- is this implying that differential equation is ONLY for physical objects? because differential equation is applied to lots of different things. why it classical mechanics being used as an example? and only that? this is undue weight. this is also doesnt seem to be a really good example 1320:
Just like ODE and PDE are defined with their own section, I think it would be appropriate to define Linear and Non-Linear equations in their own section. Right now the definition of a Linear DE is buried inside the definition of an ODE. But PDE can be linear too.
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illustrate - with visuals and/or English - why exactly a differential equation is a differential equation, and show at least one example with a complete description of usage in a real-world scenario that can be followed with natural human intuition.
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The Examples give formulas, but no indication of what real-world problems they relate to. A non-expert might well be helped by knowing that a particular formula describes behaviors that they already know about in a non-mathematical context.
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In my reading, the lead does say (in the second and third paragraph) what a differential equation is used for. Do you think those paragraphs can be improved (and if so, how), or are you concerned about something else? I don't see what part of
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to express these variables dynamically as a differential equation for the unknown position of the body as a function of time. In some cases, this differential equation (called an equation of motion) may be solved explicitly
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Differential Equations is an extremely rich field, but this wall of text does not do it justice. Even as a physicist, I am not engaged by this article... Now how interested do think an average teenager would be?
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As a side note, please fix the definition of non-linear equation: "Non-linear differential equations are formed by the products of the unknown function and its derivatives are allowed and its degree is :
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relate y to its derivative. That's why I had changed the definition to "a mathematical equation where one or more derivatives of an unknown function are presents", which I think is more appropriate.
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and places too much emphasis on ODEs for this article, which should balance PDEs and ODEs. I am going to remove most of that section (especially deleting the table) and modify the more general section
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The article has one of the funnier ones. Before we get to the article at all we have a screenfull of edi-boxes, of which the first begins "This article or section lacks a single coherent topic."
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for that content in the latter page, and it must not be deleted so long as the latter page exists. Please leave this template in place to link the article histories and preserve this attribution.
543:- what body? do you mean object? like a boat? or any physical "object" -- does body specifically refer to physically bodies or what? does it include digital objects? this is very very unclear 173: 1498: 1488: 475: 549:- what time value? what is this referring to? to the independent variable or the dependent one? where is this coming from? something said earlier? or frrom nowhere? 562:- so what is this trying to find? what does differential equation finding? is it finding where the ball will land exactly? or the radius where the ball will land? 1503: 1051: 1047: 1033: 57: 1268:
equation, although at least one derivative must be present". However such a formal definition would be confusing in the first sentence: The manual of style
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Here are some ideas: talk about analytically tractable vs. intractable DEs, with imagery illuminating both. Perhaps a lorenz attractor for the latter
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As is too often the case, a perfectly sensible Knowledge entry comes littered with colourful boxes sprinkled about by nit-wit editors.
756: 213: 310:'s and should be moved to that article, also the nomenclature should be more standard (I'm in the process of rewriting that article). 130: 91: 749:
The article says: "solutions —the set of functions that satisfy the equation" but is the class of solutions really always a set?
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When one talks of "linear differential equation" most people think "linear ODE". A witness of this is that in the article
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this article needs to improve, it's really unreadable. it's unclear. you need to make it understandable to non-experts,
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What is the problem? The class of all functions from a given set to a given set is a set; and every its subclass is.
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One cannot help but be reminded of Will Rogers's "I am a member of no organized political party. I am a Democrat."
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or does it find the change between the speed of the ball in the current second compared with the previous second?.
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to delete these "External links modified" talk page sections if they want to de-clutter talk pages, but see the
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Newton's laws allow one (given the position, velocity, acceleration and various forces acting on the body)
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and then when you edit something, ppl dont improve it, all they do is change it back to the trash it was
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If you have discovered URLs which were erroneously considered dead by the bot, you can report them with
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Could anyone write down the specific equation, rather than list the title or the name of the equation?
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and some of these articles just has who in the first sentence or 2, all articles should at least have
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http://en.wikipedia.org/search/?title=Differential_equation&diff=516518566&oldid=516434444
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http://en.wikipedia.org/search/?title=Differential_equation&diff=516518566&oldid=516434444
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on Knowledge. If you would like to participate, please visit the project page, where you can join
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approach that will work. (Look in Brittanica, 1974. The problem was not solved there, either.)
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before doing mass systematic removals. This message is updated dynamically through the template
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the lead should say what differential equation does. what it is used for and what it finds out.
