![]() | This is an archive of past discussions. Do not edit the contents of this page. If you wish to start a new discussion or revive an old one, please do so on the current talk page. |
Archive 1 | Archive 2 |
At the very beginning of this article is the strange:
" In mathematics, the Laplace transform is a technique for analyzing linear time-invariant systems such as electrical circuits, harmonic oscillators, optical devices, and mechanical systems."
However, electrical circuits, harmonic oscillators, optical devices, and mechanical systems are subjects of physics and technical sciences, not of mathematics per se. It will be more appropriate to replace mathematics with physics. On the other hand, the main use of Laplace transform in mathematics proper is for solving differential equations. I do not see this in the introduction. Lantonov 14:31, 20 July 2007 (UTC)
I wrote a new intro/definition which can be understood by persons with high-school math background which immediately leads the reader to possible applications. Lantonov 05:30, 30 August 2007 (UTC)
"The method of using the Laplace Transform to solve differential equations was developed by the English electrical engineer Oliver Heaviside." The Oliver Heaviside wikipedia article also suggests this. Can anyone site a reference supporting this?
Oliver Heaviside developed an operational calculus for solving differential equations, while similar to using the Laplace transform it is not the same. This site goes into more detail. http://www.du.edu/~jcalvert/math/laplace.htm Yardleydobon 20:04, 30 April 2007 (UTC)
I notice many texts refer to the Laplace "Transformation", particularly more classical texts. Would there be any problem with this minor addition? ... Laplace Transform (also known as Laplace Transformation)... Tparameter 06:00, 8 November 2006 (UTC)
Say I'm not familiar with him, and am looking him up in the Wikipedia for that reason. I would then like to find out what is so important about this Transform. When can it be used, and how? What is, again, the point of the LaPlace transform? The article does a poor job of informing 'me'.-- Ec5618 11:32, Apr 21, 2005 (UTC)
Yes, this article needs to be cleaned up. Maybe I'll do that sometime in the near future. I have no definite plans, but I might get around to it. If I do indeed get the gumption to do this, I'll do my best to include a way to solve a D.E. with it. In any case, I also wonder what this is used for. I know how to find the transform, and how to do the inverse. Pretty easy. I was taught in my D.E. class that it is useful in some physics problems, or at least in electrical engineering. So how can it be used in E.E.? I learn a lot better when I can comprehend how it will benefit me. Until then, it's trivial, much like the trivial solutions that no one cares about in D.E. Why should I care about it? D. F. Schmidt [[User_talk:D. F. Schmidt|(talk)]] 09:14, 16 November 2005 (UTC)
Maybe a small text like this can solve a lot of headaches:
"Laplace transformations are used as a tool to convert a complex equation in a very simple to use equation. This process involves 3 operations:
I don't speak english so someone should clean up this text and insert it in the article. Thx
I wrote a new intro/definition which can be understood by persons with high-school math background which immediately leads the reader to uses of the Laplace transform. Also ordered the sentences in the intro a bit. The intro is still too big, with an emphasis on physical and electronic applications. I do not find anything bad in this but think that they can be shortened a little without losing too much from their information content. Lantonov 05:31, 30 August 2007 (UTC)
I have always wanted to know how Laplace was led to the transform, but never could find much on the web. Anybody know of a direct account from Laplace? Here's something of interest perhaps.
http://www.math.niu.edu/~rusin/known-math/97/laplace.fourier
thanks Phil —Preceding
unsigned comment added by
74.170.68.234 (
talk)
04:08, 12 December 2007 (UTC)
How is this equation different from the one at the top? Taral 16:13, 27 May 2005 (UTC)
I think it would be helpful for those unfamiliar with it to define .
Agree, disagree? Guardian of Light 16:43, 14 July 2005 (UTC)
Somebody help find the laplace transform of exp(t-3) and exp(-(t-1))? Thanks
Does anyone know more about the history of Laplace
Is there relationship between Laplace transformations and the engineering used in the construction of German weapons during World War II?
For the lists of common transforms, I believe there are certain restrictions on the values that the variable s can take (e.g. see http://mathworld.wolfram.com/LaplaceTransform.html). Can we incorporate these into the table(s)? -- GregRM 23:16, 29 November 2005 (UTC)
I found an important error here.
"However, if the integral defining the Laplace transform does converge (possibly only as an improper integral) at s = s0, then it automatically converges absolutely for all s with Re{s} > Re{s0}."
This is false. Consider a function defined as follows (for positive reals): divide the interval in equal intervals. Let take the values and alternately in those intervals. Fourier transform at 0 converges conditionally, while it doesn't converge absolutely at 1. However both of the following are valid:
(absolute) convergence at implies (absolute) convergence for all with —Preceding unsigned comment added by 201.231.212.56 ( talk) 06:25, 24 November 2009 (UTC)
Does anyone know what the ROC is for the first two entries in the table below, the unit impulse and the unit step functions? I have filled in the table, but I am not sure if they are correct. Thanks. -- Metacomet 19:51, 30 November 2005 (UTC)
Please help: If anyone knows the correct Regions of Convergence (ROC) for any of the entries in the table where the ROC is missing, please feel free to add them to the appropriate cell in the table. Thanks. -- Metacomet 22:28, 8 December 2005 (UTC)
Where did you get the transforms for the Bessel function from? I think the exponent should be n instead of −n, but I'm not at all sure. -- Jitse Niesen ( talk) 18:49, 10 December 2005 (UTC)
The table here says that the transform of is
The table at MathWorld says that it is
I can't see how they can be the same. -- Jitse Niesen ( talk) 23:19, 10 December 2005 (UTC)
Well done. I had a feeling that the difference of squares rule would play a part! -- Metacomet 16:07, 11 December 2005 (UTC)
I have been mulling over the very same idea, and I had not come to any conclusions one way or the other. It might be a bit too much detail for this article. I am not sure how often Bessel functions come up in the context of Laplace transforms. It might be usefule to create a more detailed table of transforms to which this article could link. On the other hand, the external links section points readers to several excellent resources. I am not sure we should do anything just yet, maybe continue to think about it some more. As you said, there is no need to rush into anything in this case. -- Metacomet 03:27, 19 December 2005 (UTC)
Does anyone know how to change the background color from white to something else (in RGB) of a LaTeX equation inside the <math> tag? Please let me know. Thanks. -- Metacomet 03:40, 1 December 2005 (UTC)
I have now added this table to the main article. -- Metacomet 16:42, 4 December 2005 (UTC)
Yes, I think you are both correct. It does follow directly from the rule for frequency shifting. Good catch. -- Metacomet 22:16, 6 December 2005 (UTC)
Should the table use the heading Frequency Domain? I wonder if this might cause confusion with the Fourier Transform which is more commonly described as a Time-Frequency transform than the Laplace Transform. Would "Laplace Domain" or "S Domain" be more appropriate? jackocleebrown 21:20 , 30 Aprl 2007 (UTC)
I think the transforms used in the example should be included in the table so there can be a chance of following them. 70.133.83.60 ( talk) 20:50, 3 September 2010 (UTC)
The Laplace transform of 1 is 1/s but the Laplace Transform of the unit step function is ., 16 October 2011
Near the top of the article is a section on the "alternative defintions" of the Laplace transform,
Can someone elaborate on this? When and why are these alternative definitions used? - Monguin61 09:32, 9 December 2005 (UTC)
A good example is to look at the Laplace transforms for sine and cosine. Suppose that
Then we have
and
as expected. --
Metacomet
21:11, 9 December 2005 (UTC)
quote:
Near the top of the article is a section on the "alternative defintions" of the Laplace transform,
Can someone elaborate on this? When and why are these alternative definitions used? - Monguin61 09:32, 9 December 2005 (UTC)
Quote:
I think it would be helpful for those unfamiliar with it to define .
