## riemann curvature tensor maple and also need to ...

i) D(X,Y) , D(X,Z) ,D(Y,Z) COVARİANT DERİVATİVE ?

İİ) [X,Y] LİE OPERATOR ?

İİİ) R(X,Y)Z = D DZ - DDZ - D[X,Y] Z

## How to use pdsolve?...

This may be a stupid question, but I am having elementary trouble with pdsolve.

I have the following pde system:

PDE:=[diff(f(x,xp),x)=-(1/2)*(L*xp+2*x)*kl,diff(f(x,xp),xp)=-(1/4)*kl*L*(L*xp+2*x)];

Trying to solve it:

pdsolve(PDE)

I get this error message:

Error, (in pdsolve/sys) too many arguments; some or all of the following are wrong: [{f(x, xp)}, handlenonrationalfunctionsofdependentvariables = false]

I don't understand any of this; can someone enlighten me?

TIA

M.D.

pde.mw

## Is there any Maple code for the "domain coloring" ...

Is there any Maple code that allows to view a complex function using the "domain coloring" technique?

This technique is described for example in Wikypedia: https://en.wikipedia.org/wiki/Domain_coloring

## compute linear schrodinger equation...

how to compute example 1 of linear schrodinger equation?

[Edit: uploaded .pdf file of M.M. Mousa and S.F. Ragab, Z. Naturforsch. 63a, 140 – 144 (2008) removed for copyright reasons]

## Float undefined while solving system of linear equ...

Dear Users,

I am solving a large system of linear equation with the Hybrid solver. Up to 2400 equations, I get a solution, but if I change the number of equations to 3000, I don't get any solution in fact solution entry reads Float(undefined). All the entries in matrix and vector are floating point decimal with 32 digits of accuracy. Any idea how to overcome this?

thanks.

i attach my file

maple_pita_he.mw

## How can I transfer the results of fsolve to an ass...

Suppose I have

solution:=fsolve(f(x,y)=0,x,y)

this returns

x=<result>, y=<result>

I want to continue the computation in my worksheet by assigning values to x and y without copying the numerical values by hand.

x:=<result>

y:=<result>

Then I want to make more computations with x and y.

It is too time consuming to copy the numbers by hand each time I run the worksheet

Larry

And y

evalhf.mw

## Symbolic PDE solve with BCs...

Having problems with solving PDE with symbolic BCs.

u(x,y,t,M,A);

M,A,x are constants for this problem.

>>>>>>>>>>>>>>>>>>>>>>>>>>>>>Code Starts

pde := diff(u(x, y, t), t)-.5*(diff(u(x, y, t), y, y))-A*sin(M*x-t) = 0

bc[1] := u(x, 0, t) = 0

bc[2] := u(x, 10, t) = A*sin(M*x-t)

sys := [pde, bc[1], bc[2]]

pdsolve(sys)

>>>>>>>>>>>>>>>>Code ends

I don't get any solution after this.
Moreover, in the second BC, I would like to change 10 to inifnity.

## Parallel processing ...

Hello,

I have a matrix of size m*n and I want to apply a procedure "f" to each entry of the matrix. But I want to do this in parallel to reduce the computation time.

I used: Matrix(n, m, (i,j) -> Grid:-Seq( f (M (i,j) ) ,i=1..n, j=1..m) );

but I'm not satisfied with the result, I want the calculation to be faster. Are there any other methods?

## How to take derivative of a function with summatio...

Hi, how can you in maple take the derivitve of a function that consists of sum terms in it? (preferable in document mode)

For example I have this expression (from a math book):

f = N+k*(sum(ln(x__i-B), i = 1 .. N))-N*k*(sum((x__i-B)^k*ln(x__i-B), i = 1 .. N))/(sum((x__i-B)^k, i = 1 .. N))

What I then want to do is to derive this function with respect to k.
However just writing the expression like above it seems like mable doesn't keep the summation terms but evaluates them in a sense. So not sure how to set it up correctly in order to make the derivitive.

Taking the derivitive of f with respect to k, the solution should give something like this:

## im trying to plot a function involving "e" but kee...

I'm trying to plot a function involving exp but keep getting warnings.

How can i avoid this?

plot(2*cos(t)/sqrt((1+exp(-eps*t))*(4/a^2-1)))

but getting the warning message

"Warning, unable to evaluate the function to numeric values in the region; complex values were detected"

## How to remove the frame box on plot:-display of mu...

Hello

I have a series of plots saved in fig0 (fig0:=rtable(1..number_of_figures);).  I had them plotted using plot:-display(fig0) but I could not figure out how to remove the frame box that separates each figure nor how to control the space between them when using size.

An exaggerated example follows

Many thanks

Ed

## Fsolve doesn't provide the answer for highly non-l...

Hello everyone

I try to solve the system of nonlinear equations, where three variables are inside of integrals, for different values of the real parameter q.

It seems that  not for all values of q the system has a solution because I substitute different q but the function fsolve does not give any numerical answer or the special message even after the long evaluation.

Here the code:

```restart;
q := 70;
k0 := 100; n := 3; r := 1.1; t := 0.1e-2; Eg := n/((n+1)^(3/2)+1)^(2/3); kF2 := (1/((n+1)^(3/2)+1))^(1/3);
R1 := int(a^2*tanh(sqrt((a^2-mu)^2+d1^2)/(2*t))/sqrt((a^2-mu)^2+d1^2), a = 0 .. k0);
R2 := int(a^2*tanh(sqrt((a^2-mu+Eg)^2+d2^2)/(2*t))/sqrt((a^2-mu+Eg)^2+d2^2), a = 0 .. k0);
R3 := int(a^2*(1-(a^2-mu)*tanh(sqrt((a^2-mu)^2+d1^2)/(2*t))/sqrt((a^2-mu)^2+d1^2)), a = 0 .. k0);
R4 := int(a^2*(1-(a^2-mu+Eg)*tanh(sqrt((a^2-mu+Eg)^2+d2^2)/(2*t))/sqrt((a^2-mu+Eg)^2+d2^2)), a = 0 .. k0);
Eq1 := evalf(k0+k0*(r-1)-(1/2)*Pi*r*kF2*q-R1);
Eq2 := evalf(k0-(1/2)*Pi*kF2*q-R2);
Eq3 := evalf(2/3-R3-R4);
fsolve({Eq1, Eq2, Eq3}, {d1, d2, mu});```

I know that this system has the solution for some values of q but why I can't get the solution or the answer using fsolve?

Update. I apologize, I made some errors in expressions R2 and R4. I have corrected the question and the code. But the problem is still unresolved.

## How to export a numerical solution of dsolve prope...

I'm working on several worksheets where I solve numerical DE's. I would like to compare the solutions by plotting in one graph So I though it would be nice to have a seperate worksheet for this.

My approach:

Statements from my original sheets:
> solution:=dsolve({ODES,ICS},maxfun=0,numeric,range=0..10,output=listprocedure):
> X__br:=eval(xbr(t),solution):

I can plot these variables in my original sheet with plot(X__br(t),t=0..10).
However, when I transfer it to a different sheet by:

> save X__br, "filename.mpl"

And then load it into a new sheet by