MaplePrimes Questions

I am attempting to find the surface area of a Torus. I can create a graph very easily, but am struggling with the SurfaceArea command. The code reads so far:

(Inputting the given function for the torus):

> r := (phi,theta) -> <(cos(phi)+3)*cos(theta),(cos(phi)+3)*sin(theta),sin(phi)>:

'r(phi,theta)' = r(phi,theta); 

(Generating a graph of the torus):

>plot3d(r(phi,theta),phi=0..2*Pi,theta=0..2*Pi,scaling=constrained);

(SurfaceArea command):

>SurfaceArea(r(phi,theta),phi=0..2*pi,theta=0..2*pi);

 

I am very new to the program so the solution may be obvious. Any suggestions on how to go about it?

Hello, I am attempting to plot a vector field in Maple. I have the following code so far:

 

SetCoordinates('cartesian'[x,y,z]):

F := VectorField(<y*z*e^(x*y*z)+3*x^(2),x*z*e^(x*y*z)+2*y*z+cos(y),x*y*e^(x*y*z)+y^(2)+1>);

 

I am struggling with the fieldplot3d commands, as I am supposed to plot it in the box -1<=x,y,z<=1. How do I go about inserting these bounds?

 

I am not very familiar with maple.

Kindly help me fix the error.

I want to solve the three equations- eq1, eq2 and eq3 simultaneously by equating to zero, i.e., 

eq1= eq2= eq3= 0, to find the values of the 3 variables t[1], t[2], xi

 

Please help me out with this. It is urgent. 
FINAL2.mw


 

A := 2500;

2500

(1)

alpha := 4

4

(2)

beta := 0.2e-1

0.2e-1

(3)

c := 5

5

(4)

x[w] := 10

10

(5)

x[1] := 8

8

(6)

delta := 5

5

(7)

t[d] := .5

.5

(8)

a := 20

20

(9)

b := 25

25

(10)

theta := .5

.5

(11)

m := theta*(1-exp(-.5*xi))

.5-.5*exp(-.5*xi)

(12)

TC(t[1], t[2], xi) := (A+alpha*((1/2)*a*t[d]^2+(1/3)*a*t[d]^3)+beta*((1/6)*a*t[d]^3+(1/8)*a*t[d]^4)+t[d]*(a/(theta-m)+b*(t[d]-1/(theta-m))/(theta-m)-exp((theta-m)*(t[1]-t[d]))*(a/(theta-m)+b*(t[1]-1/(theta-m))/(theta-m)))-a*(-6*beta*b-(6*(theta-m))*(-a*beta+alpha*b)+6*(theta-m)^2*(a*beta*t[1]+alpha*b*t[d])+3*b*beta*(theta-m)^2*(-t[1]^2+t[d]^2)+6*a*alpha*(theta-m)^2+2*b*beta*(theta-m)^3*(t[1]^3-t[d]^3)+3*a*beta*(theta-m)^3*(t[1]^2-t[d]^2)+3*b*alpha*(theta-m)^3*(t[1]^2-t[d]^2)+6*a*alpha*(theta-m)^3*(t[1]-t[d])+6*exp((theta-m)*(t[1]-t[d]))*((6*(theta-m))*(-a*beta+alpha*b)-6*b*beta*(theta-m)*(t[1]-t[d])-6*((theta-m)^2*(-b*beta*t[1]*t[d]+a*beta*t[d]+alpha*b*t[1]+a*alpha)+beta*b)))/(6*(theta-m)^4)+x[1]*(2*a*t[2]*delta^2+2*b*t[1]*t[2].(delta^2)+b*t[2]*delta-2*a*delta*ln(delta*t[2]+1)-2*b*ln(delta*t[2]+1)-2*b*t[1]*delta*ln(delta*t[2]+1)-2*b*t[2]*delta*ln(delta*t[2]+1)+2*b*t[2]*delta)/(2*delta^2)+x[w]*(2*a*t[2]*delta^2+b*t[2]^2*delta^2+2*b*t[1]*t[2].(delta^2)+2*a*delta*t[2]+2*b*t[2]*delta*ln(1/(delta*t[2]+1))+2*b*ln(1/(delta*t[2]+1))+2*a*delta*ln(1/(delta*t[2]+1))+2*b*t[1]*delta*ln(1/(delta*t[2]+1)))/(2*delta^3)+c*(a*t[d]+(1/2)*b*t[d]^3+a/(theta-m)+b*(t[d]-1/(theta-m))/(theta-m)-exp((theta-m)*(t[1]-t[d]))*(a/(theta-m)+b*(t[1]-1/(theta-m))/(theta-m))-a*ln(1/(delta*t[2]+1))/delta-b*(1+delta*(t[1]+t[2]))*ln(delta*t[2]+1)/delta^2-b*t[2]/delta))/(t[1]+t[2])

