Hello,

I've a big amount of equations, i tried to solve them and get the answer as an array but for some reason it's not working, is solve the right one for this or what?

thank you

the 2 files aren't related, but both contain a system of equation i tried to solve but without avail

Advheat-ex53.mw

Advheat-ex54.mw
 

Download Advheat-ex54.mw
 

Download Advheat-ex53.mw

Hi,

I'm trying to help the daughter of one of my friends with some flux related exercises.

We have calculated this one by hand and then I wanted to repeat it in Maple to help her see how to use Maple.

My problem is that I cannot figure out how to represent the functions in Maple, so that the calculations fall out similar to what we have been doing by hand. Yes, we could just use the built in Flux operation, but that defeats the purpose here.

Please bear with me - my calculus is rusty and I only have access to Maple on my son's machine. Plus I have never used Maple before... yes, I'm that old ;-)

We want to calculate the flux of the vector field V through the surface given by r:

Then we can differentiate r wrt both u and v and calculate the normal vector for the surface:

The next step is then to do the double integral of:

This is - bar the evalVF call - almost identical to what you'd be doing by hand, so this is good.

Next is the flux out of the 3d object constrained by the square [0,1] and [-Pi/2, Pi/2] and the surface r.

The paramterisation of that is:

with w in [0,1].

At this point one applies Gauss' Divergence Theorem which means that in order to find the flux of V out of Omega we "just" have to calculate the spatial integral of the divergence of V over the body described by Omega.

But that can be calculated by integrating V(Omega(u,v,w)) times the Jacobi function.

The Jacobi function is the determinant of the output of Maple's Jacobian procedure:

In this case it is 1 - u^3.

Now comes the big problem: how do I get Div(V)(Omega(u,v,w)), ie, the divergence of V taken in the point Omega(u,v,w)?

If I do evalVF(V, Omega(u, v, w)) I get a column vector out that I cannot compute the divergence of using Divergence(%) since that only works on VectorFields.

And Divergence(V) is not a function so I cannot do

And if I change Omega to return a value in R^3 instead of a vector I cannot use Jacobian, so that stop even faster.

Defining two versions of Omega just to make Maple happy seems wrong.

I just want to write the tripple integral of Div(V)(Omega(u,v,w))*jacobi or something close to that.

Please let me know if I should provide the workbook or in some other way make all my calculations available.

Thanks in advance and sorry if my description is lacking,

Torben

Dear Maple users

I have a possibly quite easy question: How do I calculate or refer to a partial derivative evaluated at some specific point? The Maple documentation was no help to me in this regard. I hope the picture below indicate what I am looking for. I am using Maple 2D notation, but not excited about using the vertical line as evaluation. What ways can it be accomplished?

Erik

Dear Users!

Hoped everyone fine with everything. I the following maple expression, I need a matrix A for each n. Like if I take k =1 I want A[1]; if I take k=2, I want A[1], A[2]; for k=3 I want A[1], A[2], A[3] and so on. A[i]'s is square matrix having order M-1 by M-1.

Further I want to generate a block matrix for k. Like for k=1 I want a block matrix as Vector(1, {(1) = A[1]}), for k=2 I want a block matrix as Matrix(2, 2, {(1, 1) = A[1], (1, 2) = 0, (2, 1) = 0, (2, 2) = A[2]}), for k =3 I want a block matrix as Matrix(3, 3, {(1, 1) = A[1], (1, 2) = 0, (1, 3) = 0, (2, 1) = 0, (2, 2) = A[2], (2, 3) = 0, (3, 1) = 0, (3, 2) = 0, (3, 3) = A[3]}) and so on.

