## two layer thermal flux...

hello!

I'm new in Maple!!

I am try simulate the termal flux in composite material using heat equation and perfect contact between the materials. But I can't enter the fourier condiction and my code don't work!!

Any help??

> restart; with(plots); with(PDEtools); with(plottool
> eq1 := diff(u1(x, t), x, x) = k1*(diff(u1(x, t), t));
d  / d          \      / d          \
--- |--- u1(x, t)| = k1 |--- u1(x, t)|
dx \ dx         /      \ dt         /
> eq2 := diff(u2(x, t), x, x) = k1*(diff(u2(x, t), t));
d  / d          \      / d          \
--- |--- u2(x, t)| = k1 |--- u2(x, t)|
dx \ dx         /      \ dt         /
> L := 10; v1 := 20; v2 := 10; k1 = 10; k2 := 20;
10
20
10
k1 = 10
20
> bc1 := u1(0, t) = v1, u1(x, 0) = 0;
u1(0, t) = 20, u1(x, 0) = 0
> bc2 := u2(0, t) = v2, u2(x, 0) = 0;
u2(0, t) = 10, u2(x, 0) = 0
> sol1 := pdsolve({bc1, eq1});
Warning: System is inconsistent

## Trigonometric circle plot...

Hello,
I would like to display a complete trigonometric circle.like the attached photo. How to do it? Thanks

TrigonometricCircle.mw

## Sum of functions...

It is necessary that the expressions are combined in a new function. So as I'm trying not is obtained.

 >
 (1)
 >

## Export dat file for 3D plot...

Dear Users!

Hope you would be fine. I want to export dat file for 3D plot in maple and want to replot it any perfessional software like tecplot, origin.

u:=sin(x+y):
plot3d(sin(x+y), x = 0 .. 2*Pi, y = 0 .. 2*Pi);
How can I export the data in 3D. Thanks in advance for you help.

## It is possible not to translate apostrophe " ' " t...

Apostrophe '  is always interpreted as a "differentiate command", i.e., A' is always translated  to diff(A(x),x).

Is it possible to override this behaviour, it is to say, is there a way for using A' as a variable name?

In euclidean geometry of triangles, A' is a common name given to some points built from vertex A of a triangle ABC.

## How can I fix plot for system of Differential equa...

Please check this code and fix the error. And help me with the below two questions.

1- In the above image, I'm getting the error when I'm to plot my solutions.

2- How to get information from this system?

The values of x_1 and corresponding y_1 and so on and errors etc

Thanks!

## Factorizing simple expression...

How do I get Maple to factorize this simple expression without too much effort?

f:=3/2 + sqrt(8*k + 2) + 2*k

## How can I create a probability distribution table ...

I want to create a distribution table and then find expected value,variance and standard deviation.

For example : X=-1,P(X)=0.2
X=0,P(X)=0.25
X=1,P(X)=0.35

X=2,P(X)=0.2

E(X) would then equal -1*0.2+0*0.25+1*0.35+2*0.2.

How can I do all of this with Maple ?

## How should linearization a nonlinear equation with...

How should linearization a nonlinear equation with maple?

## ExpectedValue Function...

I'm trying to use the ExpectedValue function to get the next close value of a stock.

restart; with(Finance)

W := WienerProcess()

T := 1.0

S := SamplePath(W(t), t = 0 .. T, timesteps = 100, replications = 10^4)

A := S[1 .. 10^4, 50]

TI := 1

AN := 100 (Start Value)

sigma := 3.5 (volatility)

r := 0.5e-1    (interest)

ANF := AN*exp((r-(1/2)*sigma^2)*TI+sigma*W(TI))       (ANF: is the forecasting Value)

ExpectedValue(ANF, timesteps = 100, replications = 10^3)

Is this approach right?

## How to disable this things ? ...

Why it be like that and how to solve it ?