Agree, disagree? Guardian of Light 16:43, 14 July 2005 (UTC)
:Done. I discovered, somewhat by accident, that is the Euler-Mascheroni constant. -- Metacomet 05:52, 7 December 2005 (UTC)
Here's my website of example problems with Laplace transforms. Someone please put it in the external links section if you think it's helpful!
http://www.exampleproblems.com/wiki/index.php/PDE:Laplace_Transforms
Could anyone tell me why do
and
thanks...
the page of that simplied too much ,i need a lot of noting help to the result... -- HydrogenSu
I think a page of L.T. shoud give more proves below some formulas. If just showed "Formulas" might let readers confused and get some information of "just memorize them". If improving,it is nicer. :)-- HydrogenSu 12:00, 14 February 2006 (UTC)
@.Why the Applications part had to be put in an article of Laplace Trs.? It shall be put at the nearly ending.-- GyBlop 08:41, 24 February 2006 (UTC)
I think it would be very useful to have a table or list of how to transform circuit elements (like resistors capacitors inductors, sources, etc) into s-domain elements. For example, the transform of an inductor with an initial current of I is an inductor and a source in series with s-domain values... but I'm not quite sure what those are at the moment. Fresheneesz 08:53, 21 April 2006 (UTC)
I had intended to re-direct a link to 'first order lag' to this article, but although Laplace transforms are intimately related to transfer functions, this has not proved as helpful as I had hoped. The article isn't bad as it stands, but a note in the introduction to the effect that the LT provides a means of transforming differential equations into algebraic equations might motivate the non-specialist to read further, rather than dismiss the whole thing as another example of Emperor's New Clothes. Gordon Vigurs 19:16, 14 May 2006 (UTC)
Apparently this is a fairly recent discovery, and I haven't looked to see where it was published, but apparently the following holds:
If , and , then at any point of continuity of f, .
Of course, actually calculating that for arbitrary f is rather cumbersome, but it is better for complex-integralophobics. Confusing Manifestation 05:05, 16 May 2006 (UTC)
I keep comming across transfer functions that involve a term s/(a+s), for example a series RC circuit. Why is the transfer function not in the table here, and in fact not in any tables I've seen. I must be missing something key, but .. I don't know what that would be. Fresheneesz 23:29, 26 May 2006 (UTC)
Could someone post an example using a second order differential equation where the roots are complex? The sign changes associated with the real part of the root that are in the denominator of the partial fraction expansion are confusing and should be explained. Thanks.
Statum (
talk)
13:45, 25 January 2011 (UTC)
I think number 2 in the table is wrong ...
delayed nth power with frequency shift ==> ====> ||
It doesn't look right to me.
Hi, I just wanted to note, that the notation u(t) for the unit step is not very well chosen, because u(t) is also often used in electronics and control engineering for the input signal, which is often Laplace-transformed itself. I would suggest to use another name for the unit step, for example σ(t) or H(t) for the Heaviside-function. Your opinions?
I agree with the first chap. As a mathematician, I have never seen the Heaviside function denoted by anything other than H(t). —Preceding unsigned comment added by 62.31.164.38 ( talk) 21:41, 14 May 2011 (UTC)
In systems theory it is usually denoted by 1(t) which was probably Heaviside's notation. JFB80 ( talk) 19:36, 15 May 2011 (UTC)
The u(t) notation is used in engineering. The notation, however, usually carries a (power of s) subscript to denote doublet, impulse, step, ramp, etc. IIRC, u0(t) is an impluse; u-1(t) is a step. That some people have never seen it says little. Glrx ( talk) 19:48, 15 May 2011 (UTC)
Why not check up on a few standard books, e.g. Schaum's Outline. JFB80 ( talk) 12:59, 16 May 2011 (UTC)
Hello, in the table the last transform we have is:
Where I'm fairly sure that since we could express instead as:
I think this would be a better way of expressing this because it is already clear what erf(z) means in the original context of the table, but it is not clear what erfc(z) is unless the Error function article has already been read (and it seems problematic to link directly there lest erf(z) and erfc(z) be confused).
I will make this edit in a few days if no one objects, but I wanted to see if I an consensus existed as well. Please let me know your thoughts. Thanks. - SocratesJedi | Talk 08:53, 29 January 2007 (UTC)
Under Differential equation example 1 we have:
Next, we take the Laplace transform of both sides of the equation:
where
The notation was removed in favor of just keeping N(s) where N(t) represented time domain and N(s) represented s-domain signals to keep the notation simple. I reverted this to reinclude the tilde N because I think it's necessary to make it clear that N(t) and N(s) are not the same function with t --> s, but are entirely different (but related through the Laplace transform) functions. I think anyone familiar with the field would understand the N(s) notation, but I also think it would be very confusing to someone who didn't understand it thinking N(s) = N(t) where t --> s. Rather, I think
Usually I've seen this in books where they might write x(t) [lower case] and X(s) [upper case] to distinguish the functions. I recommend we stay with the tilde notation or switch to the n(t) N(s) type of notation (lower-case time/upper case laplace] for clarify and simplicity.
Could I get comments on this? I'd like to build consensus, if possible. - SocratesJedi | Talk 18:40, 2 February 2007 (UTC)
I think there should be an Re() everywhere around the s, in the ROC column.
