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6229:, which precisely demonstrates the difference with partial derivation operators mapping functions to functions. Allow me to repeat that discussion on the web is totally unsuitable for resolving anything since it encourages reacting too quickly instead of thinking things through and editors seem to prefer unreliable sources over logic. Feel free to contact me as suggested earlier, but please understand that I cannot spend time on these pages and henceforth will react only to e-mail..--
710:. As far as I know, this is unrelated to the symbol's use to denote a partial differential (I've only just started seeing this formally, so I may be wrong). I also read this on an article here on Knowledge which was about the different uses of the symbol; an article that I can't seem to locate now. If anyone can find it, I'd like to know. Anyway, I think this makes sense since the boundary of a volume
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2298:. You will most certainly get a response, if you further add your input to the answering of these questions. In general, the talk page is not the most appropriate place to post questions. Further, the problems you quote are rather simple in nature, and similar worked examples can be found in a basic textbook on multivariable calculus. --
5953:, by abuse of notation, is usually treated as the function defined by evaluating it at a given point. There are some implicit assumptions made: the domain consists of tuples only consisting of values of the specified variables and those specified variables are free of each other (otherwise either we have
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is essential, and so is the distinction between partial derivation operators mapping functions to functions and those mapping expressions to expressions. Since this distinction is conceptually clear, can there be any doubt about consensus? Consensus about notation is less important: anyone can use a
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about everyone's use of notation, so any and all materials used to make your case must ultimately end up here for everyone to see as we use what sources use. That said, if we can demonstrate the existence of a strong consensus on this distinction made here, then we should have a remark on this in the
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IP, i think the issue with your addition is that there are many, many applications in the sciences. In medical R&D partial derivatives are important in modelling blood flow (imp for cardiology, medical device development), pharmacology, medical imaging, nuclear medicine. But not doctors so much.
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at the point (1, e). Including the value as additional variable does not make any reasonable sense in my silly example, and I am not sure it does in this article (especially without a warning – for me it is just confusing). Also I don't agree with your point that some functions have multiple values
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I disagree, the total derivative is not the sum of the partials. It is possible for all the partial derivatives to exist and yet the function not even be continuous (let alone have a total derivative). This is mentioned in the section *Formal
Definition* : "even if all partial derivatives ∂f/∂ai(a)
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a) Explain what is meant by i)( ∂y/∂r)θ and ii)( ∂y/∂r)x . b) Determine the values of (i). c) Determine value of (ii) by eliminating θ in the expressions for x and y. d) Determine the value of (ii) by the method of function of a function. e) Determine the value of :( ∂y/∂r)θ .( ∂y/∂r)x using
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No, that's not what it means in that case. Read the defitions given just before that. The subscript doesn't represent any sort of derivative at all. That conflicts with the notation used elsewhere in the article, so that's potentially confusing. But the paragraph preceding that part is explicit
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in the section on partial derivatives (v. 2 pp. 220-42). He refers only to the "rounded letter" after referencing earlier partial notations, including the 'ό' and 'd'. No other scholarly sources in the math reference section or the relevant sections of book collections on math history at a good
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Thanks for the feedback. I do not argue about the correctness of the definition. It is certainly very clear for someone who already understands the concept. My point is that I find that "particularization" not explicit enough. The French version seems to me to be a bit more explicit -- though
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It seems that 68.103.26.177 has changed the introduction to say the symbol is from the Greek instead of
Cyrillic alphabet. I'm trying not to be hasty and call it vandalism, but unless there is some deeper meaning I am unaware of, the partial differential symbol looks a heck of a lot more like the
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This article discusses intuition but fails to discuss the main properties of the partial derivative; only at the end is the formal definition stated. For example, many facts found in a basic calculus textbook are not discussed, regarding the partial derivatives. What worries me, is that even the
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Prompted by the preceding discussion, I compared about a dozen accounts of partial derivatives in different textbooks. Although 100 sloppy sources don't outweigh a single careful one, I was aghast at how many sources are sloppy, so the confusion is understandable. The most careful treatment of
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I suspect doctors not taking advanced math has more to do with simply needing to focus directly on the practice of medicine which doesn't require
Calculus directly. Only the research aspects and Biomedical engineering aspects require it directly. I know several doctors have taken Differential
2143:. In retrospect (I introduced the second sentence), if the sentence is going to be included at all, there is a case that both should be parenthetical (to avoid breaking the substanive exposition) or neither (possibly as a footnote or short separate section on the origin of the notation).
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in practical use, you need both. Since I dislike public discussions on the web with everyone barging in and expecting reactions, you can send me an e-mail and I send you a paper (in preparation) on this topic. My e-mail address is easy to find but I won't advertise it
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says that the two are equal--you get the same thing regardless of the order in which you take the derivatives. (This is mentioned at the end of the subsection "Formal definition".) So it doesn't matter how you interpret the notation, though it is standard to mean
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by Thomas M. Flett (1966, before math reforms caused a dip in mathematical diligence). By coincidence (which I won't even called fortunate since variants, when used properly, work equally well), Flett's conventions are the same as the ones I mentioned earlier.
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The question above was first posed by User:82.130.38.44, on 23:35, 19 April 2009 (UTC) but later removed by him. Perhaps did (s)he find a good explanation that (s)he can give to everybody? At this moment, I rather think (s)he was right to suspect an error.
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The
Introduction chapter mentions "to find the tangent line of the above function at (1, 1, 3)", as well as other instances of "(1, 1, 3)". But the function in question is f(x,y), which takes only two arguments. Its solution at (1, 1) is 3, though, as well as
3202:(1, 1) = 3, so (1,1,3) are the (x,y,z) coordinates of a point on the surface. This is a good habit, as some functions will have multiple values of z for some x&y, in which case the derivatives at these different points will most probably be different.
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The third and the fourth paragraph, that is the discussion about the total derivative and the
Jacobian are way out of place. Those things are inserted in the middle of the discussion about the partial derivatives, and that is inappropriate.
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3055:{\displaystyle {\frac {\operatorname {d} V}{\operatorname {d} h}}=\overbrace {\frac {\pi r^{2}}{3}} ^{\frac {\partial V}{\partial h}}+\overbrace {\frac {2\pi rh}{3}} ^{\frac {\partial V}{\partial r}}{\frac {\partial r}{\partial h}}}
2886:{\displaystyle {\frac {\operatorname {d} V}{\operatorname {d} r}}=\overbrace {\frac {2\pi rh}{3}} ^{\frac {\partial V}{\partial r}}+\overbrace {\frac {\pi r^{2}}{3}} ^{\frac {\partial V}{\partial h}}{\frac {\partial h}{\partial r}}}
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applies here since saying 'that is incorrect' is not my way of clarifying issues. Some sources are self-consistent, others are not. This is a matter of logic, not notation. Whatever the notation, the distinction between a function
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we'd conclude that: Americans invented partial derivatives, and they probably spoke (a form of) English; their invention was aided by the French and quickly adopted by the Greek; and
Russians generally know nothing about partial
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In regards to your second question, I'm not really sure what you're asking, but I can tell you that, as far as I know, the partial differential symbol is used only in derivatives, so in the integral, for example, it would be just
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Regarding the font, yes, that is a common problem in
Knowledge. Since it is a collaboration it happens that content added by different people have different styles. Anyone can fix problems like that. Including you if you like.
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2157:"a partial derivative of a function of several variables is its derivative with respect to one of those variables with the others held constant (as opposed to the total derivative, in which all variables are allowed to vary"
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All depends on the sources, many of which are the cause of the confusion. Up to (rather wide) variations in notation, there are essentially two kinds of partial derivative operators: (i) those operating on functions, say,
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Very intriguing and/or paradoxical the situation you mention about applications of math in medical and physiological context, but not directly influencing the formation/education of medical professionals involved in
2655:{\displaystyle {\frac {\operatorname {d} V}{\operatorname {d} h}}=\overbrace {\frac {\pi r^{2}}{3}} ^{\frac {\partial V}{\partial h}}+\overbrace {\frac {2\pi rh}{3}} ^{\frac {\partial V}{\partial r}}{\frac {dr}{dh}}}
2486:{\displaystyle {\frac {\operatorname {d} V}{\operatorname {d} r}}=\overbrace {\frac {2\pi rh}{3}} ^{\frac {\partial V}{\partial r}}+\overbrace {\frac {\pi r^{2}}{3}} ^{\frac {\partial V}{\partial h}}{\frac {dh}{dr}}}
5651:. The aforementioned confusion causes many problems, for instance, when changing variables or formulating the chain rule. For various reasons, I prefer leaving it to the editors to make all necessary changes.--
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4. A vessel to be constructed is in the shape of a cylinder of radius r with equal conical ends, the semi-vertical angle of each cone being α. If V is the volume and S is the total surface area, show that
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university library make the
Cyrillic connection. Nor does a search of Google Scholar give any primary source for: Cyrillic "partial derivative." So, I don't believe that the Cyrillic reference meets the
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A very interesting area or (applied) science (that is) rather qualitative (math is not required, at least as I know, in the educational system preparing those professionals) is medicine! (Thoughts?)--
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the total derivative is, in fact, the sum of the partial derivatives. i seem to remember explaining this before. but no matter. keep removing other people's contributions if you dont understand them
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and not their values. Since x and y will always be understood to be free parameters (pairs of which comprise the domain) here, the partial derivative function and the partial derivative function
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1885:. I think the reason for this is that a differential is only "partial" in the context of a derivative. To me, at least, having a differential be "partial" otherwise would be meaningless.
