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Dear Maple users

Physical experiment: I dropped a ball with low mass from a height of approximately 7 meters and wanted to test if the air resistance was proportional to the square of the velocity. I filmed the fall and used the program Logger Pro to collect data: a number of datapoints (time,height) was collected. I copy/pasted the datapoints into MS Excel, from where I could import data into Maple via Tools > Assistants > Import Data ... Then I wanted to make a fit with the theoretical solution, given by a function having just one parameter: the Drag coefficient. Unfortunately I received an error "complex values encountered" (see below). I can solve the problem manual by making a number of guesses for the drag coefficient, until the theoretical curve approximates the data points well. I wanted to make Maple do the fitting job, though. I will appreciate if someone could give an idea how to fit the data properly.

NB! Mass m and g is defined above in the Maple document. The Statistics and plots package is called too.


i have an ODE like this:

I sove this ODE with plot order:

odeplot(sol, [x, (3*D1*a+4*D2)*P(x)/((1-q*S(x))*D2)], .5 .. (1/2)*Pi, tickmarks = [[seq((1/10)*i*Pi = (180*i*(1/10))*`°`, i = 1 .. 8)], default]);
my plot work very well. but i need to plot this ODE with five different parameter (q for for instance, q=0.1 & q=0.2 ....) all in one axis. something like this:

Dear collegues

Hope you are fine

I wrote a code to solve a system of ODEs.

The code solve the problem for higher values of parameter NBT>=5. When I decrease it to NBT=0.2, the code didnt converge. I did my best but I couldnt get the results.

I would be most grateful if you help me at this problem

The code is attached

Thank you



Collatz := proc (n)

    local count;

       while n != 1 do

           if `mod`(n, 2) = 0 then n := (1/2)*n

           else n := 3*n+1

           end if;

           count := count+1;

       end do;


end proc:


I wanna correct 'illegal use of formal parameter' error.

'n' always goes to 1 through 'while statement'.

Bubble := proc (X::list)

local n, i, j, t;

n := nops(X);

if n = 0 then ERROR("empty list") end if;

for i to n-1 do

   for j to n-i do

      if X[j+1] < X[j] then

          t := X[j];

          X[j] := X[j+1];

          X[j+1] := t;

      end if;

   end do;

end do;


end proc


I make bubble sort algorithm. but i can't find 'illegal use of a formal parameter'.

Hi Mapleprimes,

I have a conic section that is parametric.  Namely,

x(t) = 9t^2 + 3t  + 367
y(t) = 3t^2 + 2t + 122

How can I find the Vertex and Foci of this curve?
Also, How can I do this for the general case?



Hi fellow Maple users,

I'm trying to solve an eigenvalue problem of Ax=wx, where A is a 6 by 6 Hermitian matrix with two parameters x and y. I want to solve it for w and then plot3d it with x and y as unknowns. The way I have been doing is first find the characteristic equation Determinant(A-wI)=0 and then solve it for w, and then plot3d the solutions within a range for x and y. My problem is sometimes solve(Determinant(A-wI)=0,w) would give me the 6 solutions expressed in x and y, but sometimes when the numbers in A are changed it will only give me a Rootof solution with which I cannot plot. I'm wondering if there is a better way to do this. I'm actually not very interested in the symbolic solution of w expressed in x and y, just the plot, so if there is a numerical alternative it's good too.

Thank you in advance!

Hello everybody.

In the attached file, you find 6 equations. All of these parameters are known except "pd" and "qd". How can I find these two unknowns from 6 equations??? It should be pointed out that, "pd" and "qd" must contain "ud", "vd","wd" and "rd".

Thanks in advance.

hi.I want to dsolve set of nonlinear equations with one unknown parameter this possible with dsolve matlab this possible with bvp4c rule..please help me for this problem.if we should another rule please attached file reform.Thanks


restart; Digits := 10; F[0] := 0; F[1] := 0; F[2] := (1/2)*A; T[0] := 1; T[1] := B; M := 2; S := 1; Pr := 1

for k from 0 to 12 do F[k+3] := (-3*(sum((k+1-r)*(k+2-r)*F[r]*F[k+2-r], r = 0 .. k))+2*(sum((r+1)*F[r+1]*(k+1-r)*F[k+1-r], r = 0 .. k))+M*(k+1)*F[k+1]-T[k])*factorial(k)/factorial(k+3); T[k+2] := (-3*Pr*(sum((k+1-r)*F[r]*T[k+1-r], r = 0 .. k))-S*T[k])*factorial(k)/factorial(k+2) end do:






solve({limit(numapprox:-pade(t, x, [2, 2]), x = infinity) = 0., limit(numapprox:-pade(diff(f, x), x, [2, 2]), x = infinity) = 1}, {A, B});