I agree. It just doesnt make any sense to say s > a for a complex number s and a real number a. It is not possible to define a "consistent" ordering on the complex numbers. Anybody listening here? —Preceding unsigned comment added by 62.214.248.128 ( talk) 15:25, 3 October 2007 (UTC)
Lantanov, your edit summary indicates that the text you have inserted into the intro is the intro from the Korn & Korn reference. Perhaps I misunderstand what you mean by is but if you've copied the intro verbatim here, that's a no-no. Alfred Centauri 14:32, 30 August 2007 (UTC)
It is not verbatim, I re-wrote it and shortened it, and you can check this. Besides, I have the K&K book only in Russian translation, so I had to re-translate the text back from Russian to English. And in any case: how inventive and original can one be when he quotes a mathematical definition in which every deviation has the risk of being erroneous? For instance, you mistook my user name by not checking the original.:) -- Lantonov 15:32, 30 August 2007 (UTC)
No worries mate, just checking. Alfred Centauri 16:59, 30 August 2007 (UTC)
The explanatory notes at the bottom of the table states that "In general, the ROC for causal systems is not the same as the ROC for anticausal systems." Can someone explain what ROC stands for? —Preceding unsigned comment added by JonathonReinhart ( talk • contribs) 16:03, 3 December 2007 (UTC)
I removed a statement to the effect of `laplace x-form is in the branch of mathematics known as fourier analysis`; I looked up the history, it was originally functional analysis. —Preceding unsigned comment added by Blablablob ( talk • contribs) 19:07, 21 June 2008 (UTC)
what is bi-laterial laplace transforms step function? 80.191.172.10 ( talk) 13:00, 29 April 2009 (UTC)
using laplace transformation,show that integral of sint/2*dt from 0 to infinity=pie/2 —Preceding unsigned comment added by 175.40.52.234 ( talk) 15:05, 17 March 2010 (UTC)
I just thought I would mention, there is no need to emphasize on the + sign in front of the infinity symbol. The Laplace Transform is usually introduced into a 205 , maybe higher mathematics. By this time students studying differential equations (DE's) (where the Laplace Transform is introduced) should know it is assumed that unless there is a negative sign (-) infront of it, that it is indeed positive. For example, when you obtain a result, x, when solving an equation, it is assumed to be positive. This does not annoy me or bother me, however I figured I would mention this to help prevent monotony and drudgerous reading and writing. Also, I recall seeing in the power series the infinity symbol as the upper limit of the sum at the top of the capital Sigma (which is correct), however it did not have the positive symbol infront of it. It also contains some integrals which have an upper bounding limit of integration of infinity, which did not have the positive symbol infront of the infinity sign. Now, again, students studying mathematics at this level should already know it is implied that it is positive if it does not have a negitive sign infront of it, but "adding it here and not adding it there" is somewhat negligent and inconsistent. And those who would not understand that it is implied might have the tendency to develope a wrong way of writing such formulas and it would make it harder, much harder to understand. It creates more questions that do not need to be asked "Why is there a positive sign here, and not there?". Unfortunately we know that many people claim wikipedia is a collaboration of fallacies and misinformation. I believe it is these "errors" or "extension of courtesy" if you will that creates this side of a long going debate. I just request that one heeds this message for two reasons: For the readers better understanding and the writers time and convenience. No one asked, but if I may make an opinionated suggestion, it would be that using the positive (+) symbol for variables and other symbols (such as infinity) should be used, but at an upper bound of Intermediate Algebra (Algebra II) where infinity seems to usually be used (i.e. domains, ranges) and perhaps some elementary levels of discussion of geometry. Using this emphasis in a discussion concerning higher level mathematics is very much unnecessary. In my experience, I was enthused quite much with meanings behind mathematics terminology and symbols, so I studied them [i.e. gradients (curl), the russian "d" for partial derivatives, etc...)] long before my time of using them. Others do this as well, and it is little things such as this, and others, that make them think it is right (however it is not wrong) to write it as they have seen, and makes it difficult to write them properly when they learn it. I think it is best to use them as they are supposed to be used, accordingly. This just makes it harder on students, and if they do decide to write it improperly, eventhough it is notnecessarily incoreect, some instructors take points off. For instance, I know for a fact if one repetitively put a plus sign infrom of an upper bound of summation, for example, they would get points taken off, maybe just one or two, but those one or two count, especially in these higher level courses. Also in the integration. At the very least it is frowned upon and the instructor gets "on to" the student for it. It is not the students fault however, for this is how they first learned it, not incorrect, but not proper format. If they continue, they get points taken off (for various reasons).NOTE: WHEN TAKING LIMITS AT INFINITY AND NEGATIVE INFINITY, IT IS INDEED ACCEPTABLE AND SOMETIMES STRESSED TO USE A POSITIVE SIGN However, like I say that is an inconsistency a student needs to get used to, and they do not need to get used to any other ones that are not necessary. Let's all remember what these students must do in these classes (CALC I, II, III, DE's, Linear Algebra, and even way back before CALC I in trigonometry): They must memorize trigonometric identities, domainds and ranges, the functions, the parent functions and in CALC I and up there are about 50 integration formula's and 10 techniques of integration they must master, derivatives, limits, Series, and as I discuss here, at least 58 Laplace Transforms (not insluding inverses). I just ask that we all try to take it easy and make it easier for these students and readers. As an educator I see that this is why some people lose enthusiasm and eagerness for the subjects. However, i thank you for writing this article, it is very nice, and the other mathematical articles are nice as well. Thank you for doing all that you have done and will continue to do. You have done so much, it is very admirable, and I beg you to keep up the good work, just beg you to also try not to over do it. There is more I could say on other topics (for one, the topic of the p-series where inequalities are incorrect in the article. This I tryed to correct and gave references for proof, but it was simply ignored). If anyone wants to speak with me on this topic I would be more than happy to speak in e-mail, because the chances of me coming back here to read updates on this message are nill. Thank you for your time and forgive me for the long and drudgerous message. Education is my thing and where I am from (USA) our mathematics and science scores were some of the lowest in the world. My mission of the moment is to fix that, that's all. No disrespect or negative criticism was meant by this message and if it came off that way, my deepest sympathies. Please contact me if you wish at joegroves1986@yahoo.com. Again, thank you.
Pray believe me dear friend(s) -
J.A.G.
(Physics, Physical Sciences, Sciences, and Mathematics). —Preceding
unsigned comment added by
108.10.51.252 (
talk)
19:34, 14 April 2010 (UTC)
My attempts at a compromise wording to bring the relationship with moments again to the lead was reverted. Now, obviously, there is a relationship between the Laplace transform and moments, either by an exponential change of variables, or by means of the generating function. The issue therefore is how to address this issue constructively in a manner appropriate to the general discussion in the lead of the article. I am open to suggestions about how to proceed, but I disagree with outright removal of content from the general discussion on the grounds that it isn't sufficiently precise. Try to improve the wording if it isn't to your liking. Sławomir Biały ( talk) 22:04, 21 July 2010 (UTC)
My issue with this statement is that it doesn't belong in the introduction, as it's confusing for someone who is not already intimately familiar with the Laplace transform; should probably be in the section about moments. Let me try to move it there with more precise wording. To say that the Laplace transform "resolves a function in its moments" is just so outrageously imprecise as to be misleading. There is a relationship, but a very tenuous one, and it doesn't belong at the top of the article. Danpovey ( talk) 22:38, 21 July 2010 (UTC)
Actually, after trying to figure out how to make this statement precise I was unable to because the statement is just plain wrong. But I won't continue an edit war. I will try to persuade you instead as you are obviously a person of some mathematical sophistication who can appreciate my point. The Laplace transform does not resolve a function into its moments because for no value of s does L(s) correspond to a moment; I think the person who orginally posted that statement must have thought that was the case (e.g. they thought it was the Mellin transform). There are further transformations you can do that would reveal the moments, but that would define a different integral transform that is different from the Laplace transform (in fact, for any integral transform we can apply its inverse and then the Mellin transform and get the moments, so this isn't unique to the Laplace transform). The exponential change of variables is not relevant because then we are not talking about the moments of the original function but the transformed version. I think there should be some place for removing content when the content is inaccurate, rather than bending over backwards to interpret in such a way that it's correct. Danpovey ( talk) 22:49, 21 July 2010 (UTC)
It's well known in certain fields of instruction that the reader can not confidently understand the factual presentation without working some pertinent examples. Witness volumes from Knuth with more space devoted to exercises and answers to exercises than expository text.
The problem with the examples section is that it seems to invite expansion beyond serving the purpose of permitting the reader to double check his/her factual comprehension.
What is needed here instead of deprecating necessary corroborative material is a notice that the examples serve a corroborative purpose and that this section is not there to grow into a giant cheat sheet.