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applied in their activities. The mentioned applications with medical impact that use mathematical notions are therefore left to be developed by other categories of professionals who have
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I cannot find any passage that supports your mentioned "standard", perhaps you can elaborate? I would have chosen the opposite interpretation (my second alternative from my initial post).
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You seem to imply that readers frequently get confused. However, certainly I have not (though I'm biased as I've formally instructed this content before).--18:48, 2 October 2019 (UTC)
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Is there a WP policy that discourages arguments based on the number of Google 'hits'? If not, can someone please propose one? Here for example: From searching Google today:
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I would agree with such a section, but preferably at the bottom of the article; otherwise I would think that it may confuse more than illuminate. Some connections with the
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than the
Cyrillic Б. If no one can give an authoritative cite for Cyrillic, my vote would be for deleting sentence so suggesting it. Greek origin looks more plausible.
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1663:, right? In terms of it being a "double integral", a double integral integrates one variable, then the other. In the example I give above, only "'P'" is integrated.
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Many other mathematics-related articles have an implementation of the topic in various programming languages. Will anybody set up this page with such an example? --
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in that case. You probably think about surfaces defined by an implicit equation, and that can be described by several "charts", involving several functions. --
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Of course (1,1,3) is the point on the surface, but is it really a good way of phrasing things? You wouldn't talk of the derivative of the exponential function
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Here is my site with partial derivative example problems. Someone please put this link in the external links section if you think it's helpful and relevant.
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weight. This is what I mean by "consensus". You seem to have pointed out a great variety of treatments in textbooks but not any sources that specifically
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668:. Is it just a notational convenience or is there some rigerous extension of partial differentiation onto volumes? Also, how does this relate to the
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If someone can tell me how to attach documents to
Knowledge `Talk' items, I can do so for copies of the three relevant pages from Flett's book. --
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I am a bit perplexed as to why the formal definition is at the end and the example is at the beginning, I think some reordering is in order here!
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3614:, because derivative operators always work on the stuff, that comes after it? (So basically read from right to left, rather from left to right?)
1913:. Furthermore, the intro now purports to say that the Greek letter in question is actually a "d"—something that doesn't exist in that alphabet.
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Yeah, this is really an impressive piece of work. The introduction is really accessible, contrary to loads of the maths articles on wikipedia.
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and we must implicitly choose such a function when applying a partial derivative operator. The point of my bringing up RIGHTGREATWRONGS is
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as an 'other notation' (which he never uses) whose meaning depends on the context (a polite way of saying that it is inherently ambiguous).
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Since there is only one variable in the formula for the area of a circle, as the article mentions, isn't the example using it a bad one?
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3730:{\displaystyle {\frac {\partial ^{2}f}{\partial x\partial y}}\equiv \partial \left({\frac {\partial f}{\partial x}}\right)/\partial y,}
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If both r and α can vary, show that for a vessel of fixed volume and minimum surface area, cos α = 2/3, and determine r in terms of V.
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We should also discuss the numericalization in this article. At least illustrate how to numericalize the 2nd derivative. anyone agree?
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2045:(1928-29), still widely regarded as definitive for the period through its writing, makes no reference to the cursive Cyrillic letter
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4163:. Perhaps this has to do with a misconception of a historical nature of bad legacy having its origin in Medieval times (before the
4167:) when math was not very appreciated or developed in those medieval times when only the literary and rethorical aspects from the
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Radiologists, when determining what kind of scan to give someone maybe, but they mostly have software that does this for them.
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3817:, these subpages are now deprecated. The comments may be irrelevant or outdated; if so, please feel free to remove this section.
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2135:'∂' also corresponds to the small Greek delta 'ό' which was also used before the 20th century as partial derivative notation.
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of some math notions such as engineers. After all, the above mentioned applications can be envisioned to belong more in the
4553:{\displaystyle {\bar {G_{i}}}=\left({\frac {\partial G}{\partial n_{i}}}\right)_{T,P,n_{j\neq i},({\frac {x_{1}}{x_{3}}})}}
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You haven't asked a question or made a proposal or anything, but I'll add that essentially all science is "math-based". --
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all of these notations and the difference between them. In particular, the great majority of sources appear to agree that
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1355:{\displaystyle F(P_{d},Q)-F(P_{b},Q)=\int _{P_{b}}^{P_{d}}F'(P,Q)\partial P=\int _{P_{b}}^{P_{d}}G_{p}(P,Q)\partial P\,\!}
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5074:(Incidentally, I notice that the mathematical font used for equations is different from that used for inline formulas.)
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5044:{\displaystyle \left({\frac {\partial x_{1}}{\partial x_{2}}}\right)_{\frac {x_{1}}{x_{3}}}=-{\frac {x_{1}}{1-x_{2}}}}
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2108:"partial derivative" Amrica<. It returns ~35800 'hits'. At least, Google claims that number of hits. It can't be
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Although it's been many, many years since I've done any maths, I would agree - this example does seem pointless. --
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I recommend that the definition of partial derivative either include a hyperlink to Standard Basis or define e_i.
5444:. In this article, this distinction seems to be forgotten, leading to meaningless expressions. In particular, if
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is understood to be another function wherever it is defined. After all, the partial derivative operator acts on
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thinkers of Antiquity were highly esteemed and medicine was seen as craft or practical art in contrast with the
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In regards to your first question, the notation that I learned for partial derivatives includes, in this case,
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G of a mixture is a sum of weighted partial derivatives, weights being the molar amounts of the components n
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is says that this symmetry does only hold under special requirements, so it is not generally true, see here
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Hi, i'm currently studying on this topic(partial derivative) and i need some help to solve these problems.
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I agree with you that this is just wrong, if not vandalism. I therefore reverted it to the correct version.
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Agreed. I've never known what a partial derivate is so I decieded to check it up. Clearly and well written.
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True (almost), but there are some areas from particular sciences which are more qualitative-descriptive.--
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can not be correct, can it? I think that would be the undifferentiated function, not the derivative. --
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i) Express u in terms of A and B only. ii) Prove that u is a maximum if the triangle is equilateral.
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This sentence seems confusing to me since the quotient which is above does not contain x_i per se.
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confusing sentence: "In the above difference quotient, all the variables except xi are held fixed."
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basically means "one thin sliver of the surface"; does this relate to the difference between ∂ and
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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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Doesn't f sub x = the partial of f / the partial of x? (not the partial of f / the partial of y)
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Doesn't f sub x = the partial of f / the partial of x? (not the partial of f / the partial of y)
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All that stuff needs to go in the last section, where the gradient is discussed. Other opinions?
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is not used because it does not indicate which variable the derivative is taken with respect to.
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The answer to the question in this section title seems to be in the following classic article:
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4025:{\displaystyle f_{x}^{\prime },\ {\color {red}{f_{x}}},\ \partial _{x}f,\ D_{x}f,\ D_{1}f,...}
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can be represented geometrically/graphically in case of ternary and quaternary systems using
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Should the reference to the Cyrillic letter in the lead be deleted? For now, I believe so.
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The last relation can have the derivative taken at with respect to one of the weights, say x
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6170:{\displaystyle \textstyle {\frac {\partial }{\partial x}}\mathrm {e} ^{x}=\mathrm {e} ^{x}}
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a surface, as the boundary of an area is a path (at least intuitively). Hope this helps.
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Okay, but there is one and only one definition of a "partial derivative", which is as an
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is a function) and (ii) those operating on expressions denoting numbers, for instance
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Last edited at 20:47, 20 September 2009 (UTC). Substituted at 02:27, 5 May 2016 (UTC)
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6781:) teach with a whole lot of these notations, including differential geometry classes.
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3529:{\displaystyle {\frac {\partial ^{2}f}{\partial x\partial y}}\equiv ...\equiv f_{xy}}
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My compliments to whoever has guided this wiki page, be it a group or an individual.
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exist at a given point a, the function need not be continuous there." Brian Maurizi
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preferred variant, provided the concepts are not confused. Aside: the joke about
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http://www.exampleproblems.com/index.php/PDE:Integration_and_Seperation_of_variables
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is meaningful and a great deal of professors at my institution (one named in the
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What actually is the difference between dy/dx and δy/δx? Is it just preference?
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content of a basic calculus textbook is not adequate enough for this concept. --
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1004:{\displaystyle F(P_{d},Q)-F(P_{b},Q)=\int _{P_{b}}^{P_{d}}F(P,Q)\partial P\,\!}
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It seems that there are non-trivial aspects of the use of partial derivatives
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is obtained by diving each weight (called mole fractions) by the sum of all n
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i came to talk to say same things- best intro in any wilpedia item on math
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6222:{\displaystyle \textstyle {\frac {\partial }{\partial y}}\mathrm {e} ^{x}=0}
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it does matter how I interpret the notation. Also in your mentioned article
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Is there anyone able to enlighten me on this problems? THANKS a million...
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is unrelated to any particular choice of variable names. Proper forms are
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3. A, B and C are the angles of a triangle and u is a function defined as
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I'd like to see a section addressing the semantic difference between ∂ and
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partial derivatives, including comparison between notations, was found in
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Already in precalculus, students learn the difference between a function
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If so, please cite here. I'm doubtful based on # of hits for Google of:
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because this variable has been particularized to the 'specific values'
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The first additional relation can be expressed equivalently in term of
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equations, but it's generally not required to get into medical school.