restart; alpha := 1;
k := 2; M := 3;
printlevel := 3;

for n while n <= 2^(k-1) do

for m from 0 while m <= M-1 do

for j from 0 while j <= M-1 do

Omega[m, j] := 2^((1/2)*k)*sqrt(GAMMA(j+1)*(j+alpha)*GAMMA(alpha)^2/(Pi*2^(1-2*alpha)*GAMMA(j+2*alpha)))*(sum((-1)^i*GAMMA(j-i+alpha)*2^(j-2*i)*(sum((1/2)*binomial(m, l)*(2*n-1)^(m-l)*(1+(-1)^(j-2*i+l))*GAMMA((1/2)*j-i+(1/2)*l+1/2)*GAMMA(alpha+1/2)/GAMMA(alpha+1+(1/2)*j-i+(1/2)*l), l = 0 .. m))/(GAMMA(alpha)*factorial(i)*factorial(j-2*i)), i = 0 .. floor((1/2)*j)))/2^(k*(m+1))

end do

end do;

A[n]:=???

end do;

I am waiting for your positive response.

Thanks
 

Hello i keep getting an error saying that maple expects an integer as it's argument but i has an integer so it is sort of the same thing like when a cat has a full bowl of biscuits and it is going mental at you to feed it, in every other circumstance i would'nt get this error and i even did an assume(k::integer) for the index of the series omega appears, still no. 

I am refering to the number theory package bigomega function btw

Size of a population is given by N(t) = 10 + 2e^-0.3t sin t, t>= 0

I tried to graph it using Maple but the highest and lowest point I got ( 11.3 and 9.5) was vastly different from the supposed answer of  4.421 and1.279 .

Please help! The Maple command I used was N := t -> 10 + 2*exp(-0.3*t)*sin(t);

Plus, is there any Maple command to show what the highest and lowest point of the graph is?

Hi, this should be simple

I have a list of values here, say: [1,4,7,4,2,1] or [3,5,8,11,5,4,3]

And I want the final answer to be [1,4,7] or [3,5,8,11] respectively - i.e. just all the numbers up until the maximum value presented as a list. I believe this will be needed to be done in procedure form. 

For the particular procedure I am using the values in the list will be increasing and then decreasing. 

Thanks

Hi everyone! Just a quick question

When I use the Discrete Plot command. For example

DiscretePlot([1,2,3,4,5],[1,6,2,3,4],style=stem)

I get a graph looking like this 

Now, if possible, I would like to be able to have an indent between 0 and 1 to make it look a bit nicer.

I'm quite new to Maple but need it for work. I'm trying to work with metric tensors, and for easy examples it does work. For instance, such as here: https://gyazo.com/730e055f3393956ffe41427e11fa1b43

For more complicated problems I come into problems of recognising my tensors as actual metrics. In particular here: https://gyazo.com/58347c676b98ddf99275eea8cfecc69d

What am I doing wrong here? Is there some trick I'm missing, am I giving the data incorrectly?

Thank you,

Eivind

PS: For convenience I'm dumping the document in text format here:

> restart;
> with(PDETools); with(DifferentialGeometry); with(Tools); with(Tensor);
> k := 4;
                               4
> C := [w1, w2, z1, z2, seq(cat(x, i), i = 1 .. k), seq(cat(y, i), i = 1 .. k)];
        [w1, w2, z1, z2, x1, x2, x3, x4, y1, y2, y3, y4]
> DGsetup(C, PW, quiet);
                         frame name: PW
PW > F := [b, seq(cat(r, i), i = 1 .. k), seq(cat(s, i), i = 1 .. k)];
              [b, r1, r2, r3, r4, s1, s2, s3, s4]
PW > FunGen := proc (symb) options operator, arrow; PDETools[declare](symb(w1, w2), symb) end proc;
PW > map(FunGen, F);
              b(w1, w2) will now be displayed as b
             r1(w1, w2) will now be displayed as r1
             r2(w1, w2) will now be displayed as r2
             r3(w1, w2) will now be displayed as r3
             r4(w1, w2) will now be displayed as r4
             s1(w1, w2) will now be displayed as s1
             s2(w1, w2) will now be displayed as s2
             s3(w1, w2) will now be displayed as s3
             s4(w1, w2) will now be displayed as s4
PW > NULL;
PW > dx := proc (i) options operator, arrow; 'eval(cat(dx, i))' end proc;
PW > dy := proc (i) options operator, arrow; 'eval(cat(dy, i))' end proc;
PW > r := proc (i) options operator, arrow; cat(r, i) end proc;
PW > s := proc (i) options operator, arrow; cat(s, i) end proc;
PW > epsilon := proc (i) options operator, arrow; cat(epsilon, i) end proc;
PW > L1 := [1, b, seq(r(i), i = 1 .. k), seq(s(i), i = 1 .. k), seq(epsilon(i), i = 1 .. k)];
  [1, b, r1, r2, r3, r4, s1, s2, s3, s4, epsilon1, epsilon2,