The reason I removed the howto box is that it deflates the spirit of collaboration and draws more attention to policy than the effectiveness of the article at presenting the material. Much of the original contribution at Wikipedia was fueled by the joy of escaping this kind of pettiness. I can't see how reworking the exposition here would make the section less "how to". The only logical outcome is to remove the example section completely, which would damage the article's intelligibility. Deprecating labels should be bandied with extreme care.
Rules aren't much use if no one remains to follow them. — MaxEnt 21:46, 12 September 2010 (UTC)
It is known that for positive integer ,
Can we borrow the idea from Cauchy formula for repeated integration and have this simplification?
Doraemonpaul ( talk) 00:51, 27 September 2010 (UTC)
In fact .
Proof:
Doraemonpaul ( talk) 00:58, 6 October 2010 (UTC)
The new entry to the table is redundant with the entry on the delayed nth power frequency shift, which I think is clearer. Also, the new entry tries to do too much, by bringing in partial fractions and indicating this by a perhaps not so easily recognizable limit formula. This doesn't seem to be the sort of information that is suitable for a table entry. There is an example that discusses partial fractions already, and the article partial fractions goes into much more detail about how to find partial fraction expansions. Someone who is unfamiliar with partial fractions is likely to be totally mystified by this table entry. Someone already familiar with them is likely to have better ways to compute the decomposition than by using the limit formula. Sławomir Biały ( talk) 10:53, 5 November 2011 (UTC)
I've seen it a million times before, but now that I actually need to calculate one I can't find any reference to this particular meaning of complex integration. Nor does Wolfram Alpha help me out any. For one, why does the transform use the limit as T goes to infinity instead of simply integrating over c-i∞ to c+i∞? And does that mean I can use the fundamental theorem of calculus to evaluate the functions? For example, I have a term . Can I evaluate it as: ? ᛭ LokiClock ( talk) 02:53, 13 December 2011 (UTC)
Those entries in the table in the Properties and theorems section that contain integral symbols are incorrectly formatted by default to display the expressions using boxes or frames, as viewed in Firefox 8.0. I haven't learned the language used to represent such expressions, so I can't fix this problem. Integral expressions appearing outside of this table are displayed correctly, and in a nice, distinctive, bold italic font. Probably there is an entry in WP-space that describes how to use this language. Can anyone help? David Spector (talk) 21:42, 29 December 2011 (UTC)
I can understand your confusion if you don't see the problem. It happens because a different sublanguage is used at the two places (look at the wiki source). I've created a temporary screenshot where you can see the boxes. This might be a Firefox bug. David Spector (talk) 11:38, 30 December 2011 (UTC)
Thanks for the excellent analysis. Since this seems to be a real bug, I am submitting it as a bug. Will report status here. David Spector (talk) 15:06, 30 December 2011 (UTC)
![]() | This page is an archive of past discussions. Do not edit the contents of this page. If you wish to start a new discussion or revive an old one, please do so on the current talk page. |
An editor recently added PlanetMath citations to the article (which is a wiki, in violation of our WP:RS guideline). I removed these references, but was reverted by the same editor, with the edit summary "restore PlanetMath citations that provide derivations until they are replace by better refs". If indeed they are to be replaced in the near future by better refs, why can't we just give those better refs? There is no need to have unacceptable refs there at all if they are soon to be replaced by decent ones. However, if as I suspect these "better refs" are merely hypothetical, then we should mark the uncited items as {{ citation needed}} in hopes of encouraging people to give better references. This has a much better chance of drawing attention to uncited items than having substandard references in place. In the meantime, I have restored the original consensus revision of the article (without the PlanetMath links). What needs to be discussed ( WP:BRD) is why there should be an exception to the rule prohibiting such works as references in this case? I really see no good reason for it. Sławomir Biały ( talk) 11:43, 15 April 2012 (UTC)
The "Reference" column was recently changed into "Derivation" in the Table of selected transforms. This should be changed back, and the derivations removed. We don't generally include derivations—especially those that amount to routine calculus exercises, and certainly not in table form. This is far too textbook-ish for an encyclopedia. It serves no encyclopedic purpose whatsoever. Sławomir Biały ( talk) 00:52, 21 April 2012 (UTC)
It should be emphasize that the Laplace transform is NOT unitary as opposed to the Fourier transform. Watson1905 ( talk) 20:39, 11 February 2014 (UTC)
Why does it say it is abuse of language to define the Laplace transform of a (nonnegative) random variable? Random variables are defined as measurable functions defined on a probability space .
The Laplace transform of a random variable is defined in Billingsley's Probability and Measure (which is highly cited and authoritative in probability theory) of a random variable as where is the probability distribution (which is a measure) of ( instead of is probably a better notation for this setting), which is entirely consistent with formal Lebesgue definition of the Laplace transform above and requires no abuse.
I did originally write part of the section on the Laplace transform in probability before I made an account and it seems to have undergone some revision I don't think is quite correct. It's not the Laplace(-Stieltjes) transform of the probability density function, but rather the Laplace transform of the random variable itself, so it understandably begins to look like an abuse of language when from one side it appears the transform of the PDF and is called the transform of the random variable.
I also worry the statement that says that the Laplace transform with respect to a probability distribution can be written as may be misleading in that it assumes the Lebesgue integral with respect to the probability distribution f reduces to a Riemann integral, which isn't necessarily true (the Lebesgue integrals are defined for discrete and otherwise non-continuous distributions).
Probably a rewrite with references will clear it up, which I'd like to do when I get a chance. — Preceding unsigned comment added by Machi4velli ( talk • contribs) 06:25, 24 February 2014 (UTC)
In the lead section it is said that the Laplace transform was introduced by Pierre-Simon Laplace in the context of probability theory. Is this true? Is this so important that it belongs in the lead section? Note that the LT can be used for lots of things, not just probability theory. Sincerely, DoctorTerrella ( talk) 16:51, 14 September 2014 (UTC)
I'm trying to dope this out. Here's one example that doesn't make sense to me:
which is to say that
Now, I worked that integral by hand and found that yes, this holds. (Although I may have assumed that
which is dubious.)
But noting that the imaginary axis of the s plane is basically the Fourier transform of f, I was expecting to see delta functions, which I don't see (I just see poles). So I plug in a particular value for s: so we have
Now, clearly this integrand is a periodic function about zero that never decays. It's an odd function, so the integral from zero to infinity will never go negative. Similarly, if we pick we have
It looks like this relates to Improper_integral#Summability, which mentions the above integral of sine explicitly. Also Cesàro_summation#Ces.C3.A0ro_summability_of_an_integral. This article mentions the Lebesgue integral, which I think relates to this. What's going on here? —Ben FrantzDale ( talk) 17:58, 27 March 2015 (UTC)
What does the Laplace transformation do ? Faisale1994 ( talk) 03:01, 17 November 2015 (UTC)
Not an issue with this article, but it should be noted that there are several articles on Wikipedia now about things which are really just the Laplace transform in different notation: N-transform, Sumudu_transform, Laplace–Carson_transform. The first two, at least, appear to be attempted self-promotion of some scholarship of questionable merit.
