(1)

 (2)

## how we can solve an ode with boundaries by using R...

how we can solve an ode with boundaries by using RK4 and any other technique??

## solution for ode and how to tackle constant ...

how we can solve an ode with exat soltuion n calculate the unknw constant which aries after solving an ode.???

## Parallel curves on surfaces

by: Maple 15

Parallel curves on surfaces. The distance between the points of the curves is measured along the curves of intersection of the surface and perpendicular planes.
(According to tradition, it also does not make sense.)

equidistant_curve_surface_MP.mw

## Error in Integrating Heaviside Function...

I'm running into a very simple problem with the way that Maple integrates Heaviside functions. Naively, it should act like a step function, but it is not integrating properly. See the attached document.

 (1)

 (2)

 (3)

Note that the symbolic integration of the Heaviside function (defined to be 1 inside the unit circle and 0 outside) gives zero, whereas it should clearly give the area of the unit circle, which the numerical integration does. I even checked that the (suposedly equivalent) piecewise definition symbolically evaluates to the area, and it, too, gets the right answer.

Anyone have any clue as to why the symbolic integration of this Heaviside function is so wrong? My understanding is that if we do the integral as two nested 1D integrals, the returned function (as a function of y) is zero everywhere except at y=0, but that result cannot be right either.

Thoughts?

by: Maple 15

General description of the method of solving underdetermined systems of equations. As a particular application of the idea proposed a universal method  kinematic analysis for all kinds of  spatial and planar link mechanisms with any number degrees of freedom.  The method can be used for powerful CAD linkages.
http://www.maplesoft.com/applications/view.aspx?SID=154228

## Error, (in sprintf) number expected for floating p...

Round := proc(x,n::integer:=1)
parse(sprintf(cat("%.",n,"f"),x));
end proc:

roundcoeffs1:=proc(p,x,n:=1) local t,c;
c:=map(Round, [coeffs(p,x,t)],n);
add(i, i = zip(`*`, c, [t]));
end:

ggg:=.9940413618*y^3-1.785839107*c*A*y^3-2.357517322*c*A*y^2+.375393240*c*y*B-.3575173222*c*A*y-.2082022533*c*B-0.1787591445e-1*y^2-0.1787591445e-1*y-0.5958638151e-2+.2141608926*c*A+.7917977467*c*B*y^3+2.375393240*c*B*y^2;

roundcoeffs1(ggg, [y^3, c*A*y^3, c*A*y^2, c*y*B, c*A*y, c*B, y^2, y, c*A, c*B*y^3, c*B*y^2], 4);

Error, (in sprintf) number expected for floating point format

## how to use optimization with complex number?...

with(Optimization):

theta := Complex(1,1);
Minimize(theta^3-3*(A*theta^2+B), {0 <= theta^3-3*(A*theta^2+B)}, assume = nonnegative)

Error, (in Optimization:-NLPSolve) complex value encountered

## how to calculate implicit Cartesian equation from ...

from mathematica,

n = 5;
CalabiYau[z_, k1_, k2_] := Module[{z1 = Exp[2Pi I k1/n]Cosh[z]^(2/n), z2 = Exp[2Pi I k2/n]Sinh[z]^(2/n)}, {Re[z1], Re[z2], Cos[alpha]Im[z1] + Sin[alpha]Im[z2]}];
Do[alpha = (0.25 + t)Pi; Show[Graphics3D[Table[ParametricPlot3D[CalabiYau[x + I y, k1, k2], {x, -1, 1}, {y, 0, Pi/2}, DisplayFunction -> Identity, Compiled ->False][[1]], {k1, 0, n - 1}, {k2, 0, n - 1}], PlotRange -> 1.5{{-1, 1}, {-1, 1}, {-1, 1}}, ViewPoint -> {1, 1, 0}]], {t, 0, 1, 0.1}];

n := 5;

z1 := exp(2*3.14*I*k1/n)*cosh(z)^(2/n);
z2 := exp(2*3.14*I*k2/n)*sinh(z)^(2/n);

alpha = (0.25 + t)Pi;

xx := Re(z1);
yy := Re(z2);
uu := cos(alpha)*Im(z1) + sin(alpha)*Im(z2);

where k1, k2, alpha are variables

print([xx,yy,uu]);

i find algcurve has implicitize

how to use this implicitize to find 3d surface?