(2571.157291+220.0000000/exp(-.5*xi)+275.0000000*(.5-2.000000000/exp(-.5*xi))/exp(-.5*xi)-5.5*exp(.5*exp(-.5*xi)*(t[1]-.5))*(40.00000000/exp(-.5*xi)+50.00000000*(t[1]-2.000000000/exp(-.5*xi))/exp(-.5*xi))-53.33333334*(-3.00-298.800*exp(-.5*xi)+1.50*(exp(-.5*xi))^2*(.40*t[1]+50.0)+.3750*(exp(-.5*xi))^2*(-t[1]^2+.25)+120.00*(exp(-.5*xi))^2+.12500*(exp(-.5*xi))^3*(t[1]^3-.125)+37.65000*(exp(-.5*xi))^3*(t[1]^2-.25)+60.000*(exp(-.5*xi))^3*(t[1]-.5)+6*exp(.5*exp(-.5*xi)*(t[1]-.5))*(298.800*exp(-.5*xi)-1.500*exp(-.5*xi)*(t[1]-.5)-1.50*(exp(-.5*xi))^2*(99.750*t[1]+80.200)-3.00))/(exp(-.5*xi))^4+243*t[2]+250*t[1]*t[2]-40*ln(5*t[2]+1)-40*t[1]*ln(5*t[2]+1)-40*t[2]*ln(5*t[2]+1)+25*t[2]^2+10*t[2]*ln(1/(5*t[2]+1))-10*ln(1/(5*t[2]+1))+10*t[1]*ln(1/(5*t[2]+1))-5*(1+5*t[1]+5*t[2])*ln(5*t[2]+1))/(t[1]+t[2])

(13)

``

``

eq1 := diff(TC(t[1], t[2], xi), t[1]) = 0

-(2571.157291+220.0000000/exp(-.5*xi)+275.0000000*(.5-2.000000000/exp(-.5*xi))/exp(-.5*xi)-5.5*exp(.5*exp(-.5*xi)*(t[1]-.5))*(40.00000000/exp(-.5*xi)+50.00000000*(t[1]-2.000000000/exp(-.5*xi))/exp(-.5*xi))-53.33333334*(-3.00-298.800*exp(-.5*xi)+1.50*(exp(-.5*xi))^2*(.40*t[1]+50.0)+.3750*(exp(-.5*xi))^2*(-t[1]^2+.25)+120.00*(exp(-.5*xi))^2+.12500*(exp(-.5*xi))^3*(t[1]^3-.125)+37.65000*(exp(-.5*xi))^3*(t[1]^2-.25)+60.000*(exp(-.5*xi))^3*(t[1]-.5)+6*exp(.5*exp(-.5*xi)*(t[1]-.5))*(298.800*exp(-.5*xi)-1.500*exp(-.5*xi)*(t[1]-.5)-1.50*(exp(-.5*xi))^2*(99.750*t[1]+80.200)-3.00))/(exp(-.5*xi))^4+243*t[2]+250*t[1]*t[2]-40*ln(5*t[2]+1)-40*t[1]*ln(5*t[2]+1)-40*t[2]*ln(5*t[2]+1)+25*t[2]^2+10*t[2]*ln(1/(5*t[2]+1))-10*ln(1/(5*t[2]+1))+10*t[1]*ln(1/(5*t[2]+1))-5*(1+5*t[1]+5*t[2])*ln(5*t[2]+1))/(t[1]+t[2])^2+(-2.75*exp(-.5*xi)*exp(.5*exp(-.5*xi)*(t[1]-.5))*(40.00000000/exp(-.5*xi)+50.00000000*(t[1]-2.000000000/exp(-.5*xi))/exp(-.5*xi))-275.0000000*exp(.5*exp(-.5*xi)*(t[1]-.5))/exp(-.5*xi)-53.33333334*(.6000*(exp(-.5*xi))^2-.7500*(exp(-.5*xi))^2*t[1]+.37500*(exp(-.5*xi))^3*t[1]^2+75.30000*(exp(-.5*xi))^3*t[1]+60.000*(exp(-.5*xi))^3+3.0*exp(-.5*xi)*exp(.5*exp(-.5*xi)*(t[1]-.5))*(298.800*exp(-.5*xi)-1.500*exp(-.5*xi)*(t[1]-.5)-1.50*(exp(-.5*xi))^2*(99.750*t[1]+80.200)-3.00)+6*exp(.5*exp(-.5*xi)*(t[1]-.5))*(-1.500*exp(-.5*xi)-149.62500*(exp(-.5*xi))^2))/(exp(-.5*xi))^4+250*t[2]-65*ln(5*t[2]+1)+10*ln(1/(5*t[2]+1)))/(t[1]+t[2]) = 0