85.69.207.227 ( talk) 16:03, 12 January 2015 (UTC)
References
![]() | This is an archive of past discussions. Do not edit the contents of this page. If you wish to start a new discussion or revive an old one, please do so on the current talk page. |
Archive 1 | Archive 2 |
At the very beginning of this article is the strange:
" In mathematics, the Laplace transform is a technique for analyzing linear time-invariant systems such as electrical circuits, harmonic oscillators, optical devices, and mechanical systems."
However, electrical circuits, harmonic oscillators, optical devices, and mechanical systems are subjects of physics and technical sciences, not of mathematics per se. It will be more appropriate to replace mathematics with physics. On the other hand, the main use of Laplace transform in mathematics proper is for solving differential equations. I do not see this in the introduction. Lantonov 14:31, 20 July 2007 (UTC)
I wrote a new intro/definition which can be understood by persons with high-school math background which immediately leads the reader to possible applications. Lantonov 05:30, 30 August 2007 (UTC)
"The method of using the Laplace Transform to solve differential equations was developed by the English electrical engineer Oliver Heaviside." The Oliver Heaviside wikipedia article also suggests this. Can anyone site a reference supporting this?
Oliver Heaviside developed an operational calculus for solving differential equations, while similar to using the Laplace transform it is not the same. This site goes into more detail. http://www.du.edu/~jcalvert/math/laplace.htm Yardleydobon 20:04, 30 April 2007 (UTC)
I notice many texts refer to the Laplace "Transformation", particularly more classical texts. Would there be any problem with this minor addition? ... Laplace Transform (also known as Laplace Transformation)... Tparameter 06:00, 8 November 2006 (UTC)
Say I'm not familiar with him, and am looking him up in the Wikipedia for that reason. I would then like to find out what is so important about this Transform. When can it be used, and how? What is, again, the point of the LaPlace transform? The article does a poor job of informing 'me'.-- Ec5618 11:32, Apr 21, 2005 (UTC)
Yes, this article needs to be cleaned up. Maybe I'll do that sometime in the near future. I have no definite plans, but I might get around to it. If I do indeed get the gumption to do this, I'll do my best to include a way to solve a D.E. with it. In any case, I also wonder what this is used for. I know how to find the transform, and how to do the inverse. Pretty easy. I was taught in my D.E. class that it is useful in some physics problems, or at least in electrical engineering. So how can it be used in E.E.? I learn a lot better when I can comprehend how it will benefit me. Until then, it's trivial, much like the trivial solutions that no one cares about in D.E. Why should I care about it? D. F. Schmidt [[User_talk:D. F. Schmidt|(talk)]] 09:14, 16 November 2005 (UTC)
Maybe a small text like this can solve a lot of headaches:
"Laplace transformations are used as a tool to convert a complex equation in a very simple to use equation. This process involves 3 operations:
I don't speak english so someone should clean up this text and insert it in the article. Thx
I wrote a new intro/definition which can be understood by persons with high-school math background which immediately leads the reader to uses of the Laplace transform. Also ordered the sentences in the intro a bit. The intro is still too big, with an emphasis on physical and electronic applications. I do not find anything bad in this but think that they can be shortened a little without losing too much from their information content. Lantonov 05:31, 30 August 2007 (UTC)
I have always wanted to know how Laplace was led to the transform, but never could find much on the web. Anybody know of a direct account from Laplace? Here's something of interest perhaps.
http://www.math.niu.edu/~rusin/known-math/97/laplace.fourier
thanks Phil —Preceding
unsigned comment added by
74.170.68.234 (
talk)
04:08, 12 December 2007 (UTC)
How is this equation different from the one at the top? Taral 16:13, 27 May 2005 (UTC)
I think it would be helpful for those unfamiliar with it to define .
Agree, disagree? Guardian of Light 16:43, 14 July 2005 (UTC)
Somebody help find the laplace transform of exp(t-3) and exp(-(t-1))? Thanks
Does anyone know more about the history of Laplace
Is there relationship between Laplace transformations and the engineering used in the construction of German weapons during World War II?
For the lists of common transforms, I believe there are certain restrictions on the values that the variable s can take (e.g. see http://mathworld.wolfram.com/LaplaceTransform.html). Can we incorporate these into the table(s)? -- GregRM 23:16, 29 November 2005 (UTC)
I found an important error here.
"However, if the integral defining the Laplace transform does converge (possibly only as an improper integral) at s = s0, then it automatically converges absolutely for all s with Re{s} > Re{s0}."
This is false. Consider a function defined as follows (for positive reals): divide the interval in equal intervals. Let take the values and alternately in those intervals. Fourier transform at 0 converges conditionally, while it doesn't converge absolutely at 1. However both of the following are valid:
(absolute) convergence at implies (absolute) convergence for all with —Preceding unsigned comment added by 201.231.212.56 ( talk) 06:25, 24 November 2009 (UTC)
Does anyone know what the ROC is for the first two entries in the table below, the unit impulse and the unit step functions? I have filled in the table, but I am not sure if they are correct. Thanks. -- Metacomet 19:51, 30 November 2005 (UTC)
Please help: If anyone knows the correct Regions of Convergence (ROC) for any of the entries in the table where the ROC is missing, please feel free to add them to the appropriate cell in the table. Thanks. -- Metacomet 22:28, 8 December 2005 (UTC)
Where did you get the transforms for the Bessel function from? I think the exponent should be n instead of −n, but I'm not at all sure. -- Jitse Niesen ( talk) 18:49, 10 December 2005 (UTC)
The table here says that the transform of is
The table at MathWorld says that it is
I can't see how they can be the same. -- Jitse Niesen ( talk) 23:19, 10 December 2005 (UTC)
Well done. I had a feeling that the difference of squares rule would play a part! -- Metacomet 16:07, 11 December 2005 (UTC)
I have been mulling over the very same idea, and I had not come to any conclusions one way or the other. It might be a bit too much detail for this article. I am not sure how often Bessel functions come up in the context of Laplace transforms. It might be usefule to create a more detailed table of transforms to which this article could link. On the other hand, the external links section points readers to several excellent resources. I am not sure we should do anything just yet, maybe continue to think about it some more. As you said, there is no need to rush into anything in this case. -- Metacomet 03:27, 19 December 2005 (UTC)
Does anyone know how to change the background color from white to something else (in RGB) of a LaTeX equation inside the <math> tag? Please let me know. Thanks. -- Metacomet 03:40, 1 December 2005 (UTC)
I have now added this table to the main article. -- Metacomet 16:42, 4 December 2005 (UTC)
Yes, I think you are both correct. It does follow directly from the rule for frequency shifting. Good catch. -- Metacomet 22:16, 6 December 2005 (UTC)
Should the table use the heading Frequency Domain? I wonder if this might cause confusion with the Fourier Transform which is more commonly described as a Time-Frequency transform than the Laplace Transform. Would "Laplace Domain" or "S Domain" be more appropriate? jackocleebrown 21:20 , 30 Aprl 2007 (UTC)
I think the transforms used in the example should be included in the table so there can be a chance of following them. 70.133.83.60 ( talk) 20:50, 3 September 2010 (UTC)
The Laplace transform of 1 is 1/s but the Laplace Transform of the unit step function is ., 16 October 2011
Near the top of the article is a section on the "alternative defintions" of the Laplace transform,
Can someone elaborate on this? When and why are these alternative definitions used? - Monguin61 09:32, 9 December 2005 (UTC)
A good example is to look at the Laplace transforms for sine and cosine. Suppose that
Then we have
and
as expected. --
Metacomet
21:11, 9 December 2005 (UTC)
quote:
Near the top of the article is a section on the "alternative defintions" of the Laplace transform,
Can someone elaborate on this? When and why are these alternative definitions used? - Monguin61 09:32, 9 December 2005 (UTC)
Quote:
I think it would be helpful for those unfamiliar with it to define .
