Maple Questions and Posts

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How I can calculate integral?

Thanks


 

"restart;    f[1,1](r,theta,phi):=r^4 sin(6 theta) sin(3 phi):    L(r, theta,phi):=(2.784615385 10^10 ((∂)^2)/(∂r^2) `f__11`(r,theta,phi)+(2.784615385 10^10 (2+2 r cos(theta)) ((∂)/(∂r) `f__11`(r,theta,phi)))/(r (2+r cos(theta)))-(0.1175000000 (((∂)^4)/(∂theta^4) `f__11`(r,theta,phi)))/(r^4)-(0.1175000000 (((∂)^4)/(∂phi^4) `f__11`(r,theta,phi)))/((2+r cos(theta))^4)-(0.1175000000 (((∂)^4)/(∂phi^2∂r^2) `f__11`(r,theta,phi)))/((2+r cos(theta))^2)-(0.1175000000 (((∂)^4)/(∂r^2∂theta^2) `f__11`(r,theta,phi)))/(r^2)-(0.2350000000 (((∂)^4)/(∂phi^2∂theta^2) `f__11`(r,theta,phi)))/(r^2 (2+r cos(theta))^2)+(0.1175000000 ((cos(theta))^2 r^2+4 (cos(theta))^2 r^4+16 cos(theta) r^3-4+17 r^2) (((∂)^2)/(∂theta^2) `f__11`(r,theta,phi)))/((2+r cos(theta))^2 r^4)+(0.1175000000 (2 (cos(theta))^2 r^2+4 (cos(theta))^2 r^4+16 cos(theta) r^3+4+12 r^2) (((∂)^2)/(∂phi^2) `f__11`(r,theta,phi)))/(r^2 (2+r cos(theta))^4)-(2.784615385 10^10 (2 (cos(theta))^2 r^2+4 r cos(theta)+4) `f__11`(r,theta,phi))/(r^2 (2+r cos(theta))^2)+(0.2350000000 (((∂)^3)/(∂r∂theta^2) `f__11`(r,theta,phi)))/(r^3 (2+r cos(theta)))-(0.2350000000 (((∂)^3)/(∂phi^2∂r) `f__11`(r,theta,phi)))/(r (2+r cos(theta))^3)+(0.2350000000 sin(theta) (((∂)^3)/(∂theta^3) `f__11`(r,theta,phi)))/(r^3 (2+r cos(theta)))-(0.2350000000 sin(theta) (((∂)^3)/(∂phi^2∂theta) `f__11`(r,theta,phi)))/(r (2+r cos(theta))^3)+(0.1175000000 sin(theta) (((∂)^3)/(∂r^2∂theta) `f__11`(r,theta,phi)))/(r (2+r cos(theta)))-(0.1175000000 (2 r cos(theta)+3) sin(theta) (2 r cos(theta)+5) ((∂)/(∂theta) `f__11`(r,theta,phi)))/(r (2+r cos(theta))^3)) r^4 sin(6 theta) sin(3 phi):"

with(Student[Calculus1]); K[rr, s] := evalf(ApproximateInt(L(r, theta, phi), r = .2 .. 1, method = simpson)); KK[rr, s] := evalf(ApproximateInt(K[rr, s], theta = 0 .. 2*Pi, method = simpson)); k2 := evalf(ApproximateInt(KK[rr, s], phi = 0 .. 2*Pi, method = simpson))

``


 

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Hello,

Real beginner, never used Maplw before. I want to analyse PDE's through Lie symmetry analysis -- get the infiniteeimals and then generate the invariants. I am going through the standard examples on the help within Maple, but I am stuck on a basic issue which prompts me to think that there may be something different in my version of Maple (although I downloaded it from TTU which I presume should be the latest version).

Here's what I get >>>>>

Loading PDEtools

with(PDEtools, InfinitesimalGenerator, declare);
               [InfinitesimalGenerator, declare]

declare(u(x, t));
               u(x, t) will now be displayed as u
U: diff_table(u(x, t)):
PDE := U_x,x - U_t = 0;
                    PDE := U_x,x - U_t = 0
show;
                       U_x,x - U_t = 0
Infinitesimals(PDE)
Error, (in PDEtools:-Infinitesimals) missing dependent variables

>>>>>

 

I have also tried:

Infinitesimals(PDE, u)
Error, (in PDEtools:-Infinitesimals) not a PDE system w.r.t u

and:

Infinitesimals(PDE, U)
Error, (in PDEtools:-Infinitesimals) not a PDE system w.r.t U
 

There are many other issues, but let's deal with this one first.

 

Thanks

Best wishes

Nadeem

 

 

 

Hello all, 

Would you teach me how to cancel a denominator term by multiplying the same term?

