Maple 15 Questions and Posts Maple 15 Questions and Posts Feed

These are Posts and Questions associated with the product, Maple 15

What Maple15 commands will display a Rouleaux tetrahedron or a Meissner tetrahedron?

Hi,

I got the Real and Imaginary of an expression J1 

assume(d,real):

Gamma:=0.04:tau:=10*Pi:j:=0:

J1:=(exp((1-I*d)*Gamma*tau)-1)/((1-I*d));

J1mod:=simplify((Re(J1))^2+(Im(J1))^2): (I works here this amont is real)

################

but when I change the expression  for J1 to be

J1:=((2*e^(-2^(-j-1)*(1-I*d))-e^(-2^(-j)*(1-I*d))-1)*exp((1-I*d)*Gamma*tau)-1)/((1-I*d)):

J1mod:=simplify((Re(J1))^2+(Im(J1))^2): 

J1mod here is complex(I dont know why? it doesnt separate the real and the im )

Any comments will help

Thanks

    Intersection of surfaces:

x3-.25*(sin(4*x1)+sin(3*x2+x3)+sin(2*x2))=0;  (1)

(x1-xx1)^4+(x2-xx2)^4+(x3-xx3)^4-1=0;          (2)   

   Surface (1) and a set of surfaces (2). Point (xx1, xx2, xx3) belongs to (1). Moving along the surface (1), we compute its intersection with the surface (2).
   The program is very simple and its algorithm can be used for many other combinations of equations.

intersection_of_surfaces.mw  

Hello,
I need help on plotting in for loop.

> N := 10; h := 1/N;
> for i from 0 to 10 do x[i] := i*h; p1 := evalf(cos(x[i])) end do;
> f1 := [seq([x[i], p1], i = 1 .. N)];
> plot([cos(x), f1], x = 0 .. 1, y = 0 .. 1);



The above code gives me  cos x plot and line plot, but I want plot of points and cos x.



D_Method.mw

The classical Draghilev’s method.  Example of solving the system of two transcendental equations. For a single the initial approximation are searched 9 approximate solutions of the system.
(4*(x1^2+x2-11))*x1+2*x1+2*x2^2-14+cos(x1)=0;
2*x1^2+2*x2-22+(4*(x1+x2^2-7))*x2-sin(x2)=0; 
x01 := -1.; x02 := 1.;

Hello everybody,

I am working on a somewhat complicated analytical problem, which includes the evaluation of the following (finite and singularity free) double integral (the stated numerical parameters may vary):

Int(exp(18.1818*(Int((0.579160e-1*sqrt(x)*Ei(1., 0.500000e-4*x)+(1072.23*(.999950-1.*exp(-0.500000e-4*x)))/sqrt(x))/sqrt(x), x = 1. .. eta))-9.10000*eta)/eta, eta = 1. .. 100.)

There are no unevaluated variables inside (all the e's are real exp()s). However, when putting it through evalf(), Maple returns it (after calculating for some time) unevaluated. I have no idea why, as a simple box sum should succeed.

Any input would be appreciated. Best regards,

  K. Reuther

 

P.S.: Raw expression for further deliberations

Int(exp(18.1818*(Int((0.579160e-1*sqrt(x)*Ei(1., 0.500000e-4*x)+(1072.23*(.999950-1.*exp(-0.500000e-4*x)))/sqrt(x))/sqrt(x), x = 1. .. eta))-9.10000*eta)/eta, eta = 1. .. 100.)

How can I plot a vertical line say x = a in Maple 15 worksheet?

Thanks

Maple 15 does not allow me to do even small changes after executing even the smallest bit of command. Is there a way to overwrite this default setting and force Maple to undo? Do the newer versions of Maple provide this functionality and what is the purpose of undo getting deactivated after a command, at least it should be enabled for the input?

Greetings,

Maple 15 allows the following syntax

omega := sqrt(w0^2*(1+((z-zf)/z0)^2))

But it does not allow this one 

omega^2 := sqrt(w0^2*(1+((z-zf)/z0)^2))

Why is this so for functions and variables? Is there any way around this, I am really bugged by this issue. The Maple Math told me that the syntax was invalid so I had type the commands directly.

 

Is it possible in Maple 15 to solve an equation with a parameter for a given set of parameters? How can this be passed to the solve function, should I use some kind of list?  After obtaining the solution how can I assign the solutions to variables such as x1 for the first value of the parameter, x2 for the second value of the parameters and so on. Furthermore, is this possible with the fsolve command?

 

Thanks

Hello I am a Maple 15 user and I am using the command fsolve to solve for the intersection of two curves over a specified interval in x, namely from 0 to the lim defined in the Maple document. The specified interval contains asymptotes and when I specify the full interval only one of the three solutions is returned even if I can see that there are three distinct solutions by looking at the plot of RHS and LHS. Should I use another technique to find the solution or is my implementation of fsolve command wrong?