Agree, disagree? Guardian of Light 16:43, 14 July 2005 (UTC)
:Done. I discovered, somewhat by accident, that is the Euler-Mascheroni constant. -- Metacomet 05:52, 7 December 2005 (UTC)
Here's my website of example problems with Laplace transforms. Someone please put it in the external links section if you think it's helpful!
http://www.exampleproblems.com/wiki/index.php/PDE:Laplace_Transforms
Could anyone tell me why do
and
thanks...
the page of that simplied too much ,i need a lot of noting help to the result... -- HydrogenSu
I think a page of L.T. shoud give more proves below some formulas. If just showed "Formulas" might let readers confused and get some information of "just memorize them". If improving,it is nicer. :)-- HydrogenSu 12:00, 14 February 2006 (UTC)
@.Why the Applications part had to be put in an article of Laplace Trs.? It shall be put at the nearly ending.-- GyBlop 08:41, 24 February 2006 (UTC)
I think it would be very useful to have a table or list of how to transform circuit elements (like resistors capacitors inductors, sources, etc) into s-domain elements. For example, the transform of an inductor with an initial current of I is an inductor and a source in series with s-domain values... but I'm not quite sure what those are at the moment. Fresheneesz 08:53, 21 April 2006 (UTC)
I had intended to re-direct a link to 'first order lag' to this article, but although Laplace transforms are intimately related to transfer functions, this has not proved as helpful as I had hoped. The article isn't bad as it stands, but a note in the introduction to the effect that the LT provides a means of transforming differential equations into algebraic equations might motivate the non-specialist to read further, rather than dismiss the whole thing as another example of Emperor's New Clothes. Gordon Vigurs 19:16, 14 May 2006 (UTC)
Apparently this is a fairly recent discovery, and I haven't looked to see where it was published, but apparently the following holds:
If , and , then at any point of continuity of f, .
Of course, actually calculating that for arbitrary f is rather cumbersome, but it is better for complex-integralophobics. Confusing Manifestation 05:05, 16 May 2006 (UTC)
I keep comming across transfer functions that involve a term s/(a+s), for example a series RC circuit. Why is the transfer function not in the table here, and in fact not in any tables I've seen. I must be missing something key, but .. I don't know what that would be. Fresheneesz 23:29, 26 May 2006 (UTC)
Could someone post an example using a second order differential equation where the roots are complex? The sign changes associated with the real part of the root that are in the denominator of the partial fraction expansion are confusing and should be explained. Thanks.
Statum (
talk)
13:45, 25 January 2011 (UTC)
I think number 2 in the table is wrong ...
delayed nth power with frequency shift ==> ====> ||
It doesn't look right to me.
Hi, I just wanted to note, that the notation u(t) for the unit step is not very well chosen, because u(t) is also often used in electronics and control engineering for the input signal, which is often Laplace-transformed itself. I would suggest to use another name for the unit step, for example σ(t) or H(t) for the Heaviside-function. Your opinions?
I agree with the first chap. As a mathematician, I have never seen the Heaviside function denoted by anything other than H(t). —Preceding unsigned comment added by 62.31.164.38 ( talk) 21:41, 14 May 2011 (UTC)
In systems theory it is usually denoted by 1(t) which was probably Heaviside's notation. JFB80 ( talk) 19:36, 15 May 2011 (UTC)
The u(t) notation is used in engineering. The notation, however, usually carries a (power of s) subscript to denote doublet, impulse, step, ramp, etc. IIRC, u0(t) is an impluse; u-1(t) is a step. That some people have never seen it says little. Glrx ( talk) 19:48, 15 May 2011 (UTC)
Why not check up on a few standard books, e.g. Schaum's Outline. JFB80 ( talk) 12:59, 16 May 2011 (UTC)
Hello, in the table the last transform we have is:
Where I'm fairly sure that since we could express instead as:
I think this would be a better way of expressing this because it is already clear what erf(z) means in the original context of the table, but it is not clear what erfc(z) is unless the Error function article has already been read (and it seems problematic to link directly there lest erf(z) and erfc(z) be confused).
I will make this edit in a few days if no one objects, but I wanted to see if I an consensus existed as well. Please let me know your thoughts. Thanks. - SocratesJedi | Talk 08:53, 29 January 2007 (UTC)
Under Differential equation example 1 we have:
Next, we take the Laplace transform of both sides of the equation:
where
The notation was removed in favor of just keeping N(s) where N(t) represented time domain and N(s) represented s-domain signals to keep the notation simple. I reverted this to reinclude the tilde N because I think it's necessary to make it clear that N(t) and N(s) are not the same function with t --> s, but are entirely different (but related through the Laplace transform) functions. I think anyone familiar with the field would understand the N(s) notation, but I also think it would be very confusing to someone who didn't understand it thinking N(s) = N(t) where t --> s. Rather, I think
Usually I've seen this in books where they might write x(t) [lower case] and X(s) [upper case] to distinguish the functions. I recommend we stay with the tilde notation or switch to the n(t) N(s) type of notation (lower-case time/upper case laplace] for clarify and simplicity.
Could I get comments on this? I'd like to build consensus, if possible. - SocratesJedi | Talk 18:40, 2 February 2007 (UTC)
I think there should be an Re() everywhere around the s, in the ROC column.
