Wikipedia:Reference desk/Archives/Mathematics/2012 May 23

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May 23

Integral Calculus

Resolved

 – Seeing as how we have any number of answers that would appear satisfactory to anyone except the original poster, who is now indefinitely blocked, I'm marking this as resolved. --Kinu ^t/_c 23:38, 23 May 2012 (UTC)

What does ∫ mean? I am only drt2012 (talk) 20:01, 22 May 2012 (UTC).

The sign is the Integral Sign, without any arguments, refers to the Indefinite integral which takes afunction and maps it to a set of functions which indicate the area between the original function and the given line. For example ∫ x² = x³/3 + C. See Integral and Indefinite integral.Naraht (talk) 20:31, 22 May 2012 (UTC)

The simplified explanation is that it finds the area under the curve described by that equation. StuRat (talk) 20:36, 22 May 2012 (UTC)

What the HELL is that supposed to mean. You lost me there, MR N. Araht. You know the place, it's at drt2012 (talk) 20:43, 22 May 2012 (UTC)'s talk page, for he is me. Oh, and what does, dx, dy and ∫ with numbers on it mean?

Calculus is generally viewed as having two parts. Differential calculus and Integral calculus. Differential Calculus is where the dx and dy are first used and they are methods of describing the ratio between the change in x and the change in y at a given point. For example, for the function y=x^2 (x²), at the point 3,9, the value of dy/dx (the change in y over the change in x) is 6 because the slope of the line tangent to the function y=x^2 has a slope of 6 at that point. In fact at every point on the function y=x^2, the line which is tangent to the function has a slope equal to twice the x value, so this is written as dy/dx = 2*x. Integral calculus is the inversion of Differential calculus at that uses the Integral Sign to indicate the area under the function, either in general, or specifically between two x values (which are placed to the right of the integral sign, the lower at the bottom and the higher at the top.Naraht (talk) 20:56, 22 May 2012 (UTC)

The integrals in the convolution section above are using a terminology I'm not used to. But I'm not sure an explanation would help if Integral Calculus were not already understood.Naraht (talk) 21:00, 22 May 2012 (UTC)

Once again, you have lost me, just try something a LOT simpler than that. Also, why is the derivative of a constant 0 when,

f(x)=7 7=7^1 f'(x)=1*7^0 f'(x)=1

. Enlighten me asap, from His Majesty, Sir drt2012 (talk) 21:06, 22 May 2012 (UTC).

Basically, if I draw the curve of x^2 on a piece of graph paper, and I want to find out how many squares are between the curve and the y=0 line between say, x=0 and x=3, then I would use that sign. So I would say ∫ between 0 and 3 (x^2) =9. Its more complex than that as I've actually given you the definite integral there, but its basically what it means. — Preceding unsigned comment added by 86.147.224.178 (talk) 10:36, 23 May 2012 (UTC)

See integral and integral sign. Or read a book on calculus. Sławomir Biały (talk) 21:58, 22 May 2012 (UTC)

And please learn the difference between a link to your own user page or talk page (you use double square brackets, like any other link), and a signature to a post on a talk page (4 tildes). That's if you seriously want your desire to become an administrator to ever go anywhere. With your record of disruptive edits and conflict and blocks since 2009, it doesn't look too promising - but anything's possible, and in your case it's all up from here. -- ♬ Jack of Oz ♬ ^{[your turn]} 01:48, 23 May 2012 (UTC)

If y is a function of x, the derivative of $y^{n}$ is $n\,y^{n-1}\,y'$. You've forgotten the zero factor. —Tamfang (talk) 05:45, 23 May 2012 (UTC)

Oh, Tamfang, will you ever realise that I don't know what your "zero factor" is? I just want proper assistance, not mumbo jumbo like that. And also, I will sign my page as always, for I most certainly am drt2012 (talk) 15:19, 23 May 2012 (UTC).

With the ${\frac {d}{dx}}7$, you are applying the power rule wrong. ${\frac {d}{dx}}x^{n}=nx^{n-1}$ is only true when you are taking the derivative with respect to x. You are taking the derivative with respect to 7, so it does not apply. Also, you can use the definition of derivative to show it must equal 0. $\lim _{h\to 0}{\frac {f(x+h)-f(x)}{h}}=\lim _{h\to 0}{\frac {7-7}{h}}=\lim _{h\to 0}{\frac {0}{h}}=0$ — Preceding unsigned comment added by KyuubiSeal (talk • contribs) 16:05, 23 May 2012 (UTC)

Well done KyuubiSeal! Remember to use ~~~~ when writing posts. This will sign them and remove any unneccesary confusion. What, my gracious friends, is the $\lim _{h\to 0}$ part for? What is $h$ used for? I have to be drt2012 (talk) 16:35, 23 May 2012 (UTC).

