I am trying to calculate the integral

where

Maple cannot calculate the integral. I tried to expand theta in the series form and substitute in the integral, still cannot calculate it.

any suggestion to tackle this problem whould be helpful.

Thank you

I have a PDE with boundary conditions, from a NASA paper.  I always seem to have problems expressing the bc.

PDE := diff(u(x, t), t) = (1/4)*exp(2)*exp(-u(x, t))*(diff(diff(u(x, t), x), x))/(x^2+2);

The initial/boundary conditions are

@t=0, u(x, t) = 2-2*ln(-x^2+2)

@x=0, diff(u(x,t),x)=0  ## this is the bc I have problem expressing

@x=1, u(x,t) = 2+ln(1+t)

The exact solution given in the paper:

2 + ln(1+t) - 2*ln(2-x^2)

I tried

ics := u(x, 0) = 2*(1-ln(2-x^2));

bcs := D[1](u(0,t))=0, u(1,t)=2+ln(1+t);

PDEtools[Solve]([PDE,ics,bcs]); ## no solution

How do I do this?

Tom Dean

We have just released an update to Maple.  It includes updates to the Maple Workbook, the video component, the Physics package, and many other small improvements throughout the product. It is available through Tools>Check for Updates in Maple, and is also available from our website on the Maple 2016.2 download page.

eithne

fn1 and gn1 are the 2x2 matrices. For example
 

fn1:=Matrix(2,2,[seq(f[i],i=1..4)])
gn1:=Matrix(2,2,[seq(g[i],i=1..4)])


eq1:=evalm(Matrix(2,2, [1, 1, 0, 3])&*fn1+gn1)=Matrix(2,2,[0]);

eq2:=evalm(fn1+gn1)=Matrix(2,2, [0]);

how can we find fn1 and gn1 matrices?

Consider the following code:

LM := [
   Matrix([[1,2],[3,4]]),
   Matrix([[5,6],[7,8]])
];
A := Matrix([[0,1],[1,0]]);
map(x -> A . x,LM);
A .~ LM;

where LM is a list of two matrices (just a test example), and A is some (test)matrix that I want to multiply onto each of these two matrices from the left, say. The map-construction works, as expected, but the elementwise operation .~ produces an error. Why?

Greetings

How can I get LPSolve to output the unique subsets of {3,1,1,2,2,1} which sum to 5 (no recycling of set values)

partition.mw

(the code is a Yury/Love hybrid).

I have several maple worksheets (from the web) that have discussion blocks mixed within executable blocks.

All the executable blocks are delineated with a single '[' at the left while the discussion blocks do not.

How do I do this?

Tom Dean

I wish to apply several i-j constraints to an optimization problem that involves minimizing a function x[i,j]. 

Does anyone know of a simple way to exclude values for i and j? For instance, how do we specify the conditions, i not equal to j, i is not equal to 1, etc.?

Thanks in advance!

Hi all, i wan to write getCoeff() function get coefficient general.

Example

f := a^2*b^2*c^2 + 2*a^2*b^2 + 2*a^2*c^2 + 2*b^2*c^2 + a^2 - 6*a*b - 6*a*c + b^2 - 6*b*c + c^2 + 8

getCoeff(f,a^2*b^2*c^2) return 1.

getCoeff(f,a^2*b^2) return 2.

getCoeff(f,a*b) return -6.

getCoeff(f,a^2) return 1, ...

and how to get coefficients freedom ?

Thank you very much.

can anyone run my code?
please do it and send it for me.
thanks.