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Yes, you're right. I have corrected it, and removed the attention box.
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Yes, I agree. It appears those paragraphs have already been deleted.
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and quaternary plot in equilateral triangle and tetrahedron, etc.)--
1459:", if you have "dP", you know it's regarding P, not Q, so what does
6728:. Treating an expression as the function defined by it is a common
1029:
Yes, that is true, assuming that by the integrand you really meant
1075:
itself. Also, I believe that the differential here would be just
3114:{\displaystyle k={\frac {h}{r}}={\frac {\partial h}{\partial r}}}
874:{\displaystyle F'(P,Q)={\frac {\partial F(P,Q)}{\partial P}}\,\!}
4841:{\displaystyle {\tilde {G}}=\sum _{i=1}^{m}x_{i}{\bar {G_{i}}},}
4701:{\displaystyle {\tilde {G}}=\sum _{i=1}^{m}x_{i}{\bar {G_{i}}},}
3584:{\displaystyle {\frac {\partial ^{2}f}{\partial x\,\partial y}}}
3307:
see basic definition, where f sub a takes y to be the variable.
419:
6625:{\displaystyle \textstyle {\frac {\partial f}{\partial x_{j}}}}
3833:
see basic definition, where f sub a takes y to be the variable.
6669:{\displaystyle \textstyle {\frac {\partial }{\partial x_{j}}}}
3606:
Or does it mean, that you first differentiate with respect to
184:
15:
5673:
Sorry, that is not correct or supported by usage in sources.
4749:
varies, only the sum of the other mole fractions can vary:--
3930:
2235:
2. If u = ax +by and v = bx – ay, determine the value of:
1991:
Earlier notation used Greek small delta δ, which looks like
1945:
v. 2, p. 220 Leibniz used a 'δ' for the partial derivative.
342:
Thanks to all the writers of this page! Saved my behind (-:
3595:
Does it mean, that you first differentiate with respect to
2058:
18:50, 11 December 2006 (UTC) ('rounded' for 'curved' edit
2046:
2112:. Disagree? Okay, then tell me what hit number 10000 is.
3179:(1, 1) = 3. Perhaps it is an error that has slipped by?
1934:
I think the firs person to use that notation was leibniz
3809:
664:. My sense is that this has some underlying meaning in
6642:
6593:
6415:
6184:
6123:
5849:
4851:
From the sum of mole fractions equals 1 follows that:
4616:
in the system and using the property that the sum of x
3357:
Inconsistency regarding Second-order mixed derivatives
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5566:{\displaystyle {\frac {\partial f(x,y)}{\partial x}}}
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4332:{\displaystyle G=\sum _{i=1}^{m}n_{i}{\bar {G_{i}}},}
4269:
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abilities/skills involving mathematical thinking and
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5250:{\displaystyle f(x_{1},\ldots ,x_{i},\ldots ,x_{n})}
2139:
The problem is that that sentence follows a related
656:, it is common to denote the surface of a volume as
281:, a collaborative effort to improve the coverage of
3767:Thank you for your answer. But in the same article
2131:Deletion from the previous Edit of the article of:
535:
or it may be engineering shorthand; I'm not sure. —
6769:
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6635:c.On page 353, a few examples illustrate how both
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5183:. It is referring to the variable of the function
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4074:. I also notice some objection to the expression
2714:{\displaystyle k={\frac {h}{r}}={\frac {dh}{dr}}}
2015:, 2nd Ser., Vol. 25, No. 1 (Sep., 1923), pp. 1-46
523:. Also, in sloppy engineering notation I've seen
6770:{\displaystyle {\frac {\partial f}{\partial x}}}
5703:{\displaystyle {\frac {\partial f}{\partial x}}}
5603:{\displaystyle {\frac {\partial u}{\partial x}}}
5494:{\displaystyle {\frac {\partial f}{\partial x}}}
1578:{\displaystyle E'(P)=F'(P,Q)=\sin(P)\cos(Q)\,\!}
33:for general discussion of the article's subject.
6837:Knowledge level-4 vital articles in Mathematics
3813:, and are posted here for posterity. Following
3603:, because that is the order of the denominator?
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1443:
1394:
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1016:
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3737:as is implicit in the H matrix in the article
2324:article, I feel that the equations should be
2011:, "The History of Notations of the Calculus."
3807:The comment(s) below were originally left at
1656:{\displaystyle E'(P)dP=F'(P,Q)\partial P\,\!}
792:{\displaystyle F'(P)={\frac {dF(P)}{dP}}\,\!}
174:
8:
5956:, or the joke doesn't work, respectively).--
4737:at a constant ratio of the other 2 weights x
725:Integration equivalent of partial derivative
563:Now I see, the page I needed to look at was
3170:Three arguments to a two-variable function?
531:alone as well. This may be rigerous use of
5075:
4189:It also seems that medical doctors feel a
1958:Can we get a computerized notation set up?
1162:. In terms of full notation, should it be
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2127:Deletion of 2nd sentence of 2nd paragraph
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5257:one line before the formula in question.
6827:Knowledge vital articles in Mathematics
5298:Pervasive confusion between a function
4918:{\displaystyle dx_{3}=-(dx_{1}+dx_{2})}
3570:
3539:So my basic question is the meaning of
3399:
2224:1. The variable x and r are defined as
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1571:
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867:
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2114:And what about other search engines???
2024:from many colleges and universities.
672:you find in a volume integral? (There
515:, then what is the difference between
408:Partial derivative of Area of a circle
6842:C-Class vital articles in Mathematics
6578:{\displaystyle (x_{1},\ldots ,x_{n})}
6359:as a real-valued function called the
5949:notation section. Note though that a
5280:still far from ideal for a beginner.
4070:. An example is one connected to the
4064:in the context of math-based sciences
3852:The partial derivative of a function
2259:S = 2V/r + 2πr²(cosecα - 2/3cotα )
415:(Unsigned comment by 68.78.139.53 on
7:
2296:Knowledge:Reference desk/Mathematics
2092:"partial derivative" Greek ~12300
2089:"partial derivative" French ~24000
2086:"partial derivative" English ~36400
2083:"partial derivative" American ~54000
2075:Number of Google 'hits' inadmissable
275:This article is within the scope of
6406:b. On page 352 (top), Flett states
2227:x = r cos θ and y = r sin θ.
2043:A History of Mathematical Notations
1820:{\displaystyle \partial _{P}F(P,Q)}
676:basically means "one tiny point in
218:It is of interest to the following
23:for discussing improvements to the
6852:High-priority mathematics articles
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6256:a. On page 351 (bottom), assuming
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3847:I think the red term in the quote
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2095:"partial derivative" Cyrillic ~519
1790:
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1643:
1486:add? You could just as easily say
1466:
1342:
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1086:
991:
858:
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14:
6352:{\displaystyle \mathrm {D} _{j}f}
6096:is an expression in the variable
5835:{\displaystyle \mathrm {D} _{k}f}
5763:{\displaystyle \mathrm {D} _{k}f}
5353:requires a thorough cleaning up.
4252:The expression for the extensive
3941:
3815:several discussions in past years
1943:History of Methematical Notations
295:Knowledge:WikiProject Mathematics
6822:Knowledge level-4 vital articles
6698:{\displaystyle \mathrm {D} _{j}}
6298:{\displaystyle \mathbb {R} ^{n}}
6089:{\displaystyle \mathrm {e} ^{x}}
6060:{\displaystyle \mathrm {e} ^{x}}
4248:Example of use in thermodynamics
3810:Talk:Partial derivative/Comments
3453:Higher order partial derivatives
3335:The introduction is EXCELLENT!
2074:
527:appear alone; I think I've seen
298:Template:WikiProject Mathematics
262:
252:
231:
198:
189:
45:Click here to start a new topic.
6779:2019 college admissions scandal
6276:is a function from a subset of
3312:about what the notation means.
1448:{\displaystyle F'_{p}(P,Q)\,\!}
315:This article has been rated as
6832:C-Class level-4 vital articles
6572:
6540:
6493:for the partial derivative of
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5770:for the partial derivative of
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4371:{\displaystyle {\bar {G_{i}}}}
4362:
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4207:appreciation of the importance
4203:another conceptual perspective
4053:context of math-based sciences
3880:
3862:
3769:symmetry of second derivatives
3636:symmetry of second derivatives
3322:22:36, 20 September 2009 (UTC)
2062:20:16, 11 December 2006 (UTC))
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1479:{\displaystyle \partial P\,\!}
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1:
4161:formulating medical diagnoses
4046:02:01, 4 September 2017 (UTC)
3893:with respect to the variable
3886:{\displaystyle f(x,y,\dots )}
3254:). For me they are just not
3164:10:04, 25 February 2009 (UTC)
3145:15:00, 18 February 2009 (UTC)
2148:14:56, 29 November 2006 (UTC)
2121:01:34, 15 November 2007 (UTC)
2067:20:18, 12 December 2006 (UTC)
2029:01:08, 29 November 2006 (UTC)
2000:02:25, 28 November 2006 (UTC)
1987:"partial derivative" Cyrillic
1950:17:31, 11 December 2006 (UTC)
572:17:40, 15 December 2005 (UTC)
402:19:52, 25 December 2015 (UTC)
289:and see a list of open tasks.
42:Put new text under old text.