## How can I fix "Error, (in dsolve/numeric/process_i...

>restart;
> ODEtools[declare]((S, L, B)(t), prime = t);
ODEtools[declare](S(t), L(t), B(t), prime = t)
> DE1 := diff(S(t), t) = -L*S*beta-`&mu;S`+mu;
d
DE1 := --- S(t) = -L S beta - &mu;S + mu
dt
> DE2 := diff(L(t), t) = L*S*beta-(gamma+mu)*S;
d
DE2 := --- L(t) = beta S L - (gamma + mu) S
dt
> DE3 := diff(B(t), t) = L*gamma-gamma*mu;
d
DE3 := --- B(t) = L gamma - gamma mu
dt
> init_conds := S(0) >= 0, L(0) >= 0, B(0) >= 0;
init_conds := 0 <= S(0), 0 <= L(0), 0 <= B(0)
> sys := {init_conds, diff(B(t), t) = L*gamma-gamma*mu, diff(L(t), t) = L*S*beta-(gamma+mu)*S, diff(S(t), t) = -L*S*beta-`&mu;S`+mu};

> sol := dsolve(sys, numeric, parameters = [mu, beta, gamma, S(t), L(t), B(t)], method = rkf45);

Error, (in dsolve/numeric/process_input) system must be entered as a set/list of expressions/equations

> sol(parameters = [mu = .234, beta = 2.345, gamma = 5.678, S(t) = 6.678, L(t) = 6.789, B(t) = 7.123]);
sol(parameters = [mu = 0.234, beta = 2.345, gamma = 5.678, S(t) = 6.678, L(t) = 6.789, B(t) = 7.123])

## possible bug in pdsolve. Too many levels of recurs...

Is the following a bug? I am using Maple 2019  64 bit with latest Physics package 357 on windows 10.

 > restart;
 > pde :=  diff(w(x,y,z),x)+(y^2- a*exp(alpha*x)*(x*y-1))*diff(w(x,y,z),y)+(c*exp(beta*x)*z^2+b*exp(-beta*x))*diff(w(x,y,z),z)= 0; sol:=pdsolve(pde,w(x,y,z));

Error, (in depends) too many levels of recursion

 > restart;
 > pde :=  diff(w(x,y,z),x)+ (b*exp(alpha*x)*y^2 + a*exp(beta*x)*(beta- a*b*exp((alpha+beta)*x)))*diff(w(x,y,z),y)+(c*z^2*exp(gamma*x)+ d*z + k*exp(-gamma*x))*diff(w(x,y,z),z)= 0; sol:=pdsolve(pde,w(x,y,z));

Error, (in depends) too many levels of recursion

 > restart;
 > pde :=  x*diff(w(x,y,z),x)+ ( a1*exp(alpha*x)*y^2 + beta*y+ a1*b2^2*x^(2*beta)*exp(alpha*x))*diff(w(x,y,z),y)+(a2*x^(2*n)*z^2*exp(lamba*x)+(b2*x^n*exp(lambda*x) - n)*z + c*exp(lambda*x))*diff(w(x,y,z),z)= 0; sol:=pdsolve(pde,w(x,y,z));

Error, (in depends) too many levels of recursion

 >

## Code for a Recurrence Matrix...

I want to find following NxN matrix P                                           (N=2^k.M where k and M are a positive integers)

My Code Try: question.mw

```restart:
with(LinearAlgebra):
interface(rtablesize=20):
k:=2:
M:=4:
N:=2^k*M:
for i from 1 to M do
S:= (sqrt(2)/2^k)*Matrix(M,M, (i,j)-> `if`(`and`(i::odd,j=1) ,-1/(i*(i-2)),0)):
end do:
C:= (1/2^k)*BandMatrix( [ [ seq(-1/(2*sqrt(2)*(i-1)*(i-3)), i=4..M)], [ 1, seq(0*i,i=1..M-1) ],[ seq(4/2*(i-3),i=2..M)]
]
); #I think the matrix C is not same in the question

Gen:=proc(K::posint,A,B)
Matrix(scan=triangular[upper],[seq([A,seq(B,i=j..2^(K)-1)],j=1..2^(K))]);
end proc:
P:=Gen(k,C,S);

```

question.mw

## working with subsets...

Hello,

Is there any way to make this kind of problem in Maple?

I have to find the intersection of subsets, and if there is no intersection then to multiply elements of the subsets. For example,

A={x6,x4,x2,x7,x8,x9,x10},  B={x2,x3,x5,x8} and C={x4,x9,x11,x12,x13}.

Now, the intersection of A and B is {x2}, after that, I don't have the intersection with C, so the solution is x2x4, x2x9, x2x11, x2x11 and x2x13.

Another solution is to make the intersection of A and C and it will be {x4,x9} and after that, I don't have the intersection with B so I have to multiply x4 and x9 with elements in B (obviously, the first solution is better because it has fewer terms)

Is something like this is possible to do in Maple and how?