(14)

eq2 := diff(TC(t[1], t[2], xi), t[2]) = 0

-(2571.157291+220.0000000/exp(-.5*xi)+275.0000000*(.5-2.000000000/exp(-.5*xi))/exp(-.5*xi)-5.5*exp(.5*exp(-.5*xi)*(t[1]-.5))*(40.00000000/exp(-.5*xi)+50.00000000*(t[1]-2.000000000/exp(-.5*xi))/exp(-.5*xi))-53.33333334*(-3.00-298.800*exp(-.5*xi)+1.50*(exp(-.5*xi))^2*(.40*t[1]+50.0)+.3750*(exp(-.5*xi))^2*(-t[1]^2+.25)+120.00*(exp(-.5*xi))^2+.12500*(exp(-.5*xi))^3*(t[1]^3-.125)+37.65000*(exp(-.5*xi))^3*(t[1]^2-.25)+60.000*(exp(-.5*xi))^3*(t[1]-.5)+6*exp(.5*exp(-.5*xi)*(t[1]-.5))*(298.800*exp(-.5*xi)-1.500*exp(-.5*xi)*(t[1]-.5)-1.50*(exp(-.5*xi))^2*(99.750*t[1]+80.200)-3.00))/(exp(-.5*xi))^4+243*t[2]+250*t[1]*t[2]-40*ln(5*t[2]+1)-40*t[1]*ln(5*t[2]+1)-40*t[2]*ln(5*t[2]+1)+25*t[2]^2+10*t[2]*ln(1/(5*t[2]+1))-10*ln(1/(5*t[2]+1))+10*t[1]*ln(1/(5*t[2]+1))-5*(1+5*t[1]+5*t[2])*ln(5*t[2]+1))/(t[1]+t[2])^2+(243+250*t[1]-150/(5*t[2]+1)-250*t[1]/(5*t[2]+1)-65*ln(5*t[2]+1)-250*t[2]/(5*t[2]+1)+50*t[2]+10*ln(1/(5*t[2]+1))-25*(1+5*t[1]+5*t[2])/(5*t[2]+1))/(t[1]+t[2]) = 0

(15)