6847:C-Class mathematics articles
6533:-th coordinate at the point
6320:{\displaystyle \mathbb {R} }
5290:13:57, 7 February 2019 (UTC)
5271:15:19, 16 January 2019 (UTC)
5096:The formula doesn't contain
5090:13:02, 16 January 2019 (UTC)
5061:00:25, 27 October 2017 (UTC)
4759:16:07, 26 October 2017 (UTC)
4729:15:45, 26 October 2017 (UTC)
4589:{\displaystyle {\tilde {G}}}
4567:Gibbs energy of the mixture
4238:07:26, 24 January 2024 (UTC)
4223:11:53, 26 October 2017 (UTC)
4185:11:40, 26 October 2017 (UTC)
4154:01:30, 26 October 2017 (UTC)
4139:00:12, 26 October 2017 (UTC)
4123:21:05, 25 October 2017 (UTC)
4107:14:31, 25 October 2017 (UTC)
4092:11:35, 25 October 2017 (UTC)
3198:As 82.130.38.44 determined,
2294:Please ask this question at
2287:05:35, 2 February 2009 (UTC)
2176:20:26, 13 October 2007 (UTC)
1457:Comparison with "d" notation
610:03:17, 23 October 2019 (UTC)
559:02:59, 5 December 2005 (UTC)
540:02:00, 5 December 2005 (UTC)
489:07:18, 24 January 2024 (UTC)
454:Disagree with recent changes
441:I agree. I've removed it. --
6789:Hyperlink to Standard Basis
6719:17:06, 2 October 2019 (UTC)
6239:13:27, 2 October 2019 (UTC)
6067:works perfectly well since
5964:08:16, 2 October 2019 (UTC)
5933:07:58, 2 October 2019 (UTC)
5726:07:27, 2 October 2019 (UTC)
5718:are basically identical. --
5661:07:18, 2 October 2019 (UTC)
4745:because when the variable x
3351:07:13, 8 January 2013 (UTC)
2107:But let's also search : -->
1399:{\displaystyle F'(P,Q)\,\!}
1155:{\displaystyle F'(P,Q)\,\!}
50:New to Knowledge? Welcome!
6868:
5412:for a particular argument
4051:Use of this notion in the
3624:16:27, 10 April 2015 (UTC)
3268:10:25, 20 April 2009 (UTC)
3214:09:57, 20 April 2009 (UTC)
3194:09:17, 20 April 2009 (UTC)
2192:19:20, 21 April 2010 (UTC)
1984:"partial derivative" Greek
1775:{\displaystyle F_{P}(P,Q)}
1095:{\displaystyle \partial P}
1064:{\displaystyle F_{P}(P,Q)}
618:Vote for new external link
367:09:43, 18 March 2009 (UTC)
6803:00:25, 19 July 2023 (UTC)
5918:. For a proper treatment
3828:01:21, 23 June 2007 (UTC)
3822:
3791:12:06, 19 June 2015 (UTC)
3610:and then with respect to
3599:and then with respect to
1967:16:41, 19 July 2006 (UTC)
1928:00:29, 29 June 2006 (UTC)
881:, doesn't it follow that
466:02:27, 23 Mar 2005 (UTC)
433:09:54, 11 June 2006 (UTC)
314:
247:
226:
80:Be welcoming to newcomers
5644:{\displaystyle u=f(x,y)}
4191:less stringent necessity
3913:is variously denoted by
3295:04:35, 22 May 2009 (UTC)
2316:verify total derivatives
2310:04:38, 22 May 2009 (UTC)
2248:u = sin A sin B sin C.
2052:Knowledge: verifiability
1918:23:25, 31 May 2006 (UTC)
1890:22:49, 5 June 2006 (UTC)
1676:19:28, 4 June 2006 (UTC)
1111:03:09, 1 June 2006 (UTC)
1024:18:44, 20 May 2006 (UTC)
799:and (with respect to P)
719:23:25, 31 May 2006 (UTC)
693:23:29, 18 May 2006 (UTC)
634:Ordering of the sections
588:10:44, 3 June 2010 (UTC)
382:10:42, 3 June 2010 (UTC)
345:Thanks again, Sam Krupa
321:project's priority scale
5176:{\displaystyle a_{i}+h}
3751:20:09, 9 May 2015 (UTC)
3278:This article needs work
2211:15:22, 3 May 2008 (UTC)
1860:{\displaystyle F'(P,Q)}
654:computational mechanics
643:22:13, 5 May 2006 (UTC)
278:WikiProject Mathematics
6817:C-Class vital articles
6771:
6726:operator on a function
6699:
6670:
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6579:
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6507:
6487:
6395:
6375:
6361:partial derivative of
6353:
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6030:{\displaystyle f(x,y)}
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5405:{\displaystyle f(x,y)}
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5346:{\displaystyle f(x,y)}
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4211:biomedical engineering
4199:mathematical modelling
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1941:According to Cajori's
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511:is only a function of
75:avoid personal attacks
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6488:
6396:
6376:
6354:
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6249:Mathematical Analysis
6224:
6172:
6116:, not a function, so
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5997:
5913:
5837:
5805:
5785:
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5705:
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5605:
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5501:is meaningless since
5496:
5459:
5439:
5437:{\displaystyle (x,y)}
5407:
5372:
5348:
5313:
5252:
5178:
5145:
5143:{\displaystyle a_{i}}
5118:
5116:{\displaystyle x_{i}}
5046:
4920:
4843:
4785:
4703:
4645:
4591:
4555:
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4393:
4378:is the partial molar
4373:
4334:
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4165:Scientific Revolution
4027:
3908:
3888:
3732:
3586:
3531:
3443:
3240:
3238:{\displaystyle e^{x}}
3124:Please verify this.
3116:
3057:
2888:
2716:
2657:
2488:
2231:method of b) and c).
2141:parenthetical comment
2013:Annals of Mathematics
1862:
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1006:
876:
794:
666:differential geometry
594:functional derivative
205:level-4 vital article
100:Neutral point of view
6744:
6680:
6639:
6590:
6537:
6517:
6513:with respect to the
6497:
6412:
6385:
6381:with respect to the
6365:
6331:
6309:
6280:
6260:
6181:
6120:
6100:
6071:
6042:
6006:
5986:
5846:
5814:
5794:
5790:with respect to the
5774:
5742:
5677:
5614:
5577:
5525:
5505:
5468:
5464:is a function, then
5448:
5416:
5381:
5361:
5322:
5302:
5187:
5154:
5127:
5100:
4932:
4858:
4767:
4627:
4571:
4425:
4402:
4382:
4346:
4267:
4078:recently removed by
4072:Gibbs-Duhem equation
3917:
3897:
3856:
3643:
3543:
3462:
3372:
3222:
3069:
2900:
2731:
2669:
2500:
2331:
1972:Is modern origin of
1831:
1786:
1744:
1684:
1591:
1492:
1463:
1410:
1366:
1168:
1122:
1083:
1033:
885:
803:
733:
301:mathematics articles
105:No original research
6002:and the expression
5979:WP:RIGHTGREATWRONGS
5946:WP:RIGHTGREATWRONGS
5944:We are not here to
4076:math-based sciences
4068:applied mathematics
3934:
3775:in the general case
2238:(∂u/∂x)y.( ∂x/∂u)v
2020:accessible through
1425:
1316:
1255:
972:
592:δy/δx can denote a
6767:
6695:
6666:
6665:
6622:
6621:
6575:
6523:
6503:
6483:
6482:
6391:
6371:
6349:
6317:
6295:
6266:
6219:
6218:
6167:
6166:
6106:
6086:
6057:
6027:
5992:
5908:
5907:
5832:
5810:-th argument (and
5800:
5780:
5760:
5700:
5641:
5600:
5563:
5511:
5491:
5454:
5434:
5402:
5367:
5343:
5318:and an expression
5308:
5247:
5173:
5140:
5113:
5041:
4915:
4838:
4698:
4586:
4550:
4408:
4388:
4368:
4329:
4080:user:Deacon Vorbis
4022:
3954:
3920:
3903:
3883:
3823:Needs references.
3803:Assessment comment
3727:
3581:
3571:
3526:
3455:-section it says:
3438:
3400:
3365:-section it says:
3235:
3111:
3052:
2883:
2711:
2652:
2483:
1900:Greek or Cyrillic?
