## Inverse Laplace Transform...

Asked by:

I take the Inverse Laplace Transform on a specific function and the shown result is still an integral.

Would you like to explain it to me?

Thanks.

## Inverse laplace transform...

Asked by:

I can't take the inverse laplace transform of one kind of functions.

Would you like to help me?

Thanks.

## I am looking for a "rotate" type command that acce...

Asked by:

My last series of questions have been to do with animations. Have had some really good help. I am using a rotation type matrix so I can't readilly use the rotate command. That means painfully breaking up the body into its individual components to apply the matrix to. The matrix is derived from some very nolinear functions. I have just included a general Euler rotation matrix here. Have looked inside the rotate command but don't  have enough experience to develop my own. Now I know this sort of command would not be limited to rotating the body as a general 3x3 matrix would transform the body. That would not be a problem, could be useful for other things.

In Mathematica there is a command "GeometricTransformation" that does this.

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Download Anim_How-3.mw

## Why do piecewise and transform produce different p...

Asked by:

The piecewise plot below displays a sphere truncated by the plane z = 2 - y.

f := proc (x, y, z) options operator, arrow; piecewise(z <= 2-y, x^2+y^2+z^2-16, z-2+y) end proc; implicitplot3d(f, -4 .. 4, -4 .. 4, -4 .. 4, style = surface, numpoints = 50000);

The 3 transforms below when executed in display(T(sphere([0, 0, 0], 4, numpoints = 50000)), scaling = constrained) display the truncated sphere differently:

1) the truncating plane only partly conforms to the boundary of the truncated sphere

2) the truncated sphere is correct provided that the else condition coordinate is in the truncating plane and truncated sphere

3) the truncated sphere is correct but hollow

1) T := transform(proc (x, y, z) options operator, arrow; `if`(z <= 2-y, [x, y, z], [x, y, 2-y]) end proc)

2) T := transform(proc (x, y, z) options operator, arrow; `if`(z <= 2-y, [x, y, z], [0, 0, 2]) end proc)

3) T := transform(proc (x, y, z) options operator, arrow; `if`(z <= 2-y, [x, y, z], [`&+-`(sqrt(16-y^2-z^2)), y, 2-y]) end proc)

Please explain the different behavior of the three transforms.

## Laplace transform...

Asked by:

Hello,

I am not sure how to find the Heaviside Laplace transform

H(t-1)e^(3t-3)

Thank you:)

## Den Iseger algorithm for numerical Laplace transfo...

Asked by:

Dear Community,

Would someone have a good and easy to understand/implement description of the Den Iseger algorithm for the numerical inversion of Laplace transform? Even better if someone would have a Maple script to do it, that would be superb.

Tx in advance,

best regards

Andras

## PDETools: Variable transformation and linearising-...

Asked by:

Hello,

To summarize, I have a variable ε = order(1),  which maple has assumed is a funtion ε(x,y,z) and so when I differentiate epsilon with respect to x (or y or z) I do not get 0. I get ε(or εy, εz). How do I ensure maple does not assume this?

More detail of my process:

I declare functions,

I have the function I want to transform,

Now I transform the variables to the new co-ordinate system. i.e. from (x,n,q) to (s,Y,z)

Good! - Everything correct so far.

Now I want to linearise so i introduce x=x0+ε*x1; and the same for (Y,z),

As you can see, epsilon has derivatives, which it should not.

How I can avoid this?

Thanks in advance - im well and truely stumped over this.

P.s. if the images do not show, the script can be found here:

https://www.dropbox.com/sh/34gepa60xf4droq/AAAJlUcQ_Jwkc96topPvcxtXa?dl=0

## Transforming functions to names...

Asked by:

Hello,

I have this list :
T:=[alpha(t),beta(t)]

I would like to create this list automatically:

Tmod:=[alpha_,beta_]

In other words, how can I remove the 3 characters "(t)" and replace it by "_"

Do you have ideas to do so ?

Thanks a lot for your help

## About Fourier transform...

Asked by:

f=x^2.  It's easy to compute the fouier transform. F(y)=fourier(f,x,y).

However, I want to do more. replace the variable y with a new formula g(z)=z^2.

I tried  "subs(y=g,F)". But failed. Need your help.

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Download code.mw

## How to plot Fourier transform?...

Asked by:

Hi,

I was wondering how to go about plotting a Fourier Tranform in Maple.