For example, I got this expression:

-L2*diff(i2(t), t) + L1*diff(i1(t), t)/n12

Then, I want to come to this expression by multiplying the expression with 'n12'

-L2*n12*diff(i2(t), t) + L1*diff(i1(t), t), 

But the result from my simple attempt was this:

(-L2*diff(i2(t), t) + L1*diff(i1(t), t)/n12)*n12

Thank you in advance!

 

Hey there, I have a pretty general question.

I'm trying to fill out the entries of a matrix. Each matrix element is the result of a very complicated calculation. Currently, I am using nested do loops (two loops total) to scan through each row and column respectively. I find that this process racks up a ton of memory, and that I in fact run out of memory before the matrix has been completely specified.

First, why is this happening? And second, what is a smarter way to perform the calculation?

 

Cheers.

Hi,

Due to an unexpected maintenance operation, I had to uninstall Maple 18 from my Windows 7-64 bit PC.

Later on I installed it without any problems but, to my surprise now I can't configure it properly. This is:

* Enabling Maple Text as Input (classical input method)
* Removing numbers from equations
* Setting Maple language to English (it took Spanish by default because of Windows)
* Hiding left panel

As usual, this is performed under Tools/Options/Interface and so on...

After I modify my preferred settings, apply globally and close-open again, the program is again in its original form.

How can I do in this case? I have installed it several times. It is also worth noting that the maintenance that I performed was related to deep Windows registry modifications. 

Thanks and regards.

 

X := [0, -3]; Y := [3, 1]; Z := [5, -2]; PP := proc (M::list, N::list, K::list) local A, B, P, distPH, H, lambda, mdist; A := M; B := N; P := K; H := simplify(expand((1-lambda)*A+lambda*B)); distPH := sqrt((H[1]-P[1])^2+(H[2]-P[2])^2); mdist := diff(distPH, lambda); lambda := solve(mdist, lambda); simplify(distPH); H end proc; debug(PP); PP(X, Y, Z);#the calculation isn't finished

Would you teach me how to collect and isolate specific terms in an equation?

For example, this is a given equation:

v1(t) - R1*(-i3(t)/n13 - i2(t)/n12) - L1*diff(-i3(t)/n13 - i2(t)/n12, t) = n12*(v2(t) - R2*i2(t) - L2*diff(i2(t), t))

From this equation, I wonder if there is a way to collect and isolate the derivative terms at the RHS, like this:

(- L1/n12+(n12 * L2))*diff(i2(t), t) + (L1/n13)*diff(i3(t), t) = -v1(t) + R1*(-i3(t)/n13 - i2(t)/n12) + n12*v2(t) - n12*R2*i2(t)

Thank you in advance!

 

Hi 

Is there a way to solve it numericall

evalf(int(exp((5+I*6)*x)*sin(1+erf(x)),x=-to..to));

evalf(int(exp((5+I*6)*x)*cos(1+erf(x)),x=-to..to));

 

Would you tell me how to achieve this?

> eqn1 := e1*i1 + e2*i2 + e3*i3 = 0
Then, 

solve( { eqn1 } , { i1 } , explicit ) ;
                     /       e2 i2 + e3 i3\ 
                    { i1 = - ------------- }
                     \            e1      / 
Then, I want to replace 'e2/e1' with this expression:

> eqn2 := n12 = e1/e2;

In other words, I want to express the following:

                       /       e2 i2 + e3 i3\ 
                    { i1 = - ------------- }
                     \            e1      / 

as this:

                      /          -i2     - e3 i3\ 
                    { i1 =  ------   + ------ }
                     \            n12        e1   / 

 

Thank you in advance!

 

Does maple has surrogate optimization built in function or some codes. Thank you

Hello,

How I can separate three functions (u__ru__theta and u__phi) in the equation attached below.

Please also see attached figure. I want to calculate L11L22L33.

Thanks.

SEPARATE
 

restart

B := simplify((r*(R+r*cos(theta))^2*(mu+lambda)*(diff(`u__θ`(r, theta, phi), r, theta))+2*r^2*(R+r*cos(theta))^2*(mu+(1/2)*lambda)*(diff(u__r(r, theta, phi), r, r))+r^2*(mu+lambda)*(R+r*cos(theta))*(diff(`u__φ`(r, theta, phi), phi, r))+mu*(R+r*cos(theta))^2*(diff(u__r(r, theta, phi), theta, theta))+(diff(u__r(r, theta, phi), phi, phi))*mu*r^2-3*(R+r*cos(theta))^2*(mu+(1/3)*lambda)*(diff(`u__θ`(r, theta, phi), theta))+(2*(R+2*r*cos(theta)))*r*(R+r*cos(theta))*(mu+(1/2)*lambda)*(diff(u__r(r, theta, phi), r))-r^2*sin(theta)*(mu+lambda)*(R+r*cos(theta))*(diff(`u__θ`(r, theta, phi), r))-3*r^2*(mu+(1/3)*lambda)*cos(theta)*(diff(`u__φ`(r, theta, phi), phi))-r*mu*sin(theta)*(R+r*cos(theta))*(diff(u__r(r, theta, phi), theta))-(2*(2*cos(theta)^2*r^2+2*cos(theta)*R*r+R^2))*(mu+(1/2)*lambda)*u__r(r, theta, phi)+r*`u__θ`(r, theta, phi)*sin(theta)*(3*r*(mu+(1/3)*lambda)*cos(theta)+R*mu))/(r^2*(R+r*cos(theta))^2))

