Dear Maple Users,

This particular question is example problem 8.4.1 in the textbook: "PDE & BVP with MAPLE", 2nd Edition by George A. Articolo.

I shall paraphrase the problem here and attach the Maple Worksheet solution as detailed in the textbook.

We seek the temperature distribution u(x,t) in a thin rod whose lateral surface is insulated over the interval I = {x | 0 <x<1}. The left end of the rod is held at a fixed temperature of 10, and the right end is held at the fixed temperature of 20. There is no internal heat source. The thermal diffusivity of the rod is k = 1/20, and the rod has an intitial temperature distribution u(x,0) = f(x) given as follows.

The nonhomogeneous diffusion equation is:

u_t'(x,t) = k*u_x"(x,t) +h(x,t)

The BCs are nonhomogeneous:

u(0,t) = 10

u(1,t) = 20

The IC is:

u(x,0) = 60x -50x²+10

The internal heat source term is:

h(x,t) = 0

I have typed in the MAPLE commands exactly as in the textbook (attached), but it does not execute in my Student 2020 version of MAPLE.

Could you please take a look at the attached MAPLE worksheet and let me know if something can be done to make it work.

Thank you for your help.

Joe Thodiyil

George_A_Articolo_2ndEdition_Ex_8.4.1_PDE.mw

Dear all

I solve a given pde with some conditions given, but I get 

unable to handle PDE problem subject to boundary conditions 

solution_pdes.mw

many thanks for your help

I am trying to find one option so that  a sphere is tangent with every edge of a tetrahedron. Suppose tetrahedron OABC, here O(0,0,0), A(x1, y1, z1), B(x2, y2, z2), and C(x3, y3, z3).  How to find a sphere is tangent with every edge of a tetrahedron?

I know how to contruct an isoscele ABCD trapeze knowing the 2L length of AB and BC=CD=CD=a. But I don't know answer to that question : L being fixed together with points A and B , show that the place of C when a varies is a branch of hyberbola. Here is my code.

restart; unprotect(O, D);
with(plots):
Vdot := proc (U, V) add(U[i]*V[i], i = 1 .. 2) end:
dist := proc (M, N) sqrt(Vdot(expand(M-N), expand(M-N))) end:
_EnvHorizontalName := x: _EnvVerticalName := y:
O:=[0,0]:A:=[-L,0]:alpha:=arccos((2*L-a)^2/(2*a*(2*L-a))):h:=tan(alpha)*(2*L-a)/2:
B:=[L,0]:C:=[L-(2*L-a)/2,h]:D:=[-L+(2*L-a)/2,h]:
L := 6; a := 7;
poly := [A, B, C, D, A];tp := textplot([[A[], "A"], [B[], "B"], [C[], "C"], [D[], "D"]], color = black, 'align' = {'above', 'right'});
trapeze := polygonplot(poly, axes = normal, color = "DarkGreen", transparency = .9);
display([tp, trapeze], scaling = constrained); Thank you foryour help.

Hi everyone:

I want to write the below serie in Maple, how can I do it?

where: k = 0,.....,n

n is a Natural number.

tnx...

Dear Users!

I want to find the solution of the solution of PDEs as given bellow:

restart;
PDE1 := diff(u(y, t), t)+diff(u(y, t), t, t) = diff(u(y, t), y, y)-u(y, t);
PDE2 := v(y, t)+diff(tau(y, t), t) = diff(u(y, t), y);
ICandBC := {tau(y, 0) = 0, u(0, t) = 0, u(3, t) = 0, u(y, 0) = 0, (D[2](u))(y, 0) = 0};
pds := pdsolve({PDE1, PDE2}, ICandBC, numeric);

But got the following error

Error, (in pdsolve/numeric/process_PDEs) number of dependent variables and number of PDE must be the same
Kindly help me to fix this error. I shall be very thankful. 

Special request to:
@acer @Carl Love @Kitonum @Preben Alsholm

I have created a set of help files using the example templates. After I create the .help file and install it with my package, I can view the help pages in the help viewer. However, when I click on any link within a help page, the target page opens as a worksheet in Maple. I understand this is because I created the hyperlink with a worksheet as the target. However, I don't know where to obtain the help topic name for a help page before it has been created.  I have searched help, but can't find any applicable guidance.  Can anyone tell me how to determine the help topic name when first creating the help pages.

I have attached one of my help file worksheets.     Hlpdiracmatrices.mw

Hello,

I defined a vector (in cartesian coordinates) with Physics[Vectors] as

q_:=3 _i + 5 _j + 2 _k

Then I wanted do a transformation on this vector by multiplying it with matrix

M:=<3,4,2|5,6,2|2,1,4>
M.q_

However, I am getting a result where every element of the matrix is multiplied by the vector.

If I define q as <3,5,2> then matrix multiplication works as one would expect.

So, my question is how can I have a matrix multiplication with a vector defined with Physics[Vectors] package?