eq3 := diff(TC(t[1], t[2], xi), xi) = 0

(110.0000000/exp(-.5*xi)+137.5000000*(.5-2.000000000/exp(-.5*xi))/exp(-.5*xi)-275.0000000/(exp(-.5*xi))^2+1.375*exp(-.5*xi)*(t[1]-.5)*exp(.5*exp(-.5*xi)*(t[1]-.5))*(40.00000000/exp(-.5*xi)+50.00000000*(t[1]-2.000000000/exp(-.5*xi))/exp(-.5*xi))-5.5*exp(.5*exp(-.5*xi)*(t[1]-.5))*(20.00000000/exp(-.5*xi)+25.00000000*(t[1]-2.000000000/exp(-.5*xi))/exp(-.5*xi)-50.00000000/(exp(-.5*xi))^2)-106.6666667*(-3.00-298.800*exp(-.5*xi)+1.50*(exp(-.5*xi))^2*(.40*t[1]+50.0)+.3750*(exp(-.5*xi))^2*(-t[1]^2+.25)+120.00*(exp(-.5*xi))^2+.12500*(exp(-.5*xi))^3*(t[1]^3-.125)+37.65000*(exp(-.5*xi))^3*(t[1]^2-.25)+60.000*(exp(-.5*xi))^3*(t[1]-.5)+6*exp(.5*exp(-.5*xi)*(t[1]-.5))*(298.800*exp(-.5*xi)-1.500*exp(-.5*xi)*(t[1]-.5)-1.50*(exp(-.5*xi))^2*(99.750*t[1]+80.200)-3.00))/(exp(-.5*xi))^4-53.33333334*(149.4000*exp(-.5*xi)-1.500*(exp(-.5*xi))^2*(.40*t[1]+50.0)-.37500*(exp(-.5*xi))^2*(-t[1]^2+.25)-120.000*(exp(-.5*xi))^2-.187500*(exp(-.5*xi))^3*(t[1]^3-.125)-56.475000*(exp(-.5*xi))^3*(t[1]^2-.25)-90.0000*(exp(-.5*xi))^3*(t[1]-.5)-1.50*exp(-.5*xi)*(t[1]-.5)*exp(.5*exp(-.5*xi)*(t[1]-.5))*(298.800*exp(-.5*xi)-1.500*exp(-.5*xi)*(t[1]-.5)-1.50*(exp(-.5*xi))^2*(99.750*t[1]+80.200)-3.00)+6*exp(.5*exp(-.5*xi)*(t[1]-.5))*(-149.4000*exp(-.5*xi)+.7500*exp(-.5*xi)*(t[1]-.5)+1.500*(exp(-.5*xi))^2*(99.750*t[1]+80.200)))/(exp(-.5*xi))^4)/(t[1]+t[2]) = 0

(16)

``       

solve({eq1, eq2, eq3}, {xi, t[1], t[2]})

Warning, solutions may have been lost

 

 

``

``

``

 

``

``

``

``

 

 

 

``

solve({eq1, eq2, eq3}, {xi, t[1], t[2]});

Warning, solutions may have been lost
 

Download FINAL2.mw


           

Hi guys

I'm trying to solve this equation

eqns := {(1-sin(b_u)*sin(s)/(cos(b_u-y_f)*cos(s-y_f)))*(1/cos(s-y_f)^2-1/sin(s)^2) = -(cot(s)+tan(s-y_f)+Z)*sin(b_u)*(cos(s)/cos(s-y_f)+sin(s)*sin(s-y_f)/cos(s-y_f)^2)/cos(b_u-y_f)}

where

b_u = 1/tan(0.8)
Z = 892/(27417000*f_z)
y_f = 9*Pi/180

I have a bondary condition where s=s_0 and s_0 = (1/4)*Pi-1/2*(b_u-y_f)

And i want to solve this nonlinear equation from f_z=0.00005 to f_z=0.0005 by interval 0.000001 interval

I have tryed using this topic as an example

https://www.mapleprimes.com/questions/200995-Solve-By-Newton-Raphson-Method

But in the final i'm surprised with the error "Error, (in fsolve) initial approximation does not evaluate to float"

Could someone help me please.
Thanks

Hi

I have the following piecewise function in Maple:

sigmaP:=piecewise(u < -1,-1,u >1,1,u);

Now we can plot this function:

plot(sigmaP,u=-5..5,size=[1200,300],gridlines,discont=[showremovable]);

Next, I define a new piecewise  function as

sigmaF:=u->piecewise(u < -1,-1,u >1,1,u);

and I use this function in 

Fun:=proc(x1,x2,u1,u2)
	2*x1*(1+x2)*sigmaF(u1)+(1+x2^2)*sigmaF(u2);
end proc:

Now I need to find a minimum of this function so I use the following code 

GlobalOptimization:-GlobalSolve(Fun,x1,x2,u1,u2);

where 

x1:=-5..5;
x2:=-10..100;
u1:=-1..1;
u2:=-1..1;

And I have the problem with plot function Fun. How to plot function Fun???