I agree. It just doesnt make any sense to say s > a for a complex number s and a real number a. It is not possible to define a "consistent" ordering on the complex numbers. Anybody listening here? —Preceding unsigned comment added by 62.214.248.128 ( talk) 15:25, 3 October 2007 (UTC)
Lantanov, your edit summary indicates that the text you have inserted into the intro is the intro from the Korn & Korn reference. Perhaps I misunderstand what you mean by is but if you've copied the intro verbatim here, that's a no-no. Alfred Centauri 14:32, 30 August 2007 (UTC)
It is not verbatim, I re-wrote it and shortened it, and you can check this. Besides, I have the K&K book only in Russian translation, so I had to re-translate the text back from Russian to English. And in any case: how inventive and original can one be when he quotes a mathematical definition in which every deviation has the risk of being erroneous? For instance, you mistook my user name by not checking the original.:) -- Lantonov 15:32, 30 August 2007 (UTC)
No worries mate, just checking. Alfred Centauri 16:59, 30 August 2007 (UTC)
The explanatory notes at the bottom of the table states that "In general, the ROC for causal systems is not the same as the ROC for anticausal systems." Can someone explain what ROC stands for? —Preceding unsigned comment added by JonathonReinhart ( talk • contribs) 16:03, 3 December 2007 (UTC)
I removed a statement to the effect of `laplace x-form is in the branch of mathematics known as fourier analysis`; I looked up the history, it was originally functional analysis. —Preceding unsigned comment added by Blablablob ( talk • contribs) 19:07, 21 June 2008 (UTC)
what is bi-laterial laplace transforms step function? 80.191.172.10 ( talk) 13:00, 29 April 2009 (UTC)
using laplace transformation,show that integral of sint/2*dt from 0 to infinity=pie/2 —Preceding unsigned comment added by 175.40.52.234 ( talk) 15:05, 17 March 2010 (UTC)
I just thought I would mention, there is no need to emphasize on the + sign in front of the infinity symbol. The Laplace Transform is usually introduced into a 205 , maybe higher mathematics. By this time students studying differential equations (DE's) (where the Laplace Transform is introduced) should know it is assumed that unless there is a negative sign (-) infront of it, that it is indeed positive. For example, when you obtain a result, x, when solving an equation, it is assumed to be positive. This does not annoy me or bother me, however I figured I would mention this to help prevent monotony and drudgerous reading and writing. Also, I recall seeing in the power series the infinity symbol as the upper limit of the sum at the top of the capital Sigma (which is correct), however it did not have the positive symbol infront of it. It also contains some integrals which have an upper bounding limit of integration of infinity, which did not have the positive symbol infront of the infinity sign. Now, again, students studying mathematics at this level should already know it is implied that it is positive if it does not have a negitive sign infront of it, but "adding it here and not adding it there" is somewhat negligent and inconsistent. And those who would not understand that it is implied might have the tendency to develope a wrong way of writing such formulas and it would make it harder, much harder to understand. It creates more questions that do not need to be asked "Why is there a positive sign here, and not there?". Unfortunately we know that many people claim wikipedia is a collaboration of fallacies and misinformation. I believe it is these "errors" or "extension of courtesy" if you will that creates this side of a long going debate. I just request that one heeds this message for two reasons: For the readers better understanding and the writers time and convenience. No one asked, but if I may make an opinionated suggestion, it would be that using the positive (+) symbol for variables and other symbols (such as infinity) should be used, but at an upper bound of Intermediate Algebra (Algebra II) where infinity seems to usually be used (i.e. domains, ranges) and perhaps some elementary levels of discussion of geometry. Using this emphasis in a discussion concerning higher level mathematics is very much unnecessary. In my experience, I was enthused quite much with meanings behind mathematics terminology and symbols, so I studied them [i.e. gradients (curl), the russian "d" for partial derivatives, etc...)] long before my time of using them. Others do this as well, and it is little things such as this, and others, that make them think it is right (however it is not wrong) to write it as they have seen, and makes it difficult to write them properly when they learn it. I think it is best to use them as they are supposed to be used, accordingly. This just makes it harder on students, and if they do decide to write it improperly, eventhough it is notnecessarily incoreect, some instructors take points off. For instance, I know for a fact if one repetitively put a plus sign infrom of an upper bound of summation, for example, they would get points taken off, maybe just one or two, but those one or two count, especially in these higher level courses. Also in the integration. At the very least it is frowned upon and the instructor gets "on to" the student for it. It is not the students fault however, for this is how they first learned it, not incorrect, but not proper format. If they continue, they get points taken off (for various reasons).NOTE: WHEN TAKING LIMITS AT INFINITY AND NEGATIVE INFINITY, IT IS INDEED ACCEPTABLE AND SOMETIMES STRESSED TO USE A POSITIVE SIGN However, like I say that is an inconsistency a student needs to get used to, and they do not need to get used to any other ones that are not necessary. Let's all remember what these students must do in these classes (CALC I, II, III, DE's, Linear Algebra, and even way back before CALC I in trigonometry): They must memorize trigonometric identities, domainds and ranges, the functions, the parent functions and in CALC I and up there are about 50 integration formula's and 10 techniques of integration they must master, derivatives, limits, Series, and as I discuss here, at least 58 Laplace Transforms (not insluding inverses). I just ask that we all try to take it easy and make it easier for these students and readers. As an educator I see that this is why some people lose enthusiasm and eagerness for the subjects. However, i thank you for writing this article, it is very nice, and the other mathematical articles are nice as well. Thank you for doing all that you have done and will continue to do. You have done so much, it is very admirable, and I beg you to keep up the good work, just beg you to also try not to over do it. There is more I could say on other topics (for one, the topic of the p-series where inequalities are incorrect in the article. This I tryed to correct and gave references for proof, but it was simply ignored). If anyone wants to speak with me on this topic I would be more than happy to speak in e-mail, because the chances of me coming back here to read updates on this message are nill. Thank you for your time and forgive me for the long and drudgerous message. Education is my thing and where I am from (USA) our mathematics and science scores were some of the lowest in the world. My mission of the moment is to fix that, that's all. No disrespect or negative criticism was meant by this message and if it came off that way, my deepest sympathies. Please contact me if you wish at joegroves1986@yahoo.com. Again, thank you.
Pray believe me dear friend(s) -
J.A.G.
(Physics, Physical Sciences, Sciences, and Mathematics). —Preceding
unsigned comment added by
108.10.51.252 (
talk)
19:34, 14 April 2010 (UTC)
My attempts at a compromise wording to bring the relationship with moments again to the lead was reverted. Now, obviously, there is a relationship between the Laplace transform and moments, either by an exponential change of variables, or by means of the generating function. The issue therefore is how to address this issue constructively in a manner appropriate to the general discussion in the lead of the article. I am open to suggestions about how to proceed, but I disagree with outright removal of content from the general discussion on the grounds that it isn't sufficiently precise. Try to improve the wording if it isn't to your liking. Sławomir Biały ( talk) 22:04, 21 July 2010 (UTC)
My issue with this statement is that it doesn't belong in the introduction, as it's confusing for someone who is not already intimately familiar with the Laplace transform; should probably be in the section about moments. Let me try to move it there with more precise wording. To say that the Laplace transform "resolves a function in its moments" is just so outrageously imprecise as to be misleading. There is a relationship, but a very tenuous one, and it doesn't belong at the top of the article. Danpovey ( talk) 22:38, 21 July 2010 (UTC)
Actually, after trying to figure out how to make this statement precise I was unable to because the statement is just plain wrong. But I won't continue an edit war. I will try to persuade you instead as you are obviously a person of some mathematical sophistication who can appreciate my point. The Laplace transform does not resolve a function into its moments because for no value of s does L(s) correspond to a moment; I think the person who orginally posted that statement must have thought that was the case (e.g. they thought it was the Mellin transform). There are further transformations you can do that would reveal the moments, but that would define a different integral transform that is different from the Laplace transform (in fact, for any integral transform we can apply its inverse and then the Mellin transform and get the moments, so this isn't unique to the Laplace transform). The exponential change of variables is not relevant because then we are not talking about the moments of the original function but the transformed version. I think there should be some place for removing content when the content is inaccurate, rather than bending over backwards to interpret in such a way that it's correct. Danpovey ( talk) 22:49, 21 July 2010 (UTC)
It's well known in certain fields of instruction that the reader can not confidently understand the factual presentation without working some pertinent examples. Witness volumes from Knuth with more space devoted to exercises and answers to exercises than expository text.
The problem with the examples section is that it seems to invite expansion beyond serving the purpose of permitting the reader to double check his/her factual comprehension.
What is needed here instead of deprecating necessary corroborative material is a notice that the examples serve a corroborative purpose and that this section is not there to grow into a giant cheat sheet.
