## Air minimal between 2 curves [0,1], Answer check...

Asked by:
For which value of c is the area between f(x) and g(x) minimal?  f(x) and g(x) are both continuous   ( in the interval [0,1] )

> g := x-> piecewise(0<=x and x<=c, m1*x+b1, c<x and x<=1, m2*x+b2);

f := x-> x^3;

## Orthoganalized Eigenvectors and Diagonalisation...

Asked by:

Good Morning everyone and happy easter

I have a short question on Maples Eigenvectors procedure. I want to diagonalize a Matrix A, which works works perfectly using the following code:

A:= some quadratic (complex) float matrix

(l,L):=Eigenvectors(A):

B:=L . DiagonalMatrix(l) . MatrixInverse(L):

Excecuting this code tells me, that A=B, so it works.

## Can't send to MathMLViewer...

Asked by:

I recently installed Maple 11 and have just been looking at the Maplet Builder.  I'm having trouble with MathMLViewer.  In the simplest case, I created a maplet with 2 elements, a MathMLViewer and a button.  I set clickButton1 to evaluate the expression MathML[Export](1) with MathMLViewer1 as the target.  Then I ran the maplet and clicked the button, expecting to see 1 in the viewer.  Instead an error box titled Dispatch popped up saying, invalid input: XMLTools:-NSXML:-Parser:-processOutputString uses a 1st argument, str, which is missing.

## Separable ODE...

Asked by:

dsolve(diff(r(t),t\$1)=-r(t)*(-1+r(t)^2));

1                                  1
r(t) = ------------------------, r(t) = - ------------------------

## matrix to image...

Asked by:

Okay, I have a simple 5 X 5 matrix.  How do I view it as an image?

With a very large image 1000 X 1000, I can left click on it and view the matrix in a spreadsheet and then click on a tab that says image and view that matrix as an image.  How do I do that with small maticies?  I can't figure it out.

## substituting new functions...

Asked by:

I have an  ode system, and use  2 D Math  (I don't know how to copy here, so I type by hand)

x'(t) = -y(t) + x(t) (1 - x^2(t)  -  y^2(t)),

y'(t) = x(t) + y(t) (1 - x^2(t) - y^2(t)).

I would like to introduce  x(t) = r(t) cos(Theta(t)), y(t) = r(t) sin(Theta(t)) and manipulate the equations further.

The problem is the left hand side. In one case I obtain Dx(t), in the other case (r(t) cos(Theta(t))' without calculation on it.

I ask some help. Thanks.

## standard vector...

Asked by:

Hi guys

How can i construct the standard vector e[i]. Where e[i] is a 4 dimensional vector with 0 in all entries apart from the ith which has ?

## Simple question of solids...

Asked by:
Hello there, Would appreciate if someone could illustrate the procedure to obtain, using the plot3d command, simply the solid bound by the given set of graphs. In other words, all superfluous areas are substracted. For example, for the cone z=sqrt(x^2 + y^2) & planes z=2 & z=4, I'd like to see just the solid bound by the planes and not what appears when the following commands are executed: a:=implicitplot3d(z = sqrt(x^2+y^2), x = -5 .. 5, y = -5 .. 5, z = -5 .. 5); b:=implicitplot3d(z = 2, x = -5 .. 5, y = -5 .. 5, z = -5 .. 5);

## Easter, closer still

by: Maple

Another interesting undocumented package in the Maple 11.02 Library.

## Tricky for loop...

Asked by:

Hi Guys, i have a forloop problem.

I have a nxs matrix, where s=sum((k),k=1..n-1), so when n=3, s=3, when n=4,s=6 and so on.

I need to code each column number lexicographically for cartesian pair (i,j) where i<j, so when n=3, the columns would be

(1,2),(1,3),(2,3)

and when n=4 we have

(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)

.

## Spherical Harmonics...

Asked by:

Is there a spherical harmonics package available anywhere ?

I may have to start using vector spherical harmonics and don't really feel like fighting with Maple, and the Legendre and Associated Legendre functions on my own.

v/r,

## Embedded components, maplets, and sudoku puzzles

by: Maple

My oldest son, Stuart, recently completed a Science Fair project on sudoku puzzles. While I am fairly good at solving sudoku puzzles, the mathematics is something that is completely outside my area of expertise. After seeing the paper by Hurzberg and Murty in the Notices of the AMS (June/July 2007) and additional papers by Felgenhauer and Jarvis (http://www.afjarvis.staff.shef.ac.uk/maths/felgenhauer_jarvis_spec1.pdf)  and Russell and Jarvis (http://www.afjarvis.staff.shef.ac.uk/maths/russell_jarvis_spec2.pdf) and Jarvis' sudoku webpage (http://www.afjarvis.staff.shef.ac.uk/sudoku/), I felt that I had a reasonable understanding of some of the basic ideas involved in counting unique sudoku puzzles. While I had nothing to add to the mathematical ideas, I did see the potential to create a tool to visualize these ideas. The result is the worksheet I just uploaded to MaplePrimes:

## Default handler for division_by_zero...

Asked by:
Hello, I have a question regarding the behavior of the numeric event division_by_zero. The documentation of ?event says that "A division of a non-0 number by 0 should signal a division_by_zero event. The default action is to return a correctly signed infinity, if possible, and otherwise an undefined. This event is also properly signaled when an attempt is made to evaluate a function at an infinite singularity, e.g., ln(0)." Yet, when using the default settings, I get the following output: > NumericEventHandler( division_by_zero = default ): > 1/0;

## Setting the Contents of a Table in a Maplet...

Asked by:

I been trying to make a Maplet that will solve some numerical analysis problems, those problems or indeen the solution of them are composed of iterations.

I would like to show such value iterations on a table in a Maplet interface, with no success.

for my logic, this should work.

Set('Table1',[[1,2],[3,4],[3,4]])

But I get an error telling me that the value is not settable.

It doesn't make sense to me to have a control that I can't modify its contents at runtime?

Any ideas about how to do this?

Thanks

## integration to erf function...

Asked by:

Hey,

I am doing some ODEs and I met the following problem...

The original problem is

y(x)*(y(x)-2*x)*diff(y(x),x)=1;

and knowing the solutions contains efr function.

After several lines of calculation I got

Int(y^2*exp(1)^(y^2),y);

then maple gives me the answer

1/2*y*exp(y^2)+1/4*I*Pi^(1/2)*erf(y*I)

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