MaplePrimes Questions

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How would I turn this set into matrix form?

would it be possible to seperate the matrix form into:

v1e^(lamba*t) + v2e^(lambda2*t) .... + v^ne^(lambdan*t) where v1, v2, and vn are the eigenvectors and lamba1, lambda2, and lamban are their respective eigenvectors.

I have problem on RKF45 with result on 

"unable to convert to an explicit first order system"


 

``

restart

with(plots):

vf := .3:

kf := .2:

c := .2:

`Τt` := .3:

N := .1:

`φd` := .2:

`ρs` := 8933:

`ρf` := 997.1:

y := .1:

alpha := .5:

Pr := 6.2:

beta := .5:

`βT` := .2:

`ε` := .1:

ks := 400:

kf := .613:

cps := 385:

cpf := 4179:

delta := .5:

Ec := .2:

`Τv` := 1:

A := .5:

B := .5:

omega := 1.5:

K := (ks+2*kf-2*phi*(kf-ks))/(ks+2*kf+phi*(kf-ks))

(401.226+798.774*phi)/(401.226-399.387*phi)

(1)

Eq1 := (1-`φd`)*(diff(f(eta), eta, eta, eta))/(1-phi)^2.5-(1-`φd`)*(1-phi+phi*`ρs`/`ρf`)*((diff(f(eta), eta))^2-f(eta)*(diff(f(eta), eta, eta)))+alpha*beta*(diff(G(eta), eta)-(diff(f(eta), eta))) = 0

.8*(diff(diff(diff(f(eta), eta), eta), eta))/(1-phi)^2.5-.8*(1+7.958981045*phi)*((diff(f(eta), eta))^2-f(eta)*(diff(diff(f(eta), eta), eta)))+.25*(diff(G(eta), eta))-.25*(diff(f(eta), eta)) = 0

(2)

Eq2 := (diff(G(eta), eta))^2-G(eta)*(diff(G(eta), eta, eta))-beta*(diff(f(eta), eta)-(diff(G(eta), eta))) = 0

(diff(G(eta), eta))^2-G(eta)*(diff(diff(G(eta), eta), eta))-.5*(diff(f(eta), eta))+.5*(diff(G(eta), eta)) = 0

(3)

Eq3 := G(eta)*(diff(G(eta), eta))+beta*(f(eta)-G(eta)) = 0

G(eta)*(diff(G(eta), eta))+.5*f(eta)-.5*G(eta) = 0

(4)

Eq4 := K*(diff(theta(eta), eta, eta))/Pr+(1-phi+phi*`ρs`*cps/(`ρf`*cpf))*(f(eta)*(diff(theta(eta), eta))-2*(diff(f(eta), eta))*theta(eta))+alpha*`βT`*(H(eta)-theta(eta))+Ec*alpha*(diff(G(eta), eta)-(diff(f(eta), eta)))^2/`Τv`+(A*(diff(f(eta), eta))+B*theta(eta))/Pr = 0

.1612903226*(401.226+798.774*phi)*(diff(diff(theta(eta), eta), eta))/(401.226-399.387*phi)+(1-.1746332371*phi)*(f(eta)*(diff(theta(eta), eta))-2*(diff(f(eta), eta))*theta(eta))+.10*H(eta)-0.1935483870e-1*theta(eta)+.10*(diff(G(eta), eta)-(diff(f(eta), eta)))^2+0.8064516130e-1*(diff(f(eta), eta)) = 0

(5)

Eq5 := 2*(diff(G(eta), eta))*H(eta)-G(eta)*(diff(H(eta), eta))+y*`βT`*(H(eta)-theta(eta)) = 0

2*(diff(G(eta), eta))*H(eta)-G(eta)*(diff(H(eta), eta))+0.2e-1*H(eta)-0.2e-1*theta(eta) = 0

(6)

bcs1 := (D(f))(0) = `ε`+delta*((D@@2)(f))(0), f(0) = 0, (D(f))(10) = 0;

(D(f))(0) = .1+.5*((D@@2)(f))(0), f(0) = 0, (D(f))(10) = 0

(7)

bcs2 := (D(G))(10) = 0, G(10) = f(10);

(D(G))(10) = 0, G(10) = f(10)

(8)

bcs3 := theta(0) = 1+omega*(D(theta))(0), theta(10) = 0;

theta(0) = 1+1.5*(D(theta))(0), theta(10) = 0

(9)

bcs4 := H(10) = 0;

H(10) = 0

(10)

L := [0., 0.5e-1, .1, .15, .2]:

for k to 5 do R := dsolve(eval({Eq1, Eq2, Eq3, Eq4, Eq5, bcs1, bcs2, bcs3, bcs4}, phi = L[k]), [f(eta), G(eta), theta(eta), H(eta)], numeric, output = listprocedure); Y || k := rhs(R[3]) end do

Error, (in dsolve/numeric/bvp/convertsys) unable to convert to an explicit first-order system

 

plot([Y || (1 .. 5)], 0 .. 10)

Error, (in plot) procedure expected, as range contains no plotting variable

 

``

``

``


 

Download RKF45_A.mw

 

thank you in advance for your help and kindness.