1857:
1817:
1772:
1730:
1728:
1653:
1652:
1650:
1575:
1574:
1572:
1476:
1475:
1473:
1445:
1444:
1442:
1413:
1396:
1395:
1393:
1352:
1351:
1349:
1288:
1227:
1152:
1151:
1149:
1092:
1061:
1001:
1000:
998:
944:
871:
870:
868:
789:
788:
786:
507:. For example, if
270:Mathematics portal
214:content assessment
86:dispute resolution
47:
25:Partial derivative
6765:
6730:abuse of notation
6663:
6619:
6526:{\displaystyle j}
6506:{\displaystyle f}
6436:
6394:{\displaystyle j}
6374:{\displaystyle f}
6269:{\displaystyle f}
6198:
6137:
6109:{\displaystyle x}
5995:{\displaystyle f}
5890:
5803:{\displaystyle k}
5783:{\displaystyle f}
5716:evaluated at x, y
5698:
5598:
5561:
5514:{\displaystyle f}
5489:
5457:{\displaystyle f}
5370:{\displaystyle f}
5311:{\displaystyle f}
5092:
5080:comment added by
5039:
5000:
4972:
4832:
4779:
4692:
4639:
4583:
4543:
4480:
4444:
4411:{\displaystyle i}
4391:{\displaystyle G}
4365:
4323:
4254:Gibbs free energy
3996:
3978:
3960:
3939:
3906:{\displaystyle x}
3837:
3836:
3707:
3677:
3579:
3496:
3408:
3341:comment added by
3212:
3162:
3148:
3131:comment added by
3109:
3086:
3050:
3031:
3029:
3009:
3005:
2980:
2978:
2958:
2954:
2927:
2881:
2862:
2860:
2840:
2836:
2810:
2808:
2788:
2784:
2758:
2709:
2686:
2650:
2631:
2629:
2609:
2605:
2580:
2578:
2558:
2554:
2527:
2481:
2462:
2460:
2440:
2436:
2410:
2408:
2388:
2384:
2358:
2322:total derivatives
2290:
2273:comment added by
2178:
2166:comment added by
1724:
865:
783:
580:My 2 Cents' Worth
495:Comparison with "
491:
475:comment added by
424:
404:
392:comment added by
374:My 2 Cents' Worth
357:comment added by
335:
334:
331:
330:
327:
326:
183:
182:
66:Assume good faith
43:
6859:
6776:
6774:
6773:
6768:
6766:
6764:
6756:
6748:
6704:
6702:
6701:
6696:
6694:
6693:
6688:
6675:
6673:
6672:
6667:
6664:
6662:
6661:
6660:
6644:
6631:
6629:
6628:
6623:
6620:
6618:
6617:
6616:
6603:
6595:
6584:
6582:
6581:
6576:
6571:
6570:
6552:
6551:
6532:
6530:
6529:
6524:
6512:
6510:
6509:
6504:
6492:
6490:
6489:
6484:
6475:
6474:
6456:
6455:
6437:
6435:
6434:
6433:
6417:
6400:
6398:
6397:
6392:
6380:
6378:
6377:
6372:
6358:
6356:
6355:
6350:
6345:
6344:
6339:
6327:, Flett defines
6326:
6324:
6323:
6318:
6316:
6304:
6302:
6301:
6296:
6294:
6293:
6288:
6275:
6273:
6272:
6267:
6228:
6226:
6225:
6220:
6211:
6210:
6205:
6199:
6197:
6186:
6176:
6174:
6173:
6168:
6165:
6164:
6159:
6150:
6149:
6144:
6138:
6136:
6125:
6115:
6113:
6112:
6107:
6095:
6093:
6092:
6087:
6085:
6084:
6079:
6066:
6064:
6063:
6058:
6056:
6055:
6050:
6036:
6034:
6033:
6028:
6001:
5999:
5998:
5993:
5976:
5943:
5917:
5915:
5914:
5909:
5891:
5889:
5881:
5868:
5867:
5851:
5841:
5839:
5838:
5833:
5828:
5827:
5822:
5809:
5807:
5806:
5801:
5789:
5787:
5786:
5781:
5769:
5767:
5766:
5761:
5756:
5755:
5750:
5736:
5709:
5707:
5706:
5701:
5699:
5697:
5689:
5681:
5672:
5650:
5648:
5647:
5642:
5609:
5607:
5606:
5601:
5599:
5597:
5589:
5581:
5572:
5570:
5569:
5564:
5562:
5560:
5552:
5529:
5520:
5518:
5517:
5512:
5500:
5498:
5497:
5492:
5490:
5488:
5480:
5472:
5463:
5461:
5460:
5455:
5443:
5441:
5440:
5435:
5411:
5409:
5408:
5403:
5376:
5374:
5373:
5368:
5352:
5350:
5349:
5344:
5317:
5315:
5314:
5309:
5263:Cactus0192837465
5256:
5254:
5253:
5248:
5243:
5242:
5224:
5223:
5205:
5204:
5182:
5180:
5179:
5174:
5166:
5165:
5149:
5147:
5146:
5141:
5139:
5138:
5122:
5120:
5119:
5114:
5112:
5111:
5050:
5048:
5047:
5042:
5040:
5038:
5037:
5036:
5020:
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5010:
5002:
5001:
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4998:
4989:
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4969:
4956:
4955:
4954:
4941:
4924:
4922:
4921:
4916:
4911:
4910:
4895:
4894:
4873:
4872:
4847:
4845:
4844:
4839:
4834:
4833:
4828:
4827:
4818:
4815:
4814:
4804:
4799:
4781:
4780:
4772:
4707:
4705:
4704:
4699:
4694:
4693:
4688:
4687:
4678:
4675:
4674:
4664:
4659:
4641:
4640:
4632:
4595:
4593:
4592:
4587:
4585:
4584:
4576:
4559:
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4556:
4551:
4549:
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4541:
4532:
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4522:
4514:
4513:
4485:
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4479:
4478:
4477:
4464:
4456:
4446:
4445:
4440:
4439:
4430:
4417:
4415:
4414:
4409:
4397:
4395:
4394:
4389:
4377:
4375:
4374:
4369:
4367:
4366:
4361:
4360:
4351:
4338:
4336:
4335:
4330:
4325:
4324:
4319:
4318:
4309:
4306:
4305:
4295:
4290:
4031:
4029:
4028:
4023:
4006:
4005:
3995:
3988:
3987:
3977:
3970:
3969:
3959:
3955:
3953:
3952:
3951:
3938:
3933:
3928:
3912:
3910:
3909:
3904:
3892:
3890:
3889:
3884:
3820:
3819:
3812:
3736:
3734:
3733:
3728:
3717:
3712:
3708:
3706:
3698:
3690:
3678:
3676:
3662:
3658:
3657:
3647:
3590:
3588:
3587:
3582:
3580:
3578:
3562:
3558:
3557:
3547:
3535:
3533:
3532:
3527:
3525:
3524:
3497:
3495:
3481:
3477:
3476:
3466:
3447:
3445:
3444:
3439:
3437:
3436:
3409:
3407:
3391:
3387:
3386:
3376:
3353:
3292:
3287:
3244:
3242:
3241:
3236:
3234:
3233:
3206:
3156:
3147:
3125:
3120:
3118:
3117:
3112:
3110:
3108:
3100:
3092:
3087:
3079:
3061:
3059:
3058:
3053:
3051:
3049:
3041:
3033:
3030:
3028:
3020:
3012:
3010:
3001:
2987:
2986:
2984:
2979:
2977:
2969:
2961:
2959:
2950:
2949:
2948:
2935:
2934:
2932:
2928:
2926:
2915:
2904:
2892:
2890:
2889:
2884:
2882:
2880:
2872:
2864:
2861:
2859:
2851:
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2841:
2832:
2831:
2830:
2817:
2816:
2814:
2809:
2807:
2799:
2791:
2789:
2780:
2766:
2765:
2763:
2759:
2757:
2746:
2735:
2720:
2718:
2717:
2712:
2710:
2708:
2700:
2692:
2687:
2679:
2661:
2659:
2658:
2653:
2651:
2649:
2641:
2633:
2630:
2628:
2620:
2612:
2610:
2601:
2587:
2586:
2584:
2579:
2577:
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2559:
2550:
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2548:
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2472:
2464:
2461:
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2451:
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2441:
2432:
2431:
2430:
2417:
2416:
2414:
2409:
2407:
2399:
2391:
2389:
2380:
2366:
2365:
2363:
2359:
2357:
2346:
2335:
2307:
2302:
2289:
2267:
2197:numericalization
2161:
2153:a step backwards
1866:
1864:
1863:
1858:
1841:
1826:
1824:
1823:
1818:
1798:
1797:
1781:
1779:
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1755:
1739:
1737:
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1729:
1725:
1723:
1715:
1692:
1670:
1662:
1660:
1659:
1654:
1627:
1601:
1584:
1582:
1581:
1576:
1522:
1502:
1485:
1483:
1482:
1477:
1454:
1452:
1451:
1446:
1421:
1405:
1403:
1402:
1397:
1376:
1361:
1359:
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1353:
1326:
1325:
1315:
1314:
1313:
1303:
1302:
1301:
1263:
1254:
1253:
1252:
1242:
1241:
1240:
1214:
1213:
1186:
1185:
1161:
1159:
1158:
1153:
1132:
1101:
1099:
1098:
1093:
1070:
1068:
1067:
1062:
1045:
1044:
1018:
1010:
1008:
1007:
1002:
971:
970:
969:
959:
958:
957:
931:
930:
903:
902:
880:
878:
877:
872:
866:
864:
856:
833:
813:
798:
796:
795:
790:
784:
782:
774:
757:
743:
608:
606:
601:
565:total derivative
547:Leibniz notation
413:
369:
303:
302:
299:
296:
293:
272:
267:
266:
256:
249:
248:
243:
235:
228:
211:
202:
201:
194:
193:
185:
179:
178:
164:
95:Article policies
16:
6867:
6866:
6862:
6861:
6860:
6858:
6857:
6856:
6807:
6806:
6791:
6757:
6749:
6742:
6741:
6683:
6678:
6677:
6652:
6648:
6637:
6636:
6608:
6604:
6596:
6588:
6587:
6562:
6543:
6535:
6534:
6515:
6514:
6495:
6494:
6466:
6447:
6425:
6421:
6410:
6409:
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6382:
6363:
6362:
6334:
6329:
6328:
6307:
6306:
6283:
6278:
6277:
6258:
6257:
6200:
6190:
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6178:
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6129:
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6098:
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6074:
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6045:
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5984:
5983:
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5937:
5882:
5859:
5852:
5844:
5843:
5817:
5812:
5811:
5792:
5791:
5772:
5771:
5745:
5740:
5739:
5730:
5690:
5682:
5675:
5674:
5666:
5612:
5611:
5590:
5582:
5575:
5574:
5553:
5530:
5523:
5522:
5503:
5502:
5481:
5473:
5466:
5465:
5446:
5445:
5414:
5413:
5379:
5378:
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5358:
5355:
5320:
5319:
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5299:
5234:
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5196:
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5130:
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5124:
5103:
5098:
5097:
5069:
5028:
5021:
5011:
4990:
4980:
4961:
4957:
4946:
4942:
4936:
4935:
4930:
4929:
4902:
4886:
4864:
4856:
4855:
4819:
4806:
4765:
4764:
4748:
4744:
4740:
4736:
4714:
4679:
4666:
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4624:
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4603:
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4422:
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4399:
4380:
4379:
4352:
4344:
4343:
4310:
4297:
4265:
4264:
4259:
4250:
4195:use and develop
4060:
3997:
3979:
3961:
3943:
3915:
3914:
3895:
3894:
3854:
3853:
3845:
3808:
3805:
3699:
3691:
3685:
3663:
3649:
3648:
3641:
3640:
3634:The theorem on
3563:
3549:
3548:
3541:
3540:
3513:
3482:
3468:
3467:
3460:
3459:
3425:
3392:
3378:
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3359:
3336:
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3302:
3290:
3285:
3280:
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3220:
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3172:
3126:
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3013:
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2800:
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2505:
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2473:
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2418:
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2392:
2367:
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2336:
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2328:
2318:
2305:
2300:
2268:
2260:
2249:
2239:
2218:
2199:
2155:
2129:
2118:128.250.204.118
2077:
2054:requirement.