is there any other method to find?

i searched groebner basis can do this, but in mathematica is different from maple example

## install error and no error when using cmd to insta...

i got this error in window 8 in surface 2  then follow this post and install again still error

https://www.maplesoft.com/support/faqs/detail.aspx?sid=139020

then follow

http://www.maplesoft.com/support/faqs/detail.aspx?sid=32607

then follow and install again same error

http://www.maplesoft.com/support/faqs/detail.aspx?sid=32631

and install again same eror

then i add option -f c:\Program File (x86)\MapleXX in cmd and then no error any more

but no install succeed

where it go, it still not install

then i try again, there is no room enough to install,  hard disk do not have enough space, then i go to c:\Windows\Temp, after deleted file in it, still not enough space

i find

https://www.maplesoft.com/support/install/maple15_install.html

but template do not state how to activate later

how to write this template and how to clear the temp file created by previous failed cmd install method

## Functions defined by a procedure...

Hi,

Let, fixed an integer i and 1<=j<=2^{i}-1, for each x and y in [0,1] let the following mapping

Then, with the above procedure we can obtained, for a fixed i, all the mappings for j=1,...,2^{i}-1

However, How can I to evalute the "components" of the above procedure? For instance, I can not to compute CreaF(2)[1](0.35,0.465) (i.e., the first function in the "vector" CreaF(2), in x=0.35, y=0.465).

Thanks very much for your time.

## Saving the multiple output of an expression withou...

Hi, I am new to maple, but I think that my question should be simple.

I have a matrix where each element is an expression. I want to compute the matrix for different constant and to save it without crushing the previous matrix.

If the file that I joined, I have a first part where the constant are defined. In the second part the expression of the matrix is defined. Finally, I compute each matrix with different constant. Each results is called C_p0, C_s0, C_g0. When I called them back, only the last matrix computed remains.

I would like to be able to save each matrix to performed operation on them later.

Thank you.

Forum_Question1.mw

Homogénéisation

 Paramètre des matériaux

Tenseurs Élémentaires

Tenseur de rigidité

Matrice de rigidité

 (1.2.1.1.1)

 (1.2.1.1.2)

 (1.2.1.1.3)

 (1)

## Equidistant curves

by: Maple 15

equidistant_curve_MP.mw  Equidistant curves to the curves on the surface. (Without any sense, but real.)

## Does mtaylor ignore "assuming"?...

I have the following expression (generated by some other procedure):

This does not have a taylor expansion in pV[6] in the general case because the square roots can become negative:

taylor(xpr,pV[6]);
Error, does not have a taylor expansion, try series()

But I can get an expansion by restrictig the range of pV[6]:

taylor(xpr,pV[6]) assuming -0.01<pV[6],pV[6]<0.01;

So far things are perfectly fine. But when I try mtaylor:

mtaylor(xpr,pV[6]) assuming -0.01<pV[6],pV[6]<0.01;
Error, (in assuming) when calling 'mtaylor'. Received: 'does not have a taylor expansion, try series()'

So the assumption seems to be ignored. I can work around this by expanding in pV[6] first, using taylor, and then expanding the result from that using mtaylor (I really also want the expansions in the other pV components; 6 in total although in this example some do not show up). I'll have to convince myself that this work-around gives the correct result but I think it does. However, I don't particularly like it.

I consider this a bug and am tempted to submit an SCR. But before I do that; is there anything obvious I am missing here?

Thanks,

M.D.

PS: This was done using Maple 15. I'll check newer versions later.

mtaylor_assuming.mw

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