The reason I removed the howto box is that it deflates the spirit of collaboration and draws more attention to policy than the effectiveness of the article at presenting the material. Much of the original contribution at Wikipedia was fueled by the joy of escaping this kind of pettiness. I can't see how reworking the exposition here would make the section less "how to". The only logical outcome is to remove the example section completely, which would damage the article's intelligibility. Deprecating labels should be bandied with extreme care.
Rules aren't much use if no one remains to follow them. — MaxEnt 21:46, 12 September 2010 (UTC)
It is known that for positive integer ,
Can we borrow the idea from Cauchy formula for repeated integration and have this simplification?
Doraemonpaul ( talk) 00:51, 27 September 2010 (UTC)
In fact .
Proof:
Doraemonpaul ( talk) 00:58, 6 October 2010 (UTC)
The new entry to the table is redundant with the entry on the delayed nth power frequency shift, which I think is clearer. Also, the new entry tries to do too much, by bringing in partial fractions and indicating this by a perhaps not so easily recognizable limit formula. This doesn't seem to be the sort of information that is suitable for a table entry. There is an example that discusses partial fractions already, and the article partial fractions goes into much more detail about how to find partial fraction expansions. Someone who is unfamiliar with partial fractions is likely to be totally mystified by this table entry. Someone already familiar with them is likely to have better ways to compute the decomposition than by using the limit formula. Sławomir Biały ( talk) 10:53, 5 November 2011 (UTC)
I've seen it a million times before, but now that I actually need to calculate one I can't find any reference to this particular meaning of complex integration. Nor does Wolfram Alpha help me out any. For one, why does the transform use the limit as T goes to infinity instead of simply integrating over c-i∞ to c+i∞? And does that mean I can use the fundamental theorem of calculus to evaluate the functions? For example, I have a term . Can I evaluate it as: ? ᛭ LokiClock ( talk) 02:53, 13 December 2011 (UTC)
Those entries in the table in the Properties and theorems section that contain integral symbols are incorrectly formatted by default to display the expressions using boxes or frames, as viewed in Firefox 8.0. I haven't learned the language used to represent such expressions, so I can't fix this problem. Integral expressions appearing outside of this table are displayed correctly, and in a nice, distinctive, bold italic font. Probably there is an entry in WP-space that describes how to use this language. Can anyone help? David Spector (talk) 21:42, 29 December 2011 (UTC)
I can understand your confusion if you don't see the problem. It happens because a different sublanguage is used at the two places (look at the wiki source). I've created a temporary screenshot where you can see the boxes. This might be a Firefox bug. David Spector (talk) 11:38, 30 December 2011 (UTC)
Thanks for the excellent analysis. Since this seems to be a real bug, I am submitting it as a bug. Will report status here. David Spector (talk) 15:06, 30 December 2011 (UTC)
![]() | This page is an archive of past discussions. Do not edit the contents of this page. If you wish to start a new discussion or revive an old one, please do so on the current talk page. |
An editor recently added PlanetMath citations to the article (which is a wiki, in violation of our WP:RS guideline). I removed these references, but was reverted by the same editor, with the edit summary "restore PlanetMath citations that provide derivations until they are replace by better refs". If indeed they are to be replaced in the near future by better refs, why can't we just give those better refs? There is no need to have unacceptable refs there at all if they are soon to be replaced by decent ones. However, if as I suspect these "better refs" are merely hypothetical, then we should mark the uncited items as {{ citation needed}} in hopes of encouraging people to give better references. This has a much better chance of drawing attention to uncited items than having substandard references in place. In the meantime, I have restored the original consensus revision of the article (without the PlanetMath links). What needs to be discussed ( WP:BRD) is why there should be an exception to the rule prohibiting such works as references in this case? I really see no good reason for it. Sławomir Biały ( talk) 11:43, 15 April 2012 (UTC)
The "Reference" column was recently changed into "Derivation" in the Table of selected transforms. This should be changed back, and the derivations removed. We don't generally include derivations—especially those that amount to routine calculus exercises, and certainly not in table form. This is far too textbook-ish for an encyclopedia. It serves no encyclopedic purpose whatsoever. Sławomir Biały ( talk) 00:52, 21 April 2012 (UTC)
It should be emphasize that the Laplace transform is NOT unitary as opposed to the Fourier transform. Watson1905 ( talk) 20:39, 11 February 2014 (UTC)
Why does it say it is abuse of language to define the Laplace transform of a (nonnegative) random variable? Random variables are defined as measurable functions defined on a probability space .
The Laplace transform of a random variable is defined in Billingsley's Probability and Measure (which is highly cited and authoritative in probability theory) of a random variable as where is the probability distribution (which is a measure) of ( instead of is probably a better notation for this setting), which is entirely consistent with formal Lebesgue definition of the Laplace transform above and requires no abuse.
I did originally write part of the section on the Laplace transform in probability before I made an account and it seems to have undergone some revision I don't think is quite correct. It's not the Laplace(-Stieltjes) transform of the probability density function, but rather the Laplace transform of the random variable itself, so it understandably begins to look like an abuse of language when from one side it appears the transform of the PDF and is called the transform of the random variable.
I also worry the statement that says that the Laplace transform with respect to a probability distribution can be written as may be misleading in that it assumes the Lebesgue integral with respect to the probability distribution f reduces to a Riemann integral, which isn't necessarily true (the Lebesgue integrals are defined for discrete and otherwise non-continuous distributions).
Probably a rewrite with references will clear it up, which I'd like to do when I get a chance. — Preceding unsigned comment added by Machi4velli ( talk • contribs) 06:25, 24 February 2014 (UTC)
In the lead section it is said that the Laplace transform was introduced by Pierre-Simon Laplace in the context of probability theory. Is this true? Is this so important that it belongs in the lead section? Note that the LT can be used for lots of things, not just probability theory. Sincerely, DoctorTerrella ( talk) 16:51, 14 September 2014 (UTC)
I'm trying to dope this out. Here's one example that doesn't make sense to me:
which is to say that
Now, I worked that integral by hand and found that yes, this holds. (Although I may have assumed that
which is dubious.)
But noting that the imaginary axis of the s plane is basically the Fourier transform of f, I was expecting to see delta functions, which I don't see (I just see poles). So I plug in a particular value for s: so we have
Now, clearly this integrand is a periodic function about zero that never decays. It's an odd function, so the integral from zero to infinity will never go negative. Similarly, if we pick we have
It looks like this relates to Improper_integral#Summability, which mentions the above integral of sine explicitly. Also Cesàro_summation#Ces.C3.A0ro_summability_of_an_integral. This article mentions the Lebesgue integral, which I think relates to this. What's going on here? —Ben FrantzDale ( talk) 17:58, 27 March 2015 (UTC)
What does the Laplace transformation do ? Faisale1994 ( talk) 03:01, 17 November 2015 (UTC)
Not an issue with this article, but it should be noted that there are several articles on Wikipedia now about things which are really just the Laplace transform in different notation: N-transform, Sumudu_transform, Laplace–Carson_transform. The first two, at least, appear to be attempted self-promotion of some scholarship of questionable merit.
85.69.207.227 ( talk) 16:03, 12 January 2015 (UTC)
References