1978:
1960:
1915:Commander Nemet
1902:
1887:Commander Nemet
1834:
1829:
1828:
1789:
1784:
1783:
1747:
1742:
1741:
1727:
1726:
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1693:
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1620:
1594:
1589:
1588:
1585:, in which case
1515:
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1490:
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1407:
1369:
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1363:
1317:
1305:
1293:
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1244:
1232:
1205:
1177:
1166:
1165:
1125:
1120:
1119:
1108:Commander Nemet
1081:
1080:
1036:
1031:
1030:
961:
949:
922:
894:
883:
882:
857:
834:
806:
801:
800:
775:
758:
736:
731:
730:
727:
716:Commander Nemet
690:—Ben FrantzDale
650:
636:
620:
604:
599:
597:
551:Oleg Alexandrov
501:
464:Oleg Alexandrov
456:
410:
405:
352:
340:
300:
297:
294:
291:
290:
268:
261:
241:
212:on Knowledge's
209:
199:
121:
116:
115:
114:
91:
61:
12:
11:
5:
6865:
6863:
6855:
6854:
6849:
6844:
6839:
6834:
6829:
6824:
6819:
6809:
6808:
6790:
6787:
6786:
6785:
6782:
6763:
6760:
6755:
6752:
6707:
6706:
6692:
6687:
6659:
6655:
6651:
6647:
6633:
6615:
6611:
6607:
6602:
6599:
6574:
6569:
6565:
6561:
6558:
6555:
6550:
6546:
6542:
6522:
6502:
6481:
6478:
6473:
6469:
6465:
6462:
6459:
6454:
6450:
6446:
6443:
6440:
6432:
6428:
6424:
6420:
6408:We also write
6404:
6401:-th coordinate
6390:
6370:
6348:
6343:
6338:
6315:
6292:
6287:
6265:
6244:
6243:
6242:
6241:
6217:
6214:
6209:
6204:
6196:
6193:
6189:
6163:
6158:
6153:
6148:
6143:
6135:
6132:
6128:
6105:
6083:
6078:
6054:
6049:
6026:
6023:
6020:
6017:
6014:
6011:
5991:
5977:I don't think
5968:
5967:
5966:
5906:
5903:
5900:
5897:
5894:
5888:
5885:
5880:
5877:
5874:
5871:
5866:
5862:
5858:
5855:
5831:
5826:
5821:
5799:
5779:
5759:
5754:
5749:
5696:
5693:
5688:
5685:
5640:
5637:
5634:
5631:
5628:
5625:
5622:
5619:
5596:
5593:
5588:
5585:
5559:
5556:
5551:
5548:
5545:
5542:
5539:
5536:
5533:
5510:
5487:
5484:
5479:
5476:
5453:
5433:
5430:
5427:
5424:
5421:
5401:
5398:
5395:
5392:
5389:
5386:
5377:and its value
5366:
5354:
5342:
5339:
5336:
5333:
5330:
5327:
5307:
5296:
5295:
5294:
5293:
5292:
5274:
5273:
5258:
5246:
5241:
5237:
5233:
5230:
5227:
5222:
5218:
5214:
5211:
5208:
5203:
5199:
5195:
5192:
5172:
5169:
5164:
5160:
5137:
5133:
5110:
5106:
5068:
5065:
5064:
5063:
5035:
5031:
5027:
5024:
5018:
5014:
5008:
5005:
4997:
4993:
4987:
4983:
4976:
4968:
4964:
4960:
4953:
4949:
4945:
4939:
4926:
4925:
4914:
4909:
4905:
4901:
4898:
4893:
4889:
4885:
4882:
4879:
4876:
4871:
4867:
4863:
4849:
4848:
4837:
4831:
4826:
4822:
4813:
4809:
4803:
4798:
4795:
4792:
4788:
4784:
4778:
4775:
4746:
4742:
4738:
4734:
4712:
4709:
4708:
4697:
4691:
4686:
4682:
4673:
4669:
4663:
4658:
4655:
4652:
4648:
4644:
4638:
4635:
4617:
4613:
4609:
4605:
4601:
4598:mole fractions
4582:
4579:
4561:
4560:
4547:
4540:
4536:
4530:
4526:
4520:
4517:
4512:
4509:
4506:
4502:
4498:
4495:
4492:
4489:
4484:
4476:
4472:
4468:
4463:
4460:
4454:
4449:
4443:
4438:
4434:
4407:
4387:
4364:
4359:
4355:
4340:
4339:
4328:
4322:
4317:
4313:
4304:
4300:
4294:
4289:
4286:
4283:
4279:
4275:
4272:
4257:
4249:
4246:
4245:
4244:
4243:
4242:
4241:
4240:
4225:
4213:perspective.--
4187:
4126:
4125:
4110:
4109:
4059:
4049:
4034:
4033:
4021:
4018:
4015:
4012:
4009:
4004:
4000:
3994:
3991:
3986:
3982:
3976:
3973:
3968:
3964:
3958:
3950:
3946:
3937:
3932:
3927:
3923:
3902:
3882:
3879:
3876:
3873:
3870:
3867:
3864:
3861:
3844:
3841:
3835:
3834:
3804:
3801:
3800:
3799:
3798:
3797:
3796:
3795:
3794:
3793:
3779:Hessian matrix
3758:
3757:
3756:
3755:
3754:
3753:
3739:Hessian matrix
3726:
3723:
3720:
3716:
3711:
3705:
3702:
3697:
3694:
3688:
3684:
3681:
3675:
3672:
3669:
3666:
3661:
3656:
3652:
3627:
3626:
3604:
3577:
3574:
3569:
3566:
3561:
3556:
3552:
3537:
3536:
3523:
3520:
3516:
3512:
3509:
3506:
3503:
3500:
3494:
3491:
3488:
3485:
3480:
3475:
3471:
3449:
3448:
3435:
3432:
3428:
3424:
3421:
3418:
3415:
3412:
3406:
3403:
3398:
3395:
3390:
3385:
3381:
3358:
3355:
3329:
3326:
3325:
3324:
3301:
3298:
3279:
3276:
3275:
3274:
3273:
3272:
3271:
3270:
3232:
3228:
3171:
3168:
3167:
3166:
3122:
3121:
3107:
3104:
3099:
3096:
3090:
3085:
3082:
3077:
3074:
3063:
3062:
3048:
3045:
3040:
3037:
3027:
3024:
3019:
3016:
3008:
3004:
3000:
2997:
2994:
2991:
2983:
2976:
2973:
2968:
2965:
2957:
2953:
2947:
2943:
2939:
2931:
2925:
2922:
2919:
2914:
2911:
2908:
2894:
2893:
2879:
2876:
2871:
2868:
2858:
2855:
2850:
2847:
2839:
2835:
2829:
2825:
2821:
2813:
2806:
2803:
2798:
2795:
2787:
2783:
2779:
2776:
2773:
2770:
2762:
2756:
2753:
2750:
2745:
2742:
2739:
2722:
2721:
2707:
2704:
2699:
2696:
2690:
2685:
2682:
2677:
2674:
2663:
2662:
2648:
2645:
2640:
2637:
2627:
2624:
2619:
2616:
2608:
2604:
2600:
2597:
2594:
2591:
2583:
2576:
2573:
2568:
2565:
2557:
2553:
2547:
2543:
2539:
2531:
2525:
2522:
2519:
2514:
2511:
2508:
2494:
2493:
2479:
2476:
2471:
2468:
2458:
2455:
2450:
2447:
2439:
2435:
2429:
2425:
2421:
2413:
2406:
2403:
2398:
2395:
2387:
2383:
2379:
2376:
2373:
2370:
2362:
2356:
2353:
2350:
2345:
2342:
2339:
2317:
2314:
2313:
2312:
2265:
2258:
2254:
2247:
2244:
2241:
2237:
2234:
2223:
2217:
2214:
2198:
2195:
2168:212.159.75.167
2154:
2151:
2137:
2136:
2128:
2125:
2115:
2113:
2106:
2097:
2096:
2093:
2090:
2087:
2084:
2076:
2073:
2072:
2071:
2070:
2069:
2039:Florian Cajori
2032:
2031:
2018:
2017:
2016:
2009:Florian Cajori
1989:
1988:
1985:
1977:
1970:
1959:
1956:
1955:
1954:
1953:
1952:
1936:
1935:
1931:
1930:
1901:
1898:
1897:
1896:
1895:
1894:
1893:
1892:
1873:
1872:
1871:
1870:
1869:
1868:
1856:
1853:
1850:
1847:
1844:
1840:
1837:
1816:
1813:
1810:
1807:
1804:
1801:
1796:
1792:
1771:
1768:
1765:
1762:
1759:
1754:
1750:
1722:
1719:
1714:
1711:
1708:
1705:
1702:
1699:
1696:
1690:
1689:
1648:
1645:
1642:
1639:
1636:
1633:
1630:
1626:
1623:
1619:
1616:
1613:
1610:
1607:
1604:
1600:
1597:
1586:
1570:
1567:
1564:
1561:
1558:
1555:
1552:
1549:
1546:
1543:
1540:
1537:
1534:
1531:
1528:
1525:
1521:
1518:
1514:
1511:
1508:
1505:
1501:
1498:
1487:
1471:
1468:
1440:
1437:
1434:
1431:
1428:
1424:
1420:
1416:
1391:
1388:
1385:
1382:
1379:
1375:
1372:
1347:
1344:
1341:
1338:
1335:
1332:
1329:
1324:
1320:
1312:
1308:
1300:
1296:
1291:
1287:
1284:
1281:
1278:
1275:
1272:
1269:
1266:
1262:
1259:
1251:
1247:
1239:
1235:
1230:
1226:
1223:
1220:
1217:
1212:
1208:
1204:
1201:
1198:
1195:
1192:
1189:
1184:
1180:
1176:
1173:
1163:
1147:
1144:
1141:
1138:
1135:
1131:
1128:
1091:
1088:
1060:
1057:
1054:
1051:
1048:
1043:
1039:
996:
993:
990:
987:
984:
981:
978:
975:
968:
964:
956:
952:
947:
943:
940:
937:
934:
929:
925:
921:
918:
915:
912:
909:
906:
901:
897:
893:
890:
863:
860:
855:
852:
849:
846:
843:
840:
837:
831:
828:
825:
822:
819:
816:
812:
809:
781:
778:
773:
770:
767:
764:
761:
755:
752:
749:
746:
742:
739:
726:
723:
722:
721:
698:In topology, ∂
649:
646:
635:
632:
619:
616:
615:
614:
613:
612:
576:
575:
574:
533:Infinitesimals
500:
493:
455:
452:
451:
450:
449:
448:
436:
435:
409:
406:
385:
339:
336:
333:
332:
329:
328:
325:
324:
313:
307:
306:
304:
287:the discussion
274:
273:
257:
245:
244:
236:
224:
223:
217:
195:
181:
180:
118:
117:
113:
112:
107:
102:
93:
92:
90:
89:
82:
77:
68:
62:
60:
59:
48:
39:
38:
35:
34:
28:
13:
10:
9:
6:
4:
3:
2:
6864:
6853:
6850:
6848:
6845:
6843:
6840:
6838:
6835:
6833:
6830:
6828:
6825:
6823:
6820:
6818:
6815:
6814:
6812:
6805:
6804:
6800:
6796:
6788:
6783:
6780:
6761:
6753:
6739:
6735:
6731:
6727:
6723:
6722:
6721:
6720:
6716:
6712:
6690:
6657:
6653:
6634:
6613:
6609:
6600:
6586:and mentions
6585:
6567:
6563:
6559:
6556:
6553:
6548:
6544:
6520:
6500:
6471:
6467:
6463:
6460:
6457:
6452:
6448:
6441:
6430:
6426:
6405:
6402:
6388:
6368:
6346:
6341:
6290:
6263:
6255:
6254:
6253:
6250:
6240:
6236:
6232:
6215:
6212:
6207:
6194:
6161:
6151:
6146:
6133:
6103:
6081:
6052:
6021:
6018:
6015:
6009:
5989:
5980:
5974:
5969:
5965:
5962:
5959:
5955:
5952:
5947:
5941:
5936:
5935:
5934:
5930:
5926:
5921:
5904:
5901:
5898:
5895:
5892:
5886:
5875:
5872:
5869:
5864:
5860:
5829:
5824:
5797:
5777:
5757:
5752:
5734:
5729:
5728:
5727:
5724:
5721:
5717:
5713:
5694:
5686:
5670:
5665:
5664:
5663:
5662:
5658:
5654:
5635:
5632:
5629:
5623:
5620:
5617:
5594:
5586:
5557:
5546:
5543:
5540:
5534:
5508:
5485:
5477:
5451:
5428:
5425:
5422:
5396:
5393:
5390:
5384:
5364:
5337:
5334:
5331:
5325:
5305:
5291:
5287:
5283:
5278:
5277:
5276:
5275:
5272:
5268:
5264:
5259:
5239:
5235:
5231:
5228:
5225:
5220:
5216:
5212:
5209:
5206:
5201:
5197:
5190:
5170:
5167:
5162:
5158:
5135:
5131:
5108:
5104:
5095:
5094:
5093:
5091:
5087:
5083:
5079:
5072:
5066:
5062:
5058:
5054:
5053:82.137.12.199
5033:
5029:
5025:
5022:
5016:
5012:
5006:
5003:
4995:
4991:
4985:
4981:
4974:
4966:
4962:
4951:
4947:
4937:
4928:
4927:
4907:
4903:
4899:
4896:
4891:
4887:
4883:
4877:
4874:
4869:
4865:
4861:
4854:
4853:
4852:
4835:
4824:
4820:
4811:
4807:
4801:
4796:
4793:
4790:
4786:
4782:
4773:
4763:
4762:
4761:
4760:
4756:
4752:
4731:
4730:
4726:
4722:
4718:
4711:The weights x
4695:
4684:
4680:
4671:
4667:
4661:
4656:
4653:
4650:
4646:
4642:
4633:
4623:
4622:
4621:
4599:
4577:
4566:
4538:
4534:
4528:
4524:
4515:
4510:
4507:
4504:
4500:
4496:
4493:
4490:
4487:
4482:
4474:
4470:
4461:
4452:
4447:
4436:
4432:
4421:
4420:
4419:
4405:
4398:of component
4385:
4357:
4353:
4326:
4315:
4311:
4302:
4298:
4292:
4287:
4284:
4281:
4277:
4273:
4270:
4263:
4262:
4261:
4255:
4247:
4239:
4235:
4231:
4226:
4224:
4220:
4216:
4212:
4208:
4205:and a better
4204:
4200:
4196:
4192:
4188:
4186:
4182:
4178:
4174:
4170:
4166:
4162:
4157:
4156:
4155:
4151:
4147:
4142:
4141:
4140:
4136:
4132:
4128:
4127:
4124:
4120:
4116:
4115:82.137.11.191
4112:
4111:
4108:
4104:
4100:
4099:Deacon Vorbis
4096:
4095:
4094:
4093:
4089:
4085:
4081:
4077:
4073:
4069:
4065:
4058:
4054:
4050:
4048:
4047:
4043:
4039:
4032:
4019:
4016:
4013:
4010:
4007:
4002:
3998:
3992:
3989:
3984:
3980:
3974:
3971:
3966:
3956:
3948:
3944:
3935:
3925:
3921:
3900:
3877:
3874:
3871:
3868:
3865:
3859:
3850:
3849:
3848:
3842:
3840:
3832:
3829:
3826:
3821:
3818:
3816:
3811:
3802:
3792:
3788:
3784:
3780:
3776:
3772:
3770:
3766:
3765:
3764:
3763:
3762:
3761:
3760:
3759:
3752:
3748:
3744:
3740:
3724:
3721:
3714:
3709:
3703:
3695:
3686:
3679:
3673:
3667:
3659:
3654:
3637:
3633:
3632:
3631:
3630:
3629:
3628:
3625:
3621:
3617:
3613:
3609:
3605:
3602:
3598:
3594:
3593:
3592:
3575:
3567:
3559:
3554:
3521:
3518:
3514:
3510:
3507:
3504:
3501:
3498:
3492:
3486:
3478:
3473:
3458:
3457:
3456:
3454:
3433:
3430:
3426:
3422:
3419:
3416:
3413:
3410:
3404:
3396:
3388:
3383:
3368:
3367:
3366:
3364:
3356:
3354:
3352:
3348:
3344:
3343:220.165.68.56
3340:
3333:
3327:
3323:
3319:
3315:
3314:Michael Hardy
3310:
3309:
3308:
3305:
3299:
3297:
3296:
3293:
3288:
3277:
3269:
3265:
3261:
3257:
3253:
3249:
3230:
3226:
3217:
3216:
3215:
3210:
3205:
3204:RupertMillard
3201:
3197:
3196:
3195:
3191:
3187:
3182:
3181:
3180:
3178:
3169:
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1909:than a Greek
1908:
1907:de (Cyrillic)
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705:
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548:
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317:High-priority
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242:High‑priority
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123:Find sources:
120:
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110:Verifiability
108:
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83:
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52:Learn to edit
49:
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26:
22:
18:
17:
6795:Cahdfin13773
6792:
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5282:130.79.10.22
5082:130.79.10.22
5076:— Preceding
5073:
5070:
4850:
4751:82.137.9.233
4732:
4721:82.137.9.233
4717:ternary plot
4710:
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4564:
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4418:defined as:
4341:
4251:
4215:82.137.11.35
4206:
4202:
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4190:
4177:82.137.11.35
4173:liberal arts
4160:
4131:82.137.15.37
4084:82.137.15.34
4075:
4063:
4061:
4057:applied math
4056:
4052:
4035:
3851:
3846:
3838:
3830:
3825:Geometry guy
3806:
3783:134.60.31.73
3774:
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2105:derivatives.