Dear Maple community,

I would really appreciate it if you could tell me how I can solve numerically in Maple the following system of equations (the Maple file containing these equations can be found here: Mapleprime_Q.mw):

Thank you very much in advance for you help!

Hello,

When I create a vector in spherical coordinates and map it to cartesian coordinates with Physics[Vectors] package as follows,

restart:with(Physics[Vectors]):
q_:=a _r + b _theta + c _phi
ChangeBasis(q_,cartesian)

I get the answer:

(a*cos(phi)*sin(theta)+b*cos(phi)*cos(theta)-c*sin(phi)) i + (a*sin(theta)*sin(phi)+b*cos(theta)*sin(phi)+c*cos(phi)) j + (-b*sin(theta)+a*cos(theta)) k

which is what I would expect.

But if I try to do that with VectorCalculus package as follows,

q := SetCoordinates(<a, b, c>, spherical)
MapToBasis(q, cartesian)

This gives 

(a*sin(b)*cos(c)) ex + (a*sin(b)*sin(c)) ey + (a*cos(b)) ez

I am confused about this!

The SetCoordinates(<a, b, c>, spherical) command outputs

q:=(a) er  + (b) ephi + (c) etheta

here, a,b, and c are  depicted as the components of the vector q in spherical coordinates, but when I map to cartesian coordinates, a,b, and c are treated as if they were the coordinates in spherical coordinates rather than components-- unlike ChangeBasis in Physics[Vectors] package.

Why are these two different?

Good evening,

is it possible to construct a math table with Maple just with Code? Something like

      test_1    test_2

a       9,6        5,6

b     pending  8,4     

to be able to print it? There is

https://de.maplesoft.com/support/help/Maple/view.aspx?path=worksheet/documenting/table            and

https://de.maplesoft.com/support/help/Maple/view.aspx?path=worksheet%2freference%2ftableproperties   

, however, I do not understand how to just get any table going and assign calculated values within a procedure as is possible with a matrix for example. Thank you in advance! :)

Hello, I am trying to plot this one and I did not get the graph, I don't know where the problem. Could you please help. thank you

restart;
with(plots):

alpha := 0.005;
beta := 0.01;
                          beta := 0.01

mu := 0.005;
                          mu := 0.005

m := 0.003;
                           m := 0.003

u := 0.3;
                            u := 0.3

w := 0.3;
                            w := 0.3

v := 1;
                             v := 1

gamma = 0.1;
                          gamma = 0.1

Gamma := 0.01;
                         Gamma := 0.01

Eq := sigma^4 + sigma^3*[2*(mu*v + mu) + 2*alpha - beta*(u + w) + 2*beta*v] + sigma^2*[4*mu*m + 2*alpha*(2*mu + m) + alpha^2 - 2*beta*v(mu - 2*m) - 2*beta*(u + w)*(mu + m) + alpha*beta*(4*beta + (-u - w)) - beta^2*v*(u + w - v) + k^2*(Gamma^2 + gamma^2)] + sigma*[2*alpha*mu*(2*m - beta*(u + w)) + 2*alpha^2*(beta*v + mu) - 4*beta*mu*m*(u + w + v) + 4*alpha*beta*v*(mu + m) - 2*beta^2*v*(u + w) + 2*beta^2*v^2*(m + alpha) - alpha*beta^2*v*(u + w) + 2*Gamma^2*beta*v*k^2 + 2*k^2*(Gamma^2*mu + gamma^2*m) + gamma^2*k^2*(2*alpha - beta*(u + w))] + [Gamma^2*k^2*(2*beta*mu*v + gamma^2) + Gamma^2*beta^2*k^2*v*(Gamma*v - gamma*(u + w)) - beta*gamma^2*k^2*(u + w)*(alpha + 2*m) + alpha^2*(beta^2*v^2 + gamma^2*k^2) + 2*alpha*beta^2*v*(v*m - mu*(u + w)) + 4*beta*mu*m*v*(alpha - beta*(u + w))];
p1 := implicitplot(Eq, k = 0 .. 10, sigma = -0.1 .. 0.1);
           4
Eq := sigma 

          3                                                       
   + sigma  [2 mu v + 2 alpha + 2 mu - beta (u + w) + 2 beta v] + 

       2 [                                   2
  sigma  [4 mu m + 2 alpha (2 mu + m) + alpha 

   - 2 beta v(mu - 2 m) - 2 beta (u + w) (mu + m)

                                       2              
   + alpha beta (4 beta - u - w) - beta  v (u + w - v)

      2 /     2        2\]         [               
   + k  \Gamma  + gamma /] + sigma [2 alpha mu (2 m

                            2              
   - beta (u + w)) + 2 alpha  (beta v + mu)

   - 4 beta mu m (u + w + v) + 4 alpha beta v (mu + m)

           2                   2  2            
   - 2 beta  v (u + w) + 2 beta  v  (m + alpha)