Thanks in advance


restart

with(ListTools):

n1 := 1:

n2 := 1.50:

n3 := 1.40:

lambda := 1.3:

k0 := 2*Pi/lambda:

d := 3:

x0 := k0*d:

arg1 := sqrt(x0^2*(n2^2-n1^2)):

arg2 := sqrt(x0^2*(n2^2-n3^2)):

lim := FindMinimalElement([arg1, arg2]):

sqr1 := sqrt(x0^2*(n2^2-n1^2)-x^2):

sqr2 := sqrt(x0^2*(n2^2-n3^2)-x^2):

LHS := tan(x):

RHS := (sqr1+sqr2)/(x*(1-sqr1*sqr2/x^2)):

plot([LHS, RHS], x = 0 .. lim, y = -6 .. 6)

 

fsolve(RHS = LHS, x = (1/2)*Pi .. 3*Pi*(1/2))

2.634254816

(1)

fsolve(RHS = LHS, x = 3*Pi*(1/2) .. 9*Pi*(1/4))

5.222527128

(2)

fsolve(RHS = LHS, x = 9*Pi*(1/4) .. lim)

7.598486053

(3)

``


Download HW4Q2.mw

test.mw

Hello. As you can see the minimum of set X is 2.

the time pair in set W whose difference is 2 corresponds to elements 54 and 55. How do i locate and print these automatically?

Digits:=4:

U := [1.010, 1.110, 1.210, 1.310, 1.410, 1.510, 1.610, 1.710, 1.810, 1.910, 2.020, 2.120, 2.220, 2.320, 2.420, 2.520, 2.620, 2.720, 2.820, 2.920, 3.030, 3.130, 3.230, 3.330, 3.430, 3.530, 3.630, 3.730, 3.830, 3.930, 4.040, 4.140, 4.240, 4.340, 4.440, 4.540, 4.640, 4.740, 4.840, 4.940, 5.050, 5.150, 5.250, 5.350, 5.450, 5.550, 5.650, 5.750, 5.850, 5.950, 6.060, 6.160, 6.260, 6.360, 6.460, 6.560, 6.660, 6.760, 6.860, 6.960, 7.070, 7.170, 7.270, 7.370, 7.470, 7.570, 7.670, 7.770, 7.870, 7.970, 8.080, 8.180, 8.280, 8.380, 8.480, 8.580, 8.680, 8.780, 8.880, 8.980, 9.090, 9.190, 9.290, 9.390, 9.490, 9.590, 9.690, 9.790, 9.890, 9.990, 10.01, 11.11, 12.21]:

W := select(proc (t) options operator, arrow; .59 >= frac(t) end proc, U);

[1.010, 1.110, 1.210, 1.310, 1.410, 1.510, 2.020, 2.120, 2.220, 2.320, 2.420, 2.520, 3.030, 3.130, 3.230, 3.330, 3.430, 3.530, 4.040, 4.140, 4.240, 4.340, 4.440, 4.540, 5.050, 5.150, 5.250, 5.350, 5.450, 5.550, 6.060, 6.160, 6.260, 6.360, 6.460, 6.560, 7.070, 7.170, 7.270, 7.370, 7.470, 7.570, 8.080, 8.180, 8.280, 8.380, 8.480, 8.580, 9.090, 9.190, 9.290, 9.390, 9.490, 9.590, 10.01, 11.11, 12.21]

(1)

X:=[seq(trunc(W[i+1])*60+frac(W[i+1])*100-(trunc(W[i])*60+frac(W[i])*100),i=1..nops(W)-1)];

[10.00, 10.00, 10.00, 10.00, 10.00, 11.00, 10.00, 10.00, 10.00, 10.00, 10.00, 11.00, 10.00, 10.00, 10.00, 10.00, 10.00, 11.00, 10.00, 10.00, 10.00, 10.00, 10.00, 11.00, 10.00, 10.00, 10.00, 10.00, 10.00, 11.00, 10.00, 10.00, 10.00, 10.00, 10.00, 11.00, 10.00, 10.00, 10.00, 10.00, 10.00, 11.00, 10.00, 10.00, 10.00, 10.00, 10.00, 11.00, 10.00, 10.00, 10.00, 10.00, 10.00, 2.00, 70.00, 70.00]

(2)

NULL

min(X),{W[54],W[55]};

2.00, {9.590, 10.01}

(3)

 



Download test.mw

  Given this equation:       (chi^2*(xi^2-1)^2+1-Omega^2)*(xi^2-Omega^2)-xi^2 = 0

   chi^2=1/1200;  I want to plot xi vs Omega. Can anyone help me out?

Hi there,

Is there a way in which i can solve the following optimal control problem numerically with Maple?

 dH/dt=λ-µ H-(1-u1)β H V+δ I,

dI/dt=(1-u1)β H V-σ I,

‎dV/dt=(1-u2)k I-γ‎V,

dλ1/dt=-1+λ1µ+β‎‎V(1-u1)(λ1-λ2),‎

dλ2/dt=λ1δ+λ2σ-λ3(1-u2)k‎,‎

‎dλ3/dt=β H(λ1-λ2)(1-u1)‎‎+λ3γ.

where

u1=βHV(λ1-λ2)/A1,

u2=-λ3kI/A2,

σ = α + δ,

and

H(0)=1.7*10^8,    I(0)=0,    V(0)=400.

 

λ=5*10^5,    µ=0.003,     β=4*10^(-10),    α=0.043,    δ= 0.2                  k=6.24,       γ‎=0.65.

A1=900, A2=1000.

 

Answers and advice are very appreciated. 

Thank you all for reading.

Aylin

1 2 3 4 5 6 7 Last Page 1 of 40