    epsilon3, epsilon4]
PW > g := evalDG(`&s`(dw1, dz2)+`&s`(dw2, dz2)+b*(`&s`(dw1, dw1)+`&s`(dw2, dw2))+sum('r(i)'*(`&s`(dx(i), dw1)+`&s`(dy(i), dw2)), i = 1 .. k)+sum('s(i)'*(`&s`(dx(i), dw2)-`&s`(dx(i), dw1)), i = 1 .. k)+sum('epsilon(i)'*(`&s`(dx(i), dx(i))+`&s`(dy(i), dy(i))), i = 1 .. k));
_DG([["tensor", PW, [["cov_bas", "cov_bas"], []]], [

  [[1, 1], 2 b], [[1, 4], 1], [[1, 5], -s1 + r1],

  [[1, 6], -s2 + r2], [[1, 7], -s3 + r3], [[1, 8], -s4 + r4],

  [[2, 2], 2 b], [[2, 4], 1], [[2, 5], s1], [[2, 6], s2],

  [[2, 7], s3], [[2, 8], s4], [[2, 9], r1], [[2, 10], r2],

  [[2, 11], r3], [[2, 12], r4], [[4, 1], 1], [[4, 2], 1],

  [[5, 1], -s1 + r1], [[5, 2], s1], [[5, 5], 2 epsilon1],

  [[6, 1], -s2 + r2], [[6, 2], s2], [[6, 6], 2 epsilon2],

  [[7, 1], -s3 + r3], [[7, 2], s3], [[7, 7], 2 epsilon3],

  [[8, 1], -s4 + r4], [[8, 2], s4], [[8, 8], 2 epsilon4],

  [[9, 2], r1], [[9, 9], 2 epsilon1], [[10, 2], r2],

  [[10, 10], 2 epsilon2], [[11, 2], r3], [[11, 11], 2 epsilon3],

  [[12, 2], r4], [[12, 12], 2 epsilon4]]])
PW > Gam := Christoffel(g);
Error, (in DifferentialGeometry:-Tensor:-Christoffel) expected 1st argument to be a metric tensor. Received: _DG([["tensor", PW, [["cov_bas", "cov_bas"], []]], [`...`]])
PW > Ric := RicciScalar(g);
Error, (in DifferentialGeometry:-Tensor:-RicciScalar) expected 1st argument to be metric tensor. Received: _DG([["tensor", PW, [["cov_bas", "cov_bas"], []]], [`...`]])
PW > CovariantDerivative(g, Gam);
Error, (in DifferentialGeometry:-Tensor:-CovariantDerivative) expected 2nd argument to be an affine connection. Received: Gam
PW > LieDerivative(D_x, g);
Error, (in DifferentialGeometry:-LieDerivative) expected 1st argument to be a vector field. Received D_x
PW > CurvatureTensor(g);
Error, (in DifferentialGeometry:-Tensor:-CurvatureTensor) expected 1st argument to be a metric tensor or an  affine connection. Received: _DG([["tensor", PW, [["cov_bas", "cov_bas"], []]], [`...`]])
PW >

Hi everyone again

This one is linked to my previous 2 question.

