Maple 16 Questions and Posts

These are Posts and Questions associated with the product, Maple 16

Hi,

It might be a really silly question, but I am wondering is it possible to simplify expression like this

a^2+b^2+2*a*b+c^2. Just by looking it we know that we can write it in the form of (a+b)^2+c^2. This is the basic exmaple I come up with. I have very lengthy expressions in maple, which can be factorize like this, but factor command will not work as it will try to factorize entire expression. So I am wondering is it doable in maple or I have to do it manually by collecting terms and check whether they can be factorize or not.

Thanks in Advance.

With Regards

sunit

Hi every one

I'm having some plots in maple, but the layout is not pretty enough, I want export in to MATLAB. Does some one please have an idea on how I can go about it?.

I'm using Maple 16

Thank you in anticipation

Can anyone help me to find a solution to psi[2](r,phi) for the attached partial differential equation pde[0]?


I want to find a general solution to a partial differential equation by assuming that I know one solution, called psi[1], and trying to find another solution psi[2] by assuming that the general solution in the form of psi= psi[1]*psi[2]. I want to restrict the second solution to be in the form of psi[2](r*sin(phi)) so that it satisfies the PDE, and is a function of r times sin(phi). The latter makes error as the maple identifies that the function psi[2](r*sin(phi)) depends on only one variable r*sin(phi). Could you please help me to find a solution for psi[2] in the form psi[2]=f(r*sin(phi))?

 

Also, I have trouble with defining the operator Do in the attached file.  When it operates on psi[2](r * sin(phi)), maple gives D(D(psi[2]))(r*sin(phi)). It is not clear for me that whether this derivative is with respect to r or phi. I need is to define Do in a way so that the derivatives are correctly taken with respect to different separate variables.

 

Thank you for your help,

Ahmad

PDEs_KnownSolutoin.mw

Can anyone help me to solve the attached system of PDEs with a given expression for the HINT such as HINT = F[1](t)*F[2](r*sin(phi))

I am not able to set such an arbitray HINT function for system of PDEs.

SysPDE_HINT.mw

 

Thank you,

Ahmad

I am currently working on a project that generates a set of matrices and I want to find their eigenvalues, but using the inbuilt Maple engine takes too long. The problem is that whenever I try to use the Matlab[eig] command I get the error:

Error, (in Matlab:-setvar) unable to store '-3.*Re(X)' when datatype=float[8]
I found out that solving symbolic matrices in MATLAB requires first defining symbols with the "sym" command but I've been unable to do that in Maple.

Hi,

This might be a very silly question but it is troubling me a little bit and that's why I need to post it. During the combination of symbolic and numerical comutation this '1.0' is appearing as a coefficient for the variables whose coeffecient is just '1'. It's quite annoying as sometimes if I have to collect coefficient of a variable for an example exp(I*omega*t) then I have to write exp(1.I*omega*t), so chances of making mistake is higher. Please find the attached worksheet for this. In eq(4), you can easily see that for x[3](t) and x[1](t) this '1.0' appears in front of the variables.

I really appreciate  if someone can help me out of this.

With Regards

Sunitquestion.mw
 

restart

with(LinearAlgebra):

par := {a = 2.5, alpha = 2, k_r = .5, k_rc = .2, k_rq = .2, kappa = 0.1e-2, mu_k = .35, mu_s = .44, omega = .766620580157922, sigma_0 = 110, sigma_1 = 1.37, sigma_2 = 0.823e-1, x_s3 = -1.04003626422324936017819852700633621040584050594846801927800, zeta = 0.904504977553123318334601762827181333680096702957228781770315e-1}:

f := proc (v_r) options operator, arrow; mu_k+(mu_s-mu_k)*exp(-a*v_r) end proc:

NULL

g_exp1 := taