## Generate Matrix Directly...

Generate Matrix Automatically for solving Higher order Differential Equation For Chebyshev Polynomial

## Differential with respect by which parameter...

What is the concept of these terms?

(D[2, 2](T))(x, 0) = 0, (D[1, 1](T))(x, 0) = 0 ? I want to know these terms show

with respect by which parameter?

## How to remove summation from both sides?...

At a point in a worksheet I end up with an equation that has summations on both sides.  The range of summation is the same but the summands are different.  I want to remove the summations from both sides, keeping the equation with just the summands. How can this be done?  The only way I have found is to manually select each summand with the mouse and paste it into a new line which breaks the 'automation' of the script.

## simplify expression to complete derivative...

This

`expr:='1/r^2*diff(r^2*diff(v(r),r),r)'`

gives

And when evaluated second time it gives

`expr`

The question is, how to put expr back to its original form shown at the top?

I tried simplify, combine, etc.. but nothing puts back to same form.

The reason I am asking, is that I need put more complicated expression in form that resembles when I am looking at in textbook. For an example, the Laplacian

```VectorCalculus:-Laplacian(u(r,theta,phi),'spherical'[r,theta,phi])
```

But the above should be the same as

So I figured if I can rewrite each term to look like in the shorter version above (complete derivative version), it will be easier for me to compare what Maple gives and the text book shows,

ps. I found that the following command in Maples gives a little clearer Laplacian, but it is still not as simplified as the book but it is better than using VectorCalculus:-Laplacian

```Physics[Vectors]:-Laplacian(u(r,theta,phi));
```

At least this has each term a little more seprated.

## Discontinuities even with "discont=true"?...

Hello everyone,

Even using the command "discont=true", some of the functions I plot still present discontinuities, but some of them do not present.

How can I fix this? This one file ilustrates perfectly the problem.

file_discont.mw

## auto legend for plot...

Is there any way to automatically create a legend for a plot of a list of functions? The problem is, I'd rather not specify the legend and maple require the exact number so I cannot specify a generic length such as [1,2,3,4,5,6,7,8].

plot([f1(x), f2(x), f3(x), sin(x)*cos(x)*sin(3x^2 + cos(x))], x=1..34)

The point is that I do not want or care what the legend is(except the names shouldn't be long). I just want to be able to use it to select the plots easily and to be able to reference them(so the naming matters in that the order shoudl be obvious).

## Closed geodesics at regular tetrahedron...

Hello. I can not realize such a thing. There is an equal tetrahedron NET on the plane. Choose a point on the edge and start a vector from it (the sum of red vectors with some integer coefficients). We obtain a closed geodesic. Depending on the coefficients, the geodesic will intersect the edges and faces in a different sequence. How to unNET into tetrahedron and so that the geodesic is displayed on it? Thank you in advance.

## numpoints=x, x ~> 2000 lines are thick and jagged...

When I try to get a higher resolution plot using numpoints, the lines are jagged and look lower resolution.

You can see the difference, the first does not look anti-aliased whil ethe second does(although the 2nd looks far better on my comp)

## Matrix with the Help of loop...

A way to define a N *N matrix with the help of loop

## Unable to evalulate plot of Fourier transform for ...

```with(inttrans):
sinc := x->piecewise(x = 0, 1, sin(Pi*x)/x/Pi):
S := x->sinc(x):
SE := x->sinc(x)*exp(-x^2):
plot(abs(fourier(SE(x),x,s)),s=0..5)

```

works fine for S but when trying to plot SE I get

Warning, unable to evaluate the function to numeric values in the region; see the plotting command's help page to ensure the calling sequence is correct

I simply want to plot the fourier transform of a function so I can see it's frequency response. Maple seems to be breaking for more complex functions. It seems to be doing this when it can't evaluate the function exactly, which I don't care for plots.

## ternary strings...

Hi

Let s_n be the number of ternary strings (of 0s, 1s and 2s) of length n that have no
For example, s_0 = 1 (the empty string),
s1 = 3 (the strings 0, 1 and 2),

while s2 = 5:  01; 10; 11; 12; 21;

We can compute by hand  Find s3; and we obtain 11
My question how can use maple to get a general recurrence relation for s_n.

Give the following functions find Domain, Range, Possible Asymptotes, Intercepts, Critical Points, Intervals of Increase, Decrease, Relative and Absolute Extrema, and Concavity.

A) f(x)=x(x^2-6x+8)

B) f(x) =x^3/4 -3x

## Maple unable to compute the Jacobian of a multivar...

After two days of trying to take the Jacobian of a multi-variable mapping in Maple, I'm still finding no way. Here is an example of what I mean by "multi-variable mapping":

`(x,y) -> x^2-y^2`

Every AP high-school student knows how to take the partial derivatives of that, but Maple's "Jacobian" feature doesn't work on mappings. It only works on expressions.

So I spent today trying to leverage off the "D" feature, only to find it rendered useless by bugs: https://mapleprimes.com/questions/227007-How-To-Take-Partial-Derivative-Of-A-Mapping

It took me less than two days to do it in Mathematica, by way of comparison.

On the website, they show a photo of a man elated to be doing math in Maple, but that's not how it's gone for me. I'm cursing outloud, and my blood pressure is high. I'm angry that I lost money on a product that can't take the Jacobian of a mapping, and I'm angry that I lost two days of my life doing tedious debugging while paying money instead of getting paid for my work.

Maple pays math PhD's to release a commercial CAS that can't take the Jacobian of a mapping. So much for the value of a PhD.

## Error in plot3d...

I need to find the intersection of 3 planes.

I managed to get the intersection using LinearSolve but I keep getting an error when I try to plot out the planes using plot3d. What can I change in the commands for it to work?

 >
 (1)
 >
 (2)
 >
 (3)
 >
 (4)
 >
 >
 >
 >
 >

## How to Take Partial Derivative of a Mapping?...

Here's how to break Maple's 'D' function:

```~\$ cmaple mapleBug.mpl
|\^/|     Maple 2018 (X86 64 WINDOWS)
._|\|   |/|_. Copyright (c) Maplesoft, a division of Waterloo Maple Inc. 2018
<____ ____>  Waterloo Maple Inc.
|       Type ? for help.
> D[1]((x, y) ->x^2-y^2);
(x, y) -> 2 x

> D[2]((x, y) ->x^2-y^2);
(x, y) -> -2 y

> with(VectorCalculus):
> assume(x, 'real');
> assume(y, 'real');
> D[1]((x, y) ->x^2-y^2);
(x, y) -> 0

> D[2]((x, y) ->x^2-y^2);
(x, y) -> 0

> quit
memory used=2.4MB, alloc=8.3MB, time=0.06

~\$```

What if a person needs to have these lines:

```> with(VectorCalculus):
> assume(x, 'real');
> assume(y, 'real');```

and then he wants to take partial derivatives? Not possible? Once you load VectorCalculus and declare x and y real, Maple stops doing partial derivatives? Why.

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