Best

 

Hello,

Would you please help me with this integral : 


 

restart

int(exp(i*x*t)/((x-a)*(x+a)), x = -infinity .. infinity)

piecewise(Im(a) = 0, undefined, int(exp(i*x*t)/((x-a)*(x+a)), x = -infinity .. infinity, method = _UNEVAL))

(1)

``


 

Download Integrale.mw

MAPLE CODE [below link]:


Dispersion.mw

range of "kx" variable [0 to 8x106] and range of "f" variable  [80x1012 to 220x1012]

Why different between calculate two form? I use maple 2017

evalf(sech(20)^2); evalf(sech(-20)^2);
                                     
                       1.699341702 *10^ -17  
                                     
                       1.699341702 *10^ -17  
evalf(1-tanh(20)^2); evalf(1-tanh(-20)^2);
                               0.
                               0.

 

i want to calculate the eigenvalues and eigenvectors of two matrices ,i get these results, can anyone explain to me the meaning ?

A:=linalg[matrix](3,3,[-1,2,0,4,-2,3,0,1,-3]);
> B:=linalg[matrix](3,3,[2,0,1,4,-1,1,2,0,-5]);

> eigenvalues(A);

                  8                                    4
1/2 %2 + -------------------- - 2, - 1/4 %2 - --------------------
                      1/2 1/3                              1/2 1/3
         (20 + 4 I 231   )                    (20 + 4 I 231   )

                  1/2 /                  8          \
     - 2 + 1/2 I 3    |1/2 %2 - --------------------|, - 1/4 %2
                      |                      1/2 1/3|
                      \         (20 + 4 I 231   )   /

                4
     - -------------------- - 2
                    1/2 1/3
       (20 + 4 I 231   )

              1/2 /                  8          \
     - 1/2 I 3    |1/2 %2 - --------------------|
                  |                      1/2 1/3|
                  \         (20 + 4 I 231   )   /

               1
%1 := --------------------
                   1/2 1/3
      (20 + 4 I 231   )

                   1/2 1/3
%2 := (20 + 4 I 231   )

eigenvectors(B);
               1/2      [            1/2  65          1/2   ]
[- 3/2 + 1/2 57   , 1, {[7/4 + 1/4 57   , -- + 9/28 57   , 1]}],
                        [                 28                ]

                   1/2      [            1/2  65          1/2   ]
    [- 3/2 - 1/2 57   , 1, {[7/4 - 1/4 57   , -- - 9/28 57   , 1]}],
                            [                 28                ]

    [-1, 1, {[0, 1, 0]}]

such a list H:=
                     [0, 4, 8, 1, 2, 1, 4, 2, 8]

what is the diffrence between these 2 commands ? has(H,integer), type(H,integer);

how to obtain the sequence of sin(((Kπ)/4)), where the integer K  is varying from 1 to 8, and then to delete the zeros.

i'm triying to solve this sytem ,

solve({x^2+y^2=3,x^2+2*y^2=3},{x,y});
{y = 0, x = RootOf(_Z^2-3)}
what is the meaning of RootOf

maple gives me this, can anyone explain to me,the signification of the solutions ?

Dear Users!

Hope you would be fine with everying. I want to solve the following 2nd order linear differential equation. 

(1+B)*(diff(theta(eta), eta, eta))+C*A*(diff(theta(eta), eta)) = 0;
where A is given as

A := -(alpha*exp(-sqrt((omega+1)*omega*(M^2+alpha+1))*eta/(omega+1))*omega+alpha*exp(-sqrt((omega+1)*omega*(M^2+alpha+1))*eta/(omega+1))+exp(-sqrt((omega+1)*omega*(M^2+alpha+1))*eta/(omega+1))*omega-alpha*omega+exp(-sqrt((omega+1)*omega*(M^2+alpha+1))*eta/(omega+1))-alpha-omega-1)/sqrt((omega+1)*omega*(M^2+alpha+1));
I want solution for any values of omega, alpha, M, B, C and L. The BCs are below:

BCs := (D(theta))(0) = -1, theta(L) = 0.

I am waiting your response, 

Write a command maple to count each two elements distincts of a list L ?

Hello,

There is a error happened when i use the command "eliminate" ,

And,the target two equations is:

[190.0315457*d^6-7.601261828*d^4+344.0*c^2*d^2-2.677685950*c^4, 0.6830134554e-2*c^4+2084.317025*d^8-166.7453620*d^6+3.334907240*d^4-c^2*d^2]

The error is happened like that shown below.

Error, (in unknown) invalid arguments to divide: 4903.60312, 1.000000000 to use eliminate command!

I wonder why this error happened, could anyone help me!

Thanks!!!

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