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Homeomorphically here, the article has no coherent topic. It is about differential equations.
537:- yawns, i dont understand why some of articles are so dragged out and never get to the point0 522:
specifically whenever a deterministic relation involving some continuously varying quantities
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Why is it not allowed to mention some programs that are able to solve differential equations:
1219: 914: 868: 826: 668: 479: 1199:", but I can't find any mentions of this equation online. Does this equation actually exist? 1000:
https://web.archive.org/web/20060829045130/http://www.alberteinstein.info/gallery/gtext3.html
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More images helping to explain concepts or provide examples/representations would be nice.
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1" is not grammatical. It also does not consider non-linear terms like y^(1/2) or sin(y).
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https://moodle.insa-toulouse.fr/pluginfile.php/35347/mod_label/intro/LorenzAttractor.png
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Two of them were added by a drive-by editor without any explanation. I removed them. --
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http://en.wikipedia.org/search/?title=Time_series&diff=518032407&oldid=516614772
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anyway, i'll break it down for anyone who likes to make readable articles on wikipedia:
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If you found an error with any archives or the URLs themselves, you can fix them with
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the Laplace equation, are all taught in an introductory differential equation class.
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Actually, the editor did somewhat explain his reasoning when he added those tags (
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Why not separate Linear Differential Equation definition from ODE definition?
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that's just one example, i'll add more after the first problem is cleared up
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im not sure why it doesn't come earlier. the 5ws includes who, what, etc.
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introduction for the layman,) here's something you might be able to use.
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http://en.wikipedia.org/Wikipedia:Make_technical_articles_understandable
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Differential equations arise in many areas of science and technology,
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I'm not sure how to deal with these problems, but here goes nothing.
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is described by its position and velocity as the time value varies.
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The lead sentence should informally define or describe the subject
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if not, then is it finding how fast the ball will go every second?
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I have never heard of this. I am going to remove that redlink. –
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the article was just trash orginally and nobody was improving it
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Blend/remove classification summary and nomenclature sections
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When you have finished reviewing my changes, please set the
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I stand corrected. No idea how I could have missed that. --
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for additional information. I made the following changes:
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if so, is that the only thing differential equation does?
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Differential_equation#Non-linear_differential_equations
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ALL ARTICLES SHOULD BE DOING THIS IN THE FIRST SENTENCE
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if not, then is it finding how fast the ball will go?
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That table is quite useful to have, but its only on