2100:
2099:
2098:
2078:
2042:
2012:
1992:
1990:
1979:
1973:
1961:
1942:
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1882:
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1665:
1456:
1362:, or should
1116:
1115:Actually, I
1103:
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1072:
1019:
1013:
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711:
707:
702:denotes the
699:
685:
681:
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669:
661:
657:
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637:
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528:
524:
520:
516:
512:
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471:— Preceding
468:
461:
457:
414:
411:
388:— Preceding
371:
359:88.114.90.71
350:
347:
344:
341:
316:
276:
220:WikiProjects
203:
171:
165:
157:
150:
144:
138:
132:
122:
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19:This is the
5958:Jasper Deng
5720:Jasper Deng
4565:total molar
3843:f´(x)=f(x)?
3451:But in the
3127:—Preceding
2269:—Preceding
2162:—Preceding
2145:Thomasmeeks
2064:Thomasmeeks
2060:Thomasmeeks
2056:Thomasmeeks
2026:Thomasmeeks
1997:Thomasmeeks
1947:Thomasmeeks
1071:instead of
680:" whereas ∂
353:—Preceding
292:Mathematics
283:mathematics
239:Mathematics
148:free images
31:not a forum
6811:Categories
5951:polynomial
4620:equals 1.
3328:Good Job!!
1669:Kaimbridge
1017:Kaimbridge
499:" notation
430:A bit iffy
6705:are used.
5712:functions
3256:functions
2216:Need Help
1976:Cyrillic?
648:Surfaces?
338:Thanks!!!
208:is rated
88:if needed
71:Be polite
21:talk page
6738:critique
5078:unsigned
4169:Classics
4038:Yukterez
3363:Notation
3339:unsigned
3300:Question
3141:contribs
3133:Landroni
3129:unsigned
2283:contribs
2271:unsigned
2164:unsigned
2110:verified
1905:cursive
704:boundary
485:contribs
473:unsigned
390:unsigned
355:unsigned
56:get help
29:This is
27:article.
5923:here.--
4608:where x
4230:Nickalh
3361:In the
2203:Jackzhp
1964:kanzure
1925:PanchoS
640:Retardo
624:Tbsmith
477:Nickalh
319:on the
210:C-class
154:WP refs
142:scholar
6734:WP:DUE
5973:Jasper
5961:(talk)
5733:Jasper
5723:(talk)
5610:where
4596:using
4342:where
4146:Jytdog
3773:]. So
3743:Loraof
2116:—DIV (
1782:, and
1079:, not
729:Since
605:gundam
443:Spoon!
417:17 May
216:scale.
126:Google
6711:Boute
6231:Boute
5940:Boute
5925:Boute
5669:Boute
5653:Boute
4741:and x
2275:Xpsky
2022:JSTOR
1911:delta
1117:meant
521:dy/dx
517:∂y/∂x
351:---
197:This
169:JSTOR
130:books
84:Seek
6799:talk
6715:talk
6676:and
6235:talk
6177:and
5929:talk
5657:talk
5286:talk
5267:talk
5150:and
5086:talk
5057:talk
4755:talk
4725:talk
4234:talk
4219:talk
4181:talk
4150:talk
4135:talk
4119:talk
4103:talk
4088:talk
4066:aka
4042:talk
3787:talk
3747:talk
3620:talk
3347:talk
3318:talk
3264:talk
3260:Bdmy
3246:at (
3209:Talk
3190:talk
3186:Bdmy
3159:Talk
3137:talk
2279:talk
2207:talk
2188:talk
2172:talk
600:wing
584:talk
555:talk
519:and
481:talk
420:2006
398:talk
378:talk
363:talk
311:High
162:FENS
136:news
73:and
6305:to
5920:and
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3860:f
3785:(
3745:(
3725:,
3722:y
3715:/
3710:)
3704:x
3696:f
3687:(
3674:y
3668:x
3660:f
3655:2
3618:(
3612:x
3608:y
3601:y
3597:x
3576:y
3568:x
3560:f
3555:2
3522:y
3519:x
3515:f
3508:.
3505:.
3502:.
3493:y
3487:x
3479:f
3474:2
3434:y
3431:x
3427:f
3423:=
3420:.
3417:.
3414:.
3411:=
3405:x
3397:y
3389:f
3384:2
3345:(
3316:(
3291:T
3262:(
3252:y
3248:x
3231:x
3227:e
3211:)
3207:(
3200:ƒ
3188:(
3177:ƒ
3161:)
3157:(
3135:(
3106:r
3098:h
3089:=
3084:r
3081:h
3076:=
3073:k
3047:h
3039:r
3026:r
3018:V
3003:3
2999:h
2996:r
2990:2
2982:+
2975:h
2967:V
2952:3
2946:2
2942:r
2930:=
2924:h
2918:d
2913:V
2907:d
2878:r
2870:h
2857:h
2849:V
2834:3
2828:2
2824:r
2812:+
2805:r
2797:V
2782:3
2778:h
2775:r
2769:2
2761:=
2755:r
2749:d
2744:V
2738:d
2706:r
2703:d
2698:h
2695:d
2689:=
2684:r
2681:h
2676:=
2673:k
2647:h
2644:d
2639:r
2636:d
2626:r
2618:V
2603:3
2599:h
2596:r
2590:2
2582:+
2575:h
2567:V
2552:3
2546:2
2542:r
2530:=
2524:h
2518:d
2513:V
2507:d
2478:r
2475:d
2470:h
2467:d
2457:h
2449:V
2434:3
2428:2
2424:r
2412:+
2405:r
2397:V
2382:3
2378:h
2375:r
2369:2
2361:=
2355:r
2349:d
2344:V
2338:d
2306:T
2277:(
2205:(
2186:(
2170:(
1993:∂
1974:∂
1855:)
1852:Q
1849:,
1846:P
1843:(
1839:′
1836:F
1815:)
1812:Q
1809:,
1806:P
1803:(
1800:F
1795:P
1770:)
1767:Q
1764:,
1761:P
1758:(
1753:P
1749:F
1721:P
1713:)
1710:Q
1707:,
1704:P
1701:(
1698:F
1672:~
1666:~
1647:P
1641:)
1638:Q
1635:,
1632:P
1629:(
1625:′
1622:F
1618:=
1615:P
1612:d
1609:)
1606:P
1603:(
1599:′
1596:E
1569:)
1566:Q
1563:(
1554:)
1551:P
1548:(
1539:=
1536:)
1533:Q
1530:,
1527:P
1524:(
1520:′
1517:F
1513:=
1510:)
1507:P
1504:(
1500:′
1497:E
1470:P
1439:)
1436:Q
1433:,
1430:P
1427:(
1423:′
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1390:)
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1384:,
1381:P
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1374:′
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1340:)
1337:Q
1334:,
1331:P
1328:(
1323:p
1319:G
1311:d
1307:P
1299:b
1295:P
1286:=
1283:P
1277:)
1274:Q
1271:,
1268:P
1265:(
1261:′
1258:F
1250:d
1246:P
1238:b
1234:P
1225:=
1222:)
1219:Q
1216:,
1211:b
1207:P
1203:(
1200:F
1194:)
1191:Q
1188:,
1183:d
1179:P
1175:(
1172:F
1146:)
1143:Q
1140:,
1137:P
1134:(
1130:′
1127:F
1104:Q
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1038:F
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1014:~
995:P
989:)
986:Q
983:,
980:P
977:(
974:F
967:d
963:P
955:b
951:P
942:=
939:)
936:Q
933:,
928:b
924:P
920:(
917:F
911:)
908:Q
905:,
900:d
896:P
892:(
889:F
862:P
854:)
851:Q
848:,
845:P
842:(
839:F
830:=
827:)
824:Q
821:,
818:P
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811:′
808:F
780:P
777:d
772:)
769:P
766:(
763:F
760:d
754:=
751:)
748:P
745:(
741:′
738:F
708:S
700:S
686:d
682:V
678:V
662:V
658:S
582:(
553:(
513:x
509:y
505:d
497:d
479:(
422:)
396:(
376:(
361:(
323:.
222::
172:·
166:·
158:·
151:·
145:·
139:·
133:·
128:(
58:.
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