My assignment is to plot a simple harmonic equation as a Fourier transform, depicting amplitude against fequency.

I've been given: x'' + w^2 x = 0

And want to obtain both the f(x) = a0 sin(wt) + b0cos(wt) form, and a graph of the the amplitude (c^2 =a0^2 + b0^2) against frequency.

I know how to do this on paper but not in Maple, so any help with line commands and layout would be very much appreciated.

Thanks

## How to solve it by Laplace transform?...

Asked by:

How evaluate system of two integral equation by laplace transform ?

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## Conditions in plottools:-transform...

Asked by:

In Maple 15 it seems that plottools:-transform only accepts this form of conditional statement:

`if`(conditional expression, true expression, false expression).

Is there any way to have plottools:-transform process more than one condition? Do later versions of Maple permit this?

## Problem with involution...

Asked by:

Hi everyone,

Consider this maple 18 doc: Euler18.mw

The code is regular code for Julia sets of the exponential.

To see how the Julia set behaves at infinity, I apply the transform mu(z)=1/z.

The plot3d command correctly plots the Julia set at an appropriate neighborhood of infinity, but:

1) Axes are not transformed

2) Saving as .eps produces an empty plot, sans the axes (plot is saved correctly, when not applying mu(z))

Is there any trick to force the axes to also show correctly with the transformed ranges?

Seems that this misalignment is bothering the .eps renderer, which probably plots the graph in twilight zone, given the false ranges of the untransformed axes.

Any ideas on how to force the saveas .eps to work in this case?

Many thanks,

Yiannis

## Navier Stokes equations in toroidal coordinates...

Asked by:

Hallo everybody,

I just started to use maple and I think I need some help from more experienced users.
I would like to transform the stationary Navier Stokes equations to toroidal coordinates.

The definition of my coordinate system is as follows:
x = -r * cos(sigma)
y = cos(Theta) * ( R + r * sin(sigma) )
z = sin(Theta) * ( R + r * sin(sigma) )

I tried to define the coordinate system and transform each term of the equation:

div( rho * CC) = -grad(p) + div(Tau)

I can transform the pressure gradient. However, I get an error for the divergence of the tensors.
Could someone please give me a hint on how to get the divergences?

Thanks!
Uwe

My code is printed below:

restart: with(plots): with(LinearAlgebra): with(VectorCalculus): with(linalg):

#torus defintion
x := -r*cos(sigma);
y := cos(Theta)*(R+r*sin(sigma));
z := sin(Theta)*(R+r*sin(sigma));
R := .35;
AddCoordinates(torus1[r, sigma, Theta], [cos(Theta)*(R+r*sin(sigma)), sin(Theta)*(R+r*sin(sigma)), -r*cos(sigma)]);
SetCoordinates(torus1[r, sigma, Theta]);

#pressure gradient
PressureGradient := Gradient(p(r, sigma, Theta, t));

#left hand side
c := vector(3, ([Cr, Ctheta, Cx])(r, sigma, Theta, t));
rhoCC := rho*multiply(c, transpose(c));
LHS := Divergence(rhoCC)

## What causes that error?...

Asked by:

Hi all,

I'm trying to implement the smithChart on Maple, but this error "Error, (in unknown) invalid transform: output is not 2 or 3 element" keeps popping up for some reason. I have no idea how to fix it. Can anyone help me with this? Here is the smithChart:

smithChart.mw

smithChart := proc(r)
local i, a, b, c;
a := PLOT(seq(plottools[arc]([-i*r/4, 0], i*r/4, 0..Pi),
i = 1..4),

plottools[arc]([0, r/2], r/2,
Pi-arcsin(3/5)..3*Pi/2),
plottools[arc]([0,r], r, Pi..Pi+arcsin(15/17)),
plottools[arc]([0, 2*r], 2*r,
Pi+arcsin(3/5)..Pi+arcsin(63/65)),
plottools[arc]([0,4*r], 4*r,
Pi+arcsin(15/17)..Pi+arcsin(63/65)));

b := plottools[transform]((x, y) -> [x-y])(a);
c := plottools[line]([0,0], [-2*r, 0]):
plots[display](a, b, c, axes = none, scaling = constrained, args[2..nargs]);
end proc:

smithChart(1);
Error, (in unknown) invalid transform: output is not 2 or 3 elements

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