restart;
with(plottools): with(LinearAlgebra): with(plots):
ode := `assuming`([diff(Y(X), `$`(X, 2))+2*alpha*(diff(Y(X), X))+beta^2*Y(X) = 0], [alpha >= 0, beta >= 0, alpha+beta > 0]):
F := unapply(solve(subs({X = x, Y(X) = y, diff(Y(X), X) = yp, diff(Y(X), `$`(X, 2)) = yz}, ode), yz), x, y, yp):
Fp := unapply(solve(subs({X = x, Y(X) = y, diff(Y(X), X) = yp, diff(Y(X), `$`(X, 2)) = yz, diff(Y(X), `$`(X, 3)) = yt}, diff(ode, X)), yt), x, y, yp, yz):
Ni := seq(i, i = 0 .. 9), 15, 20:
for ni in Ni do
print(ni);
st := time[real]();
f[0, ni] := F(x[0], y[0, ni], yp[0, ni]);
fp[0, ni] := Fp(x[0], y[0, ni], yp[0, ni], f[0, ni]);
f[1, ni] := F(x[1], y[1, ni], yp[1, ni]);
fp[1, ni] := Fp(x[1], y[1, ni], yp[1, ni], f[1, ni]);
y[2, 0] := y[0, ni]+2*h*yp[0, ni]+(6/5)*f[0, ni]*h^2+(4/15)*fp[0, ni]*h^3+(4/5)*f[1, ni]*h^2+(4/15)*fp[1, ni]*h^3;
yp[2, 0] := yp[0, ni]+2*f[0, ni]*h+(2/3)*fp[0, ni]*h^2+(4/3)*fp[1, ni]*h^2;
for j to ni do
f[2, j-1] := F(x[2], y[2, j-1], yp[2, j-1]);
fp[2, j-1] := Fp(x[2], y[2, j-1], yp[2, j-1], f[2, j-1]);
y[2, j] := y[1, ni]+h*yp[1, ni]+(7/20)*f[1, ni]*h^2+(1/20)*fp[1, ni]*h^3+(3/20)*f[2, j-1]*h^2-(1/30)*fp[2, j-1]*h^3;
yp[2, j] := yp[1, ni]+(1/2)*f[1, ni]*h+(1/12)*fp[1, ni]*h^2+(1/2)*f[2, j-1]*h-(1/12)*fp[2, j-1]*h^2;
end do:
Ms := Matrix(4, 4); Ms[1, 3] := 1; Ms[2, 4] := 1;
y[2, ni] := collect(algsubs(h*alpha = H1, expand(algsubs(h*beta = H2, expand(y[2, ni])))), {y[0, ni], y[1, ni], yp[0, ni], yp[1, ni]});
Ms[3, 1] := coeff(y[2, ni], y[0, ni]);
Ms[3, 2] := coeff(y[2, ni], yp[0, ni])/h;
Ms[3, 3] := coeff(y[2, ni], y[1, ni]);
Ms[3, 4] := coeff(y[2, ni], yp[1, ni])/h;
hyp[2, ni] := collect(algsubs(h*alpha = H1, expand(algsubs(h*beta = H2, expand(h*yp[2, ni])))), {y[0, ni], y[1, ni], yp[0, ni], yp[1, ni]});
Ms[4, 1] := coeff(hyp[2, ni], y[0, ni]);
Ms[4, 2] := coeff(hyp[2, ni], yp[0, ni])/h;
Ms[4, 3] := coeff(hyp[2, ni], y[1, ni]);
Ms[4, 4] := coeff(hyp[2, ni], yp[1, ni])/h;
sol := Eigenvalues(Ms);
print(time[real]()-st);
st := time[real]();
SR[ni, 1] := implicitplot(max(seq(abs(sol[ii]), ii = 1 .. numelems(sol))) <= 1, H1 = 0 .. 3, H2 = 0 .. 3, filledregions, gridrefine = 3, axes = Boxed, view = [-2 .. 3, -3 .. 3], labels = [H[1], H[2]], labeldirections = ["horizontal", "vertical"]);
SR[ni, 2] := implicitplot(max(seq(abs(sol[ii]), ii = 1 .. numelems(sol))) <= 1, H1 = -2 .. 3, H2 = -2 .. 3, gridrefine = 3, axes = Boxed, view = [-2 .. 3, -3 .. 3], labels = [H[1], H[2]], labeldirections = ["horizontal", "vertical"]);
print(time[real]()-st);
end do;
for i in Ni do
i;
display({SR[i, 1], SR[i, 2], line([-1, 0], [3, 0], color = red, linestyle = dash), line([0, -3], [0, 3], color = red, linestyle = dash)});
end do;
display({seq(SR[i, 2], i = 0 .. Ni)});

This is my code

restart; L := [];
for a from -10 to 10 do
for b from -10 to 10 do
for c from -10 to 10 do
k := (-a*b*c+a*b*z+a*c*y+b*c*x)/igcd(a*b, b*c, c*a, a*b*c); if a*b*c <> 0 then L := [op(L), [[a, 0, 0], [0, b, 0], [0, 0, c]], k*signum(lcoeff(k)) = 0] end if end do end do end do; nops(L); L

I think my code was error, because  a from -10 to 10. 

[Delta][4*4]*{b}[4*1]={0}

Which {b} is an eigenvector

When I try the example from Maple Help for LPSolve (I use Windows)

with(Optimization);
LPSolve(-4*x-5*y, {0 <= x, 0 <= y, x+2*y <= 6, 5*x+4*y <= 20});

I do not get the same solution like in the example: [-19., [x = 2.66666666666667, y = 1.66666666666667]]
Instead I get

Warning, problem appears to be unbounded
            [0., [x = HFloat(0.0), y = HFloat(0.0)]]

My Professor uses the same version, but with Linux and do not have such problems. Why my installation does not solve the standart Help example?

Thank you

Hi

Let D={ Z=x+I*y,    -Pi*(n+1/2) <= x, y <= Pi*(n+1/2)}  

z belong the boundary of the previous square.

I would like to compute the modul of this function  f (z) =  coth(z) using the usual function  cos(x) cos(y), sinh(x) or cosh(y)  and show that | f(z)|  is less than one

Many thanks for any help

Hello, im a total begineer with maple and i need help defining a matrix, i need to get this into a matrix

 anyone knows how could i put this in a matriz of n x 1?   (the one thats only a column)

any help would be greatly appreciated

Thanks in advance!