``

``

 


 

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Dear all,

How can I decide that the product a*n appears on the list [1-a*n*xy, x+y]? I used from the following function but the result is false.

I am looking forward to hearing from you.

Sincerely yours

i have a problem with a nonlinear equation containing Heaviside step function. fsolve does not return anything and SolveEquation command also returns incorrect answer. How can i solve this equation? any method or help is appreciated.


 

 

restart:

with(DirectSearch):

F:=x*(Heaviside(x-(S0))/(1-DD)+Heaviside(-x+S0)/(1-HH*DD));

x*(Heaviside(x-S0)/(1-DD)+Heaviside(-x+S0)/(-DD*HH+1))

(1)

EQ:=F-E*Y;

-E*Y+x*(Heaviside(x-S0)/(1-DD)+Heaviside(-x+S0)/(-DD*HH+1))

(2)

HH:=0.2;
DD:=0.579350262599427;
S0:=1e8;
E:=70e9;
Y:=0.001668993263529;

.2

 

.579350262599427

 

0.1e9

 

0.70e11

 

0.1668993263529e-2

(3)

EQ

-116829528.5+x*(2.377274752*Heaviside(x-0.1e9)+1.131055455*Heaviside(-x+0.1e9))

(4)

fsolve(EQ)

fsolve(-116829528.5+x*(2.377274752*Heaviside(x-0.1e9)+1.131055455*Heaviside(-x+0.1e9)), x)

(5)

SolveEquations(EQ)

Warning, complex or non-numeric value encountered; trying to find a feasible point

 

[1.3868049384289111*10^13, Vector(1, {(1) = -3723983.000}), [x = 9.999999999999999*10^7], 231]

(6)

eval(EQ,x = 1.00000000000000*10^8)

Float(undefined)

(7)

 


 

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Hello, I bring here a problem with maple that in result the  "".

I can remove '' in final results?

Thanks


 


  ;
  ):


  X= (R+r*costheta)*sinphi):
  = (R+r*costheta)*cosphi):
  Z= (r*sintheta)):

  
  r, theta, phi,
    X, Y, Z
  ):

 


   
  
    (1/2*Curl
      
        < u__rrtheta, phi),
            u__thetartheta, phi),
            u__phirtheta, phi)
          >,
          rtheta, phi
        )
      )
    )
  );

Vector(3, {(1) = (1/2)*csgn(r)*csgn(R+r*cos(theta))*(csgn(1, R+r*cos(theta))*(R+r*cos(theta))*`#msub(mi("u"),mi("&phi;",fontstyle = "normal"))`(r, theta, phi)+((R+r*cos(theta))*(diff(`#msub(mi("u"),mi("&phi;",fontstyle = "normal"))`(r, theta, phi), theta))-r*sin(theta)*`#msub(mi("u"),mi("&phi;",fontstyle = "normal"))`(r, theta, phi))*csgn(R+r*cos(theta))-csgn(r)*r*(diff(`#msub(mi("u"),mi("&theta;",fontstyle = "normal"))`(r, theta, phi), phi)))/(r*(R+r*cos(theta))), (2) = -(csgn(1, R+r*cos(theta))*(R+r*cos(theta))*`#msub(mi("u"),mi("&phi;",fontstyle = "normal"))`(r, theta, phi)+((R+r*cos(theta))*(diff(`#msub(mi("u"),mi("&phi;",fontstyle = "normal"))`(r, theta, phi), r))+cos(theta)*`#msub(mi("u"),mi("&phi;",fontstyle = "normal"))`(r, theta, phi))*csgn(R+r*cos(theta))-(diff(`#msub(mi("u"),mi("r"))`(r, theta, phi), phi)))*csgn(R+r*cos(theta))/(2*r*cos(theta)+2*R), (3) = (1/2)*(-(diff(`#msub(mi("u"),mi("r"))`(r, theta, phi), theta))+csgn(r)*r*(diff(`#msub(mi("u"),mi("&theta;",fontstyle = "normal"))`(r, theta, phi), r))+`#msub(mi("u"),mi("&theta;",fontstyle = "normal"))`(r, theta, phi)*(r*csgn(1, r)+csgn(r)))*csgn(r)/r})

(1)

``


 

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