Download question_13.12.06.mw

I have following expression

f:=t->((1/8)*s^2*sinh(4*t)+t+(1/2)*s^2*t+s*sinh(2*t))/(1+s*cosh(2*t))

which is 1 solution of the ODE

ode2 := -(diff(y(t), t, t))+(4-12/(1+s*cosh(2*t))+(8*(-s^2+1))/(1+s*cosh(2*t))^2)*y(t) = 0

Now I wanted to construct 2 linear independent solutions via:

f1:=f(t_b-t)

f2:=f(t-t_a)

and calculate the Wronskian:

with(LinearAlgebra); with(VectorCalculus)

Determinant(Wronskian([f(t_b-t), f(t-t_a)], t))

Since I know these functions are solutions of the second order ODE which does not contain any first order derivative the Wronskian should be a constant. Unfortunately Maple has a hard time to simplify it since the epxression is a little big. Is it my fault or has anyone an idea what to do?

Hello, I am trying to do a fourier transfrom using the package < DiscreteTransfroms >.

The function is an gaussian function for now,

Here is the code I tried

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

restart

with(DiscreteTransform):

> X := Vector(1000, proc (k) options operator, arrow; (1/200)*k-5/2 end proc);
> Y := Vector(1000, proc (k) options operator, arrow; evalf(exp(-10*((1/100)*k-5)^2)) end proc);

> X2, Y2 := FourierTransform(X, Y);
Vector[column](%id = 18446744080244879358),

Vector[column](%id = 18446744080244879478)
> plot(X2, Re(Y2));

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

The program returns two vector, X2 and Y2 who are supposed to be the fourier transforme of a gaussian so.. a gausian but when I plot the result X2 on the horizontal and Y2 on vertical, the graph doesn't resemble a gaussian function or any function at all.

Please help!!

Alex

4th_order.mw How can one solve this problem with maple?

> restart;
> Digits := 10;
> m := 11;
> P := 100;
> alpha := 1;
> F[0] := 0;
> F[1] := epsilon;
> epsilon := 0;
> F[2] := A;
> T[0] := -T[1]/alpha-1;
> T[1] := B;
> for k from 0 to m do F[k+3] := (-(sum(F[k-r+2]*F[r]*(k-r+2)*(k-r+1), r = 0 .. k))-1+sum(F[r+1]*F[k-r+1]*(r+1)*(k-r+1), r = 0 .. k))*factorial(k)/factorial(k+3); T[k+2] := -P*(sum(F[r]*T[k-r+1]*(k-r+1), r = 0 .. k))*factorial(k)/factorial(k+2) end do;
> f := 0;
> t := 0;
>
> for k from 0 to m do f := f+F[k]*eta^k; t := t+T[k]*eta^k end do;
> print(f);
> print(t)

> with(numapprox);
> pade(f, eta, [4, 4]);

>pade(t, eta, [4, 4])

>solve({limit(pade(f, eta, [4, 4]), eta = infinity) = 0., limit(pade(t, eta, [4, 4]), eta = infinity) = 0.}, [A, B])

Hi!

Say, I got an expression that depends on two variables, x and y. How can I tell Maple, that y is actually just a (real) constant, so y does not depend on x?

Because when I apply a differentiation with the "D" - command, it would always also write out expressions, where y is differentiated w.r.t. x.

Thanks!

Hi There,

Can any one correct me the mistake in the following differentiation:

Above command gives the following error:

Error, (in simpl/abs) abs is not differentiable at non-real arguments

The differential equation I'm solving for is:

I have a problem in excuting this differential equation in maple it takes a long time but yet no result.

> restart;

> Delta:= epsilon[2]-epsilon[1];

> epsilon[y] := epsilon[2]-(1/4)*Delta*(1-tanh(a*y))^2;

 > z:= tanh(a*y) ;

 > ODE[4]:= diff(Y(y),y,y)- ( a/2* Delta *(1-z)*(z^2-1))/(epsilon[2]- Delta*(1-z)/4)* diff(Y(y),y)-( beta^2+ mu[0]*epsilon[y]*omega^2)*Y(y) = 0;

> dsolve(ODE[4],Y(y));

does this always occur or i do have problem with my version of maple 15, 7 and 16.

Thank you, looking forward for your answers.

I have created a simple proc to return true or false depending on the value in a list of values.  now i would like to filter out the falses and return the actual value that is true from the list.

I am having some difficulty animating the function shown in the attached file.  I am going to create an animation which will show the curve as a function of t.  My first question is that there is no way to compute K_n because the initial conditions I have are only given as arbritary functions F(z),G(z).  So I am not really sure how to proceed here.

My second question is that I also want to plot the Z dependent part of y as a function of z/b.  I have tried to incorporate this into Maple, however, all I get back is that there are 'unexpected variables present'

Thanks.

Is it possible to assign a matrix given values/expressions?

Instead of assigning each element separately like in the example below:

with(combinat):
list1 := permute([a, b, a, b, a, b], 3);
list1a := subs(b=1,subs(a=0, list1));
list1a := permute([seq(seq(k,k=0..1),k2=1..3)], 3);
list2 := permute([a, b, c, d, e, f, g, h, a, b, c, d, e, f, g, h, a, b, c, d, e, f, g, h], 3);
list3 := subs(h=18,subs(g=17,subs(f=16,subs(e=15,subs(d=14,subs(c=13,subs(b=12,subs(a=11,list2))))))));
list3 := permute([seq(seq(k,k=11..18),k2=1..3)], 3);
list5 := Matrix(nops(list1a)*nops(list3), 1);
count := 1;
for n from 1 to nops(list3) do
temp1 := subs(1=list1a[1],list3[n]);
for k from 11 to nops(list1a)+10 do
temp1 := subs(k=list1a[k-10],temp1);
od;
list5[count] := temp1;
count := count + 1;
od;
list6 := permute(list5, 2);

Error, (in combinat:-permute) 1st argument must be a list, set or a non-negative integer

I have a bit of an issue.

I'm trying to solve this:

eq1:= exp(-lambda)*exp(k)/factorial(k) > .95

lambda:=2

solve(eq1,k)

Warning, solutions may have been lost

Good afternoon sir.

I request your kind support to the above cited query.

With thanks & Regards

M.Anand

Assistant Professor in Mathematics

SR International Institute of Technology,

Hyderabad, Andhra Pradesh, INDIA.