I am using a maple workbook to develop, test, and install a package I am developing.  Several days ago, I noticed that the workbook was not updating the package to reflect the most recent versions of my source code (.mpl). I initially assumed the problem caused by some unintentional change I made to the file, but in the end I found there is a general problem with the URIs in the maple workbook. Everything worked in 2019.1 and I hadn't made any changes after I updated to 2019.2.1.

To confirm the problem, I created a new directory(in fully updated Windows 10 ) and copied my source file into the directory. Then I created a worksheet in maple and saved it into the directory as xx.mw. Using the Navigator panel I then saved the worksheet as a workbook creating xx.maple in the directory.  I then tried to attach the mpl file to the workbook.  In the Navigator menu, the item "attach a file" is unavailable( greyed out).  This is also the case in any of the other earlier workbooks I have created.  I have confirmed the problem is not affecting worksheets because I was able to read my mpl file into a worksheet and load the module using a with(modulename) command.

Please advise.


 

eqs := [II-(phi+mu)*DD+tau*D__g, phi*DD+lambda__2*D__a+lambda__3*D__H-(lambda__4+lambda__1*D__a/(S+D__g)+mu)*D__g, lambda__1*D__g*D__a/(S+D__g)-(lambda__2+beta+mu)*D__a, beta*D__a-(lambda__3+mu+gamma__t)*D__H+lambda__4*D__g, gamma__t*D__H-(delta+mu)*D__c];

[II-(phi+mu)*DD+tau*D__g, phi*DD+lambda__2*D__a+lambda__3*D__H-(lambda__4+lambda__1*D__a/(S+D__g)+mu)*D__g, lambda__1*D__g*D__a/(S+D__g)-(lambda__2+beta+mu)*D__a, beta*D__a-(lambda__3+mu+gamma__t)*D__H+lambda__4*D__g, gamma__t*D__H-(delta+mu)*D__c]

(1)

Sol := {DD = (II+B*tau)/(phi+mu), D__H = E/P, D__a = ((lambda__3+mu+gamma__t)*E/P-lambda__4*B)/beta, D__c = gamma__t*E/((delta+mu)*P), D__g = B};

{DD = (II+B*tau)/(phi+mu), D__H = E/P, D__a = ((lambda__3+mu+gamma__t)*E/P-lambda__4*B)/beta, D__c = gamma__t*E/((delta+mu)*P), D__g = B}

(2)

Inter := [B = S*(lambda[2]+beta+mu)/(lambda[1]-lambda[2]-beta-mu), C = 1/(S+B), E = lambda[2]*lambda[4]*B/beta+B*lambda[4]+mu*B-(lambda[4]*B/beta*B)*C-(phi*II+B*tau*phi)*P/(phi+mu) and lambda[2]*lambda[4]*B/beta+B*lambda[4]+mu*B-(lambda[4]*B/beta*B)*C-(phi*II+B*tau*phi)*P/(phi+mu) = lambda[2]*(lambda[3]+mu+gamma[t])/beta+lambda[3]-lambda[1]*(lambda[3]+mu+gamma[t])*C*B/beta];

[B = S*(lambda[2]+beta+mu)/(lambda[1]-lambda[2]-beta-mu), C = 1/(S+B), false]

(3)

simplify(eval(eqs, eval[recurse](Sol, Inter)))

Error, invalid input: eval expects its 2nd argument, eqns, to be of type {integer, equation, set(equation)}, but received Inter

 

``


 

Download tes.mwtes.mw

Dear experts

I have a complex equation (eq=0) which is a function of K, Q, p and s. K and Q can be complex variables and pa and s are parameters.

equation is

eq:= (K*( Q*sinh(K)*cosh(Q)-K*cosh(K)*sinh(Q))*(1+s*K^2)
   +p*(-4*K^2*Q*(K^2+Q^2)
       +Q*(Q^4+2*K^2*Q^2+5*K^4)*cosh(K)*cosh(Q)
       -K*(Q^4+6*K^2*Q^2+K^4)*sinh(K)*sinh(Q)))/(K^2*Q*cosh(Q)) =0 :

and we know that Q:= sqrt(K^2-I*omega); where omega is complex variable

i) How can I study and plot K vs p if Q is 1) real and 2) pure imaginary. 3) complex variable and vice versa

ii) How can I study and plot p vs s

 

How to display  3 figures (matrixplot(A),matrixplot(B),matrixplot(C)) in a row  

plots:-matrixplot(A):

plots:-matrixplot(B):

plots:-matrixplot(C):

thanks in advance

Can anyone help me with the question? Keep getting the error. I don't know what is going on. Thank you in advance.