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The former page's 1445: 1372: 1113: 982:I have just modified one external link on 278: 80: 787:Add real-world grounding to the Examples 1489:Knowledge vital articles in Mathematics 933:Sections could benefit by adding images 745:Is the class of solutions always a set? 653:...it is used for signal detection and 82: 41: 1273: 633:very important example of what is good 18:Talk:Degree of a differential equation 1504:B-Class vital articles in Mathematics 1021:to let others know (documentation at 573:if so, it's made incrediably complex. 7: 206:List of named differential equations 128:This article is within the scope of 27:Old talk moved (along with page) to 71:It is of interest to the following 29:Talk:Ordinary differential equation 25: 1514:Top-priority mathematics articles 986:. Please take a moment to review 615:- ok, i think i'll stop here... 148:Knowledge:WikiProject Mathematics 1484:Knowledge level-4 vital articles 1397: 643:someone actually made it better 226: 193: 151:Template:WikiProject Mathematics 115: 105: 84: 51: 42: 1190: 1133:Nonlinear differential equation 168:This article has been rated as 1494:B-Class level-4 vital articles 968:02:54, 14 September 2014 (UTC) 352:Ordinary differential equation 1: 1346:Partial differential equation 1270:MOS:MATH#Article introduction 1224:12:20, 20 November 2018 (UTC) 1209:05:54, 20 November 2018 (UTC) 1100:00:06, 13 December 2016 (UTC) 891:), but it is easy to miss. — 831:14:11, 12 December 2013 (UTC) 142:and see a list of open tasks. 1509:B-Class mathematics articles 1338:Linear differential equation 923:13:57, 14 January 2014 (UTC) 901:11:16, 14 January 2014 (UTC) 877:08:31, 14 January 2014 (UTC) 862:05:13, 12 January 2014 (UTC) 738:21:22, 13 January 2014 (UTC) 701:07:51, 16 October 2012 (UTC) 540:where the motion of a body 494:list of problems in the lead 488:09:19, 12 October 2012 (UTC) 421:10:35, 8 October 2012 (UTC) 359: 311: 1530: 1464:16:39, 25 April 2020 (UTC) 1063:(last update: 5 June 2024) 979:Hello fellow Wikipedians, 781:19:12, 11 April 2013 (UTC) 765:15:30, 11 April 2013 (UTC) 348:Ordinary DE classification 1414:22:18, 20 June 2019 (UTC) 1391:20:22, 20 June 2019 (UTC) 1358:18:59, 20 June 2019 (UTC) 1331:17:28, 20 June 2019 (UTC) 1301:20:15, 20 June 2019 (UTC) 1286:18:40, 20 June 2019 (UTC) 1252:17:25, 20 June 2019 (UTC) 1185:07:15, 21 June 2018 (UTC) 1162:05:10, 21 June 2018 (UTC) 385:07:08, 18 June 2012 (UTC) 293:13:48, 3 March 2020 (UTC) 167: 100: 79: 1126:) 19:06, 26 January 2016 813:05:41, 30 May 2013 (UTC) 478:you are refering to. -- 350:is already contained in 337:10:02, 23 May 2012 (UTC) 174:project's priority scale 35:20:54, 23 Jan 2005 (UTC) 1195:This article mentions " 1140:This page redirects to 1109:The section of physics 975:External links modified 637:look at the changes on 131:WikiProject Mathematics 1479:B-Class vital articles 1105:The section on physics 512:breaking down the lead 1197:the Sagnik's equation 984:Differential equation 428:article is unreadable 202:Differential equation 58:level-4 vital article 1152:. 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1244:Amanfroi 1237:D.Lazard 1116:unsigned 1084:Cheers.— 964:contribs 952:unsigned 809:contribs 797:unsigned 753:unsigned 734:contribs 726:Arch5280 722:unsigned 687:Coginsys 623:Coginsys 525:- ok... 465:contribs 457:Coginsys 453:unsigned 417:contribs 409:Coginsys 405:unsigned 281:unsigned 233:Archives 1452:MacApps 1261:editor 1216:Tea2min 1171:Dolphin 1011:checked 988:my edit 823:Krushia 697:undated 210:history 172:on the 63:B-class 1201:Jarble 1154:Jarble 1019:failed 69:scale. 1426:Maple 1403:Fixed 369:E+v×B 321:E+v×B 50:This 31:. -- 1456:talk 1440:and 1438:Xcas 1410:talk 1383:talk 1354:talk 1327:talk 1297:talk 1282:talk 1248:talk 1220:talk 1205:talk 1158:talk 1124:talk 1015:true 960:talk 919:talk 897:talk 888:diff 873:talk 858:talk 827:talk 805:talk 777:talk 761:talk 730:talk 691:talk 627:talk 484:talk 461:talk 444:see 413:talk 289:talk 272:Flow 1370:--> 1052:RfC 1029:). 1017:or 1002:to 693:) 374:⇄ ∑ 326:⇄ ∑ 308:ODE 164:Top 1475:: 1462:) 1458:• 1436:, 1432:, 1428:, 1412:) 1389:) 1385:• 1356:) 1329:) 1299:) 1284:) 1259:To 1250:) 1222:) 1207:) 1160:) 1065:. 1060:}} 1056:{{ 1027:}} 1023:{{ 966:) 962:• 921:) 899:) 875:) 860:) 829:) 811:) 807:• 779:) 763:) 736:) 732:• 663:, 650:" 629:) 505:. 486:) 467:) 463:• 419:) 415:• 367:q( 319:q( 291:) 1454:( 1408:( 1381:( 1352:( 1325:( 1318:: 1314:@ 1295:( 1280:( 1265:: 1246:( 1239:: 1235:@ 1218:( 1203:( 1182:) 1179:t 1176:( 1156:( 1122:( 1097:) 1093:( 1080:. 1073:. 958:( 917:( 895:( 871:( 856:( 825:( 803:( 775:( 759:( 728:( 689:( 625:( 482:( 459:( 411:( 380:i 378:c 376:i 371:) 364:= 362:F 332:i 330:c 328:i 323:) 316:= 314:F 287:( 176:. 75:: 20:)

Index

Talk:Degree of a differential equation
Talk:Ordinary differential equation
Walt Pohl

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Differential equation
List of named differential equations
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Archive 1
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70.127.17.241
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13:48, 3 March 2020 (UTC)
ODE
F =

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