Can I have a reply please? I answer to drt2012 (talk) 17:40, 23 May 2012 (UTC).

Certainly - clear off and stop wasting everyone's time. Consider coming back when you've learned some manners. In the event that you're a serious enquirer, refer to the integral article which you've already been referred to.>109.148.243.127 (talk) 18:55, 23 May 2012 (UTC)

But I don't understand that article, for I = drt2012 (talk) 19:07, 23 May 2012 (UTC).

Take a calculus course! --COVIZAPIBETEFOKY (talk) 19:35, 23 May 2012 (UTC)

$\lim _{h\to 0}$ is an example of a limit. It's part of the definition of a derivative, and I shouldn't have to tell you what a derivative is because you already know all about derivatives, right? —Tamfang (talk) 21:39, 23 May 2012 (UTC)

/∫/ is the International Phonetic Alphabet symbol for the last consonant in the word English. —Tamfang (talk) 21:41, 23 May 2012 (UTC)

Plouffe's Inverter

[1] seems to be hung up. Do you happen to know anything? —Tamfang (talk) 05:59, 23 May 2012 (UTC)

http://isc.carma.newcastle.edu.au/

Count Iblis (talk) 02:56, 24 May 2012 (UTC)

Meni Rosenfeld links us to this New inverse symbolic calculator in Wikipedia:Reference_desk/Mathematics#Primorials (soon Wikipedia:Reference desk/Archives/Mathematics/2012 July 23#Primorials). – b_jonas 09:59, 26 July 2012 (UTC)

Column vector to diagonal matrix

To go from an NxN diagonal matrix D to an Nx1 column vector V, you just multiply D by a column vector of ones.

What about the other way around - turning a column vector V into a diagonal matrix D (where the diagonal entries are the row entries of V)?

The reason I want to do this is because I want to turn another column vector W into a vector (call it X), where each entry of W is divided by the equivalent entry of column vector V. So that X(1)=W(1)/V(1), X(2)=W(2)/V(2) etc.

I know that if I can turn the column vector V into a diagonal matrix, I can then invert it, and multiply it by W to get X. But I'm not sure how to get that diagonal matrix. Or maybe there's another way to get X? — Preceding unsigned comment added by 202.14.156.14 (talk) 06:46, 23 May 2012 (UTC)

This can't be done in general. You want to multiply your Nx1 matrix by a matrix A to get an NxN (diagonal) matrix. For the multiplication to be well-defined, A must either have 1 row, and multiply the vector on the right, or have N columns, and multiply it on the left. But since an NxM matrix times an MxP matrix results in an NxP matrix, we see that to end up with an NxN matrix, A must multiply the vector on the right, and be a 1xN matrix. If we assume that the vector has a non-zero entry in the ith position, then A must have a 1 in its ith position, for their product to have that same entry as its ith diagonal entry. In order for all other entries in this ith column to be zero, you need to have started with a very restrictive set of conditions on your vector... Hope that helps! (Is there a reason you can't simply take the vector and write it as a diagonal matrix 'by hand'?) Icthyos (talk) 14:11, 23 May 2012 (UTC)

In particular if you multiply a column vector by a row vector, the resulting matrix will always have rank at most 1. On the other hand, a diagonal matrix has rank equal to the number of non-zero entries. The only sorts of diagonal matrices you can get from multiplying a column vector and a row vector are the ones with at most 1 non-zero entry. Rckrone (talk) 05:51, 24 May 2012 (UTC)

It can't be done using matrix multiplication, but there's nothing to stop you saying something like "let D be the diagonal matrix whose diagonal elements are the elements of V (in the natural order)". It's a common enough computational need that many computer languages with matrix facilities (MATLAB, Maple, Maxima, NumPy, R, SAS, Stata ...) have a diag() function that does this. Diagonal matrix#Matrix operations also introduces a similar notation. Qwfp (talk) 13:16, 24 May 2012 (UTC)