               2                    2         2
   - alpha beta  v (u + w) + 2 Gamma  beta v k 

        2 /     2           2  \
   + 2 k  \Gamma  mu + gamma  m/

          2  2                         ]   [     2  2 /           
   + gamma  k  (2 alpha - beta (u + w))] + [Gamma  k  \2 beta mu v

          2\        2     2  2                            
   + gamma / + Gamma  beta  k  v (Gamma v - gamma (u + w))

               2  2                      
   - beta gamma  k  (u + w) (alpha + 2 m)

          2 /    2  2        2  2\
   + alpha  \beta  v  + gamma  k /

                 2                     
   + 2 alpha beta  v (v m - mu (u + w))

                                         ]
   + 4 beta mu m v (alpha - beta (u + w))]

[k1,0], [k2,0], [k3,0], ...) , where k_{n}=2*n*Pi/L and the domain [0,L] 
L:=10.0;
p2:=pointplot([seq([2*n*Pi/L,0],n=0..10)],color=red,symbolsize=15):
display(p1,p2);
                           L := 10.0

       /            /     4
display\implicitplot\sigma 

          3                                                       
   + sigma  [2 mu v + 2 alpha + 2 mu - beta (u + w) + 2 beta v] + 

       2 [                                   2
  sigma  [4 mu m + 2 alpha (2 mu + m) + alpha 

   - 2 beta v(mu - 2 m) - 2 beta (u + w) (mu + m)

                                       2              
   + alpha beta (4 beta - u - w) - beta  v (u + w - v)

      2 /     2        2\]         [               
   + k  \Gamma  + gamma /] + sigma [2 alpha mu (2 m

                            2              
   - beta (u + w)) + 2 alpha  (beta v + mu)

   - 4 beta mu m (u + w + v) + 4 alpha beta v (mu + m)

           2                   2  2            
   - 2 beta  v (u + w) + 2 beta  v  (m + alpha)

               2                    2         2
   - alpha beta  v (u + w) + 2 Gamma  beta v k 

        2 /     2           2  \
   + 2 k  \Gamma  mu + gamma  m/

          2  2                         ]   [     2  2 /           
   + gamma  k  (2 alpha - beta (u + w))] + [Gamma  k  \2 beta mu v

          2\        2     2  2                            
   + gamma / + Gamma  beta  k  v (Gamma v - gamma (u + w))

               2  2                      
   - beta gamma  k  (u + w) (alpha + 2 m)

          2 /    2  2        2  2\
   + alpha  \beta  v  + gamma  k /

                 2                     
   + 2 alpha beta  v (v m - mu (u + w))

                                         ]               
   + 4 beta mu m v (alpha - beta (u + w))], k = 0 .. 10, 

                     \                                         
  sigma = -0.1 .. 0.1/, pointplot([[0., 0], [0.6283185308, 0], 

  [1.256637062, 0], [1.884955592, 0], [2.513274124, 0], 

  [3.141592654, 0], [3.769911184, 0], [4.398229716, 0], 

  [5.026548246, 0], [5.654866778, 0], [6.283185308, 0]], 

                               \
  color = red, symbolsize = 15)/

Hello.

I plot  F1:=1/(x + μ) + x - 1 and on the graph i get the line x = -μ. How can I get rid of it? I try the discont option but I get an error. Do I need, maybe, a specific with command?

The command I use is the next one:

diagd1_1 := implicitplot(F1 = 0, mu = -8 .. 8, x = -4 .. 4, gridrefine = 5, crossingrefine = 15, rational, color = blue, thickness = 2, numpoints = 100000, resolution = 3000, rangeasview)

The error I get:

Error, (in plot/options2d) unexpected option: discont = True

Thanks a lot !!!

I recently found this piece of code while using showstat:

if type(i,{'symbol', not ('symbol')}) then
...
end if

At first glance, this felt strange to me, because it looked like if we were checking whether "i" was of the "symbol" type or of a type other than "symbol", and therefore the test was still true.

Doing a simple test I obtain this

if type(s,{'symbol', not ('symbol')}) then "TRUE" else "FALSE" end if;
                             "TRUE"
if type(cos(c),{'symbol', not ('symbol')}) then "TRUE" else "FALSE" end if;
                            "FALSE"

Could you explain me what  not ('symbol') really means?

TIA

I have this equation: 
cpd = 2/(1 + exp(-0.004*200)) - 1

i want it to give me a new equation for cp (not solving the equation). 
what i've tried:

2/(1 + exp(-0.004*200)) - 1 = cpd = 0.379948962
q1 := 0.379948 = 2/(1 + exp(-0.004*cp)) - 1
isolate(q1, cp) = cp = 199.99 (this is the answer but i want the equation)

if this is not clear enough then i will give a simpe example: 

given equation: x-2 = 5
WHAT I DON'T WANT: x = 3

WHAT I WANT: x=5-2