{A = -.7359903327, B = 1.324616408}, {A = -0.7307377025e-1+2.009578912*I, B = .3744177908+.5971332133*I}, {A = .6936483785+.1660915631*I, B = .1622123331+.9257041678*I}, {A = -2.182873922*I, B = .8203849935*I}, {A = .3431199285*I, B = 1.783825109*I}, {A = -.6936483785+.1660915631*I, B = -.1622123331+.9257041678*I}, {A = 0.7307377025e-1+2.009578912*I, B = -.3744177908+.5971332133*I}, {A = .7359903327, B = -1.324616408}, {A = 0.7307377025e-1-2.009578912*I, B = -.3744177908-.5971332133*I}, {A = -.6936483785-.1660915631*I, B = -.1622123331-.9257041678*I}, {A = 2.182873922*I, B = -.8203849935*I}, {A = -.3431199285*I, B = -1.783825109*I}, {A = .6936483785-.1660915631*I, B = .1622123331-.9257041678*I}, {A = -0.7307377025e-1-2.009578912*I, B = .3744177908-.5971332133*I}


solve({limit(numapprox:-pade(t, x, [3, 3]), x = infinity) = 0., limit(numapprox:-pade(diff(f, x), x, [3, 3]), x = infinity) = 1}, {A, B});

{A = 4.154051132, B = 17.13248053}, {A = .5466914672+.2697341397*I, B = .1291930705+.9494499975*I}, {A = .4506017673+.3824137679*I, B = -.2437153257+1.192091322*I}, {A = .5458260296+.5776530367*I, B = .3085138074+1.260130057*I}, {A = .3007754662+.5799020019*I, B = 0.8347381159e-1+1.033103936*I}, {A = .3916946210+1.036293227*I, B = .9202208108+1.239552889*I}, {A = .1349186305+.5994923360*I, B = 1.926737919+1.099451808*I}, {A = .5141206762+2.582294380*I, B = -.7917198503+.5287783790*I}, {A = 1.669898274*I, B = 1.659206265*I}, {A = 3.170666197*I, B = -.6372670837*I}, {A = -.5141206762+2.582294380*I, B = .7917198503+.5287783790*I}, {A = -.1349186305+.5994923360*I, B = -1.926737919+1.099451808*I}, {A = -.3916946210+1.036293227*I, B = -.9202208108+1.239552889*I}, {A = -.3007754662+.5799020019*I, B = -0.8347381159e-1+1.033103936*I}, {A = -.5458260296+.5776530367*I, B = -.3085138074+1.260130057*I}, {A = -.4506017673+.3824137679*I, B = .2437153257+1.192091322*I}, {A = -.5466914672+.2697341397*I, B = -.1291930705+.9494499975*I}, {A = -4.154051132, B = -17.13248053}, {A = -.5466914672-.2697341397*I, B = -.1291930705-.9494499975*I}, {A = -.4506017673-.3824137679*I, B = .2437153257-1.192091322*I}, {A = -.5458260296-.5776530367*I, B = -.3085138074-1.260130057*I}, {A = -.3007754662-.5799020019*I, B = -0.8347381159e-1-1.033103936*I}, {A = -.3916946210-1.036293227*I, B = -.9202208108-1.239552889*I}, {A = -.1349186305-.5994923360*I, B = -1.926737919-1.099451808*I}, {A = -.5141206762-2.582294380*I, B = .7917198503-.5287783790*I}, {A = -1.669898274*I, B = -1.659206265*I}, {A = -3.170666197*I, B = .6372670837*I}, {A = .5141206762-2.582294380*I, B = -.7917198503-.5287783790*I}, {A = .1349186305-.5994923360*I, B = 1.926737919-1.099451808*I}, {A = .3916946210-1.036293227*I, B = .9202208108-1.239552889*I}, {A = .3007754662-.5799020019*I, B = 0.8347381159e-1-1.033103936*I}, {A = .5458260296-.5776530367*I, B = .3085138074-1.260130057*I}, {A = .4506017673-.3824137679*I, B = -.2437153257-1.192091322*I}, {A = .5466914672-.2697341397*I, B = .1291930705-.9494499975*I}








Digits := 19:

inf := 28.5:

equ1 := diff(f(eta), eta, eta, eta)+3*(diff(f(eta), eta, eta))*f(eta)-2*(diff(f(eta), eta))^2-M*(diff(f(eta), eta))+theta(eta) = 0;

diff(diff(diff(f(eta), eta), eta), eta)+3*(diff(diff(f(eta), eta), eta))*f(eta)-2*(diff(f(eta), eta))^2-M*(diff(f(eta), eta))+theta(eta) = 0


equ2 := diff(theta(eta), eta, eta)+3*Pr*f(eta)*(diff(theta(eta), eta))+S*theta(eta) = 0;

diff(diff(theta(eta), eta), eta)+3*Pr*f(eta)*(diff(theta(eta), eta))+S*theta(eta) = 0


FNS := f(eta), theta(eta);

f(eta), theta(eta)


s := 0:

BC := f(0) = s, (D(f))(0) = 0, (D(f))(inf) = 1, theta(0) = 1, theta(inf) = 0;

f(0) = 0, (D(f))(0) = 0, (D(f))(28.5) = 1, theta(0) = 1, theta(28.5) = 0


CODE := [M = 2, Pr = 1, S = 1]:

S1 := dsolve({BC, subs(CODE, equ1), subs(CODE, equ2)}, {f(eta), theta(eta)}, type = numeric):


[eta = 0., f(eta) = 0., diff(f(eta), eta) = 0., diff(diff(f(eta), eta), eta) = .7424080874401649594, theta(eta) = 1.000000000000000000, diff(theta(eta), eta) = .9438662130843066161]






Thank you so much for your time. Here's the real problem

f'''(η) + 3f(η)f''(η) - 2[f'(η)] 2 + θ(η) - m*f'(η) = 0

θ''(η) + 3*Pr*f(η)θ'(η) + s*θ(η) = 0

Boundary conditions are:

at η=0: f(η)=f'(η)=0; θ(η)=1;

as η→∞ f'(η)=1; θ(η)=0;

Where m = magnetic parameter (in this case taken as 2)

S = shrinking parameter (in this case taken as 1)

Pr = taken as 1 too

I haven't been able to solve this using differential transforms method (i.e getting the values of f''(0) and θ'(0) denoted by A and B respectively) but shooting method works just fine. :( I seriously need help with this. Thanks you in advance.
I've attached my codes above and i'm hoping someone helps me out real soon. thanks very one.

Hi everyone. Can enuone help with small parameter method?


eq := diff(x(t), `$`(t, 2))-epsilon(alpha*x(t)^4-beta)*(diff(x(t), t))-x(t)+x(t)^3;

subs(x(t) = 1+epsilon*x[1](t)+epsilon^2*x[2](t), eq);

pls help with this...

Let I  be a polynomial in K[A][X] s.t. A is a sequence of parameters (coefficients of f in F) and X is a sequence of variables. I want to extract the variables from ideal I.

For example if I=[(a-1)x*y^2-b+x, x-y+x^2-c] s.t. a,b,c are parameters and x,y are variables. I want {x,y} as the output of algorithm.

hi , kindly guide me how to draw combine graphs for velocity profile at different values of one parameter.  For example we have 3rd order ODE and A is parameter that is multiple of equation. now we want to see the effects of that parameter on this 3rd  order ODE.  Now  how can i sketch the  combine graph of Df(o) at A=1, 2, 3. (for example.)




My problem is the following; Let's say that I want to make a simple program of designing of a steel beam. In order to do so, there is a respectable number of parameters that have to be taken into account - forces, geometrical characteristics etc -. So for example, I have an excel file that has the following rows

1) A row of variables  :                          LENGTH   MOMENT_OF_INERTIA   AXIAL_FORCE    HEIGHT_OF_SECTION
2)A row of a value for each one variable :      5                556                       130                       300

the traditional approach in maple to intoduce these values to the program would be:

AXIAL_FORCE:=130                etc etc

and then when for example we write



..but for problems like this the variables may be 50 in number, even more.. and it would be very timeconsuming to define all these parameters one by one..
so what I have been looking for so much these days is a predefined maple procedure - if there is one.. - that takes a matrix which we have created in advance and that includes all the names of the variables that we want to have in the problem - let's name it VARIABLES - takes as well a matrix that we also have created in advance and includes the value that we want each of our variables to get in the problem - let's name it VALUES - and make the correspondense automatically, so as to when we introduce an epression in maple thereafter, like     MOMENT_OF_INERTIA/LENGTH, when we press enter to get  556/5=111.2  (and not just a reproducing of what we already wrote , MOMENT_OF_INERTIA/LENGTH ..).. Do you think that there is an easy way to do so??

many thanks in advance!



Last week I made a question, which was kindly answered with the conclusion there might be no solutions.
Now as this cannot be (I'll explain later), I have eliminated all extra aspects of the program to just show the code where the problem is occuring. You can find it via this link

The problem is as follows:
I have 3 points, of which I need to determine the distances from the 0,0 point. The distance between the points are known and the angle between the neutral axis and the line through a point are also known. The set-up is shown in the rough sketch. (k1,k2,k3,corner 1, corner 2, corner 3 are known; a,b,c are unknown.). With these values known, I can easily calculate a,b,c via the cosine rule.

However I want to make a sensitivity analysis for a parameter that determines the 3 corners (called f in the code). Herefore I need to become an answer of a,b,c in function of f and only f (as I need them in following calculations which are not shown in the code). However this doesnt seem to work. The program does not return a solution.

Do you guys know how I can make sure that this program is runnable, so I can get my a,b,c values in function of f? I'd be very very very thankful as I'm stuck with this crucial part of my calculation for weeks.

With kind regards


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