Essentially I am trying to use a procedure to reproduce the formula:

S(j) = (1 + sum(H_j*T_j,j=1..n))/(1 + sum(1/(H_j*T_j),j=1..n))

BigProc:= proc(H::list,T::list)
local Form, i;
Form:=[];
for i from 1 to nops(H) do
Form := [op(Form),(1 + [sum(H[1..i]*~T[1..i],i=1..5)])/~(1 + [sum(1/~(H[1..i]*~T[1..i]),i=1..5)])]
end do:
end proc:
MainProc([1,3,5],[3,6,8])

Error, (in sum) summation variable previously assigned, second argument evaluates to 1 = 1 .. 5
 

The actual answer should be (3, 396/25,22320/509)

ie 

S(1) = (1+ 3)/(1+(1/3)) = 3

S(2) = (1 +(3+18))/(1+1/3 + 1/18)) = 396/25

S(3) = (1 +(3+18+40))/(1+1/3 + 1/18 +1/40) = 22320/509

I feel like I am missing a few things to my procedure. Any help would be greatly appreciated!

The output of a solve command was:

solution := {p[1] = 2.788944999, p[2] = 4.940143518}, { p[1] = 15.29764736, p[2] = 4.946617373}

My question is: How to capture these 4 numbers in a 2 by 2 matrix ?

I tried assign, subs commands. Did not succeed. Could some one help, please?

Hi

I would like to be able to use a procedure in order to create a sequence using a list. Here is an example of what I am trying to achieve:

X = [1,3,4, 50,10]

T_n = 1 + sum^n_j=1 X_j

So T_1 = 1 + 1 = 2

T_2 = 1 + [1+3] = 5

T_3 = 1 +[1+3 +4] = 9

T_4 = 1 + [1+3+4+50] = 59

T_5 = 1+ [1+3+4+50+10] = 69

So my final list would be [2,5,9,59,69]

I am quite new to this forum so i was not sure how to create the Sum from j = 1 to n bit. I know the command for creating a summation but not in a procedure sense.

How do I get a graph from Maple for function f(x) that is continuous on [0,2] except at x=1, where f(1)=4, lim_{x approaching 1^-} f(x)=2, and lim_{x approaching 1⁺} f(x)=3?

Duarte and Agustí (1998) investigatedthe CO2 balance o f  aquati  c ecosystems. They related thecommunity respiration rates (R) to the gross primary production rates (P) of aquatic ecosystems. (Both quantities were measured in the same units.) They made the following statement:

Our results  confirm the generality of earlier reports that the relation between community respiration rate andgross production is not linear. Community respirationis scaled as the approximate two-thirds power of grossproduction.

(a) Suppose that you obtained data on the gross production and respiration rates of a number of freshwater lakes. How would you display your data graphically to quickly convince an audience that the exponent b in the power equation relating Rand P is indeed approximately 2/3? (Hint: Use an appropriate log transformation in Maple)

(c) The r atio R/P for an ecosystem is important in assessing the global CO2 budget. If respiration exceeds production (i.e., R >P), then the ecosystem acts as a carbon dioxide source, whereas if production exceeds respiration (i.e., P > R), then the ecosystema cts as a carbon dioxide sink. Assume now that the exponent inthe power equation relating R and P is 2/3. Show that the ratio R/P, as a function of P, is continuous for P > 0. Furthermore,show that
           lim R/P =∞
            P→0+

and
            lim R/P= 0
            P→∞


How to use Maple to sketch the graph of the ratio R/P as  afunction of P for P > 0. (Experiment with the graphing calculatorto see how the value of a affects the graph.)

Hyperbolic functions are used in the sciences. The hyperbolic sine , sinh x;the hyperbolic cosine, cosh x; and the hyperbolic tangent, tanh x,defined respectively as

sinh x = e^x − e^−x/ 2, x ∈ R
cosh x = e^x + e^−x/2, x ∈ R
tanh x = e^x − e^−x/e^x + e^−x , x ∈ R

How do I show that these three hyperbolic functions are continuous forall x ∈ R using Maple?