QUESTION_6.docx
 

Loading Student:-Calculus1

``

f := proc (x) options operator, arrow; (x-1)^2 end proc

proc (x) options operator, arrow; (x-1)^2 end proc

(1)

g := proc (x) options operator, arrow; x+1 end proc

proc (x) options operator, arrow; x+1 end proc

(2)

Pi*(int((f(x)-4)^2-(g(x)-4)^2, x = 0 .. 3))

(108/5)*Pi

(3)

``Error, (in plot) incorrect first argument HFloat(2.0)-HFloat(7.504824013780844e-232)*I

``


 

Download Question_6_maple.mw

 

matrixplot(A, style=surface,axes=normal, lightmodel=light2, labels=["n","d","C"], heights=histogram, gap=0.00000000000000000001, colorscheme=["xyzcoloring", (x,y,z)->x*y*z]);

 

For a matrix about 500x70. It doesn't seem that it should crap out with such a small matrix to plot. Maple seems to be slow in general even small plotting of 3D things. Specifically I'm talking about rendring and rotating.

Hi everybody:

I have an equation that attached with this question and my goal is to solve it, how can do it?

Note: in this equation must be considered 49.32883964 <= x and x is real.

solve_equation.mw

 

 

Hello all

 

I need to calculate the distance L in a curvefitting. The calculation has been made in MathCAD and I need to copy it in Maple, but I cant seem to make it solve.

Here are the two pictures of my problem:

 

In MathCAD:

In Maple:

 

Here is the copy of Maple:

V[Ed13] := [257.184, 230.4, 184.3, 138.2, 92.2, 46.1, 0];
 = 
    V[Ed13] := [257.184, 230.4, 184.3, 138.2, 92.2, 46.1, 0]


x[12];
 = 
            [-149, 208, 567, 925, 1283, 1642, 2000]

L[1] := x[13];
 = 
         L[1] := [0, 358, 717, 1075, 1433, 1792, 2150]


solve(V[Rdc] = CurveFitting:-ArrayInterpolation(x[12], V[Ed13], L[1]), L[1]);
 = 
Error, invalid input: solve expects its 1st argument, eqs, to be of type {`and`, `not`, `or`, algebraic, relation(algebraic), ({list, set})({`and`, `not`, `or`, algebraic, relation(algebraic)})}, but received 153.25 = [HFloat(246.00524369747902), HFloat(211.1381615598886), HFloat(164.98435754189944), HFloat(118.92625698324022), HFloat(72.93816155988858), HFloat(26.784357541899443), HFloat(-19.315642458100548)]

Find 
L[1];


Answer should be 808
 

 

Hope someone can help as I honestly have no idea how to do this :-)

Hi, 

Moving the sliders clean the plot.
Does any one can show me how to fix this (PS: this piece of code is a part of a procedure whose arguments are RV and SliderRanges and I need this unusual coding to make the procedure generic ... at least I guess so)

Thanks in advance


 

restart:

interface(version);

`Standard Worksheet Interface, Maple 2015.2, Mac OS X, December 21 2015 Build ID 1097895`

(1)

with(Statistics):

RV   := RandomVariable(Normal(a, b)):
law  := [attributes(RV)][3]:
pars := law:-Parameters;

[a, b]

(2)

SliderRanges := [-5.0..5.0, 1.0..3.0]:
[seq(pars[k]=SliderRanges[k], k=1..numelems(pars))]

[a = -5.0 .. 5.0, b = 1.0 .. 3.0]

(3)

f := PDF(RV, x);
# Explore(plot(f, x=-3..3), parameters=[seq(pars[k]=SliderRanges[k], k=1..numelems(pars))]);

(1/2)*2^(1/2)*exp(-(1/2)*(x-a)^2/b^2)/(Pi^(1/2)*b)

(4)

 


 

Download Explore_Problem.mw

I want to calculate the below triple integral numerically. I tried different methods and reduced accuracy but nothing works.

Anyone capable?

Thanks

 

restart;
Digits := 15;
with(VectorCalculus);
v1 := <0, 0, 1>;
v2 := <sin(theta2), 0, cos(theta2)>;
v3 := <VectorCalculus:-`*`(sin(theta3), cos(phi3)), VectorCalculus:-`*`(sin(theta3), sin(phi3)), cos(theta3)>;
v1v2 := CrossProduct(v1, v2);
v2v3 := CrossProduct(v3, v2);
DotProduct(v1v2, v2v3);
(simplify(VectorCalculus:-`*`(%, VectorCalculus:-`*`(Norm(v1v2), Norm(v2v3))^VectorCalculus:-`-`(1))) assuming (0 < theta2, theta2 < Pi, 0 < theta3, theta3 < Pi));
evalf(VectorCalculus:-`*`(Int(VectorCalculus:-`*`(arccos(%), sin(theta3)), [theta2 = 0 .. Pi, theta3 = 0 .. Pi, phi3 = 0 .. VectorCalculus:-`*`(2, Pi)], epsilon = 0.001, method = _d01akc), VectorCalculus:-`*`(VectorCalculus:-`*`(VectorCalculus:-`*`(VectorCalculus:-`*`(VectorCalculus:-`*`(2, Pi), 2), Pi), 4), Pi)^VectorCalculus:-`-`(1)));

Hi,

I am new to Maple. I am attempting to find the asymptotic expression for the confluent Heun function (HeunC) under certain set of parameters (i.e. still symbolic and possibly complex, but less parameters compared to the general case).

From the literature, it seems that for certain cases there are such closed analytic expressions.

Is it possible to find such in Maple? I tried using "asympt", which gave me a generic error (...unable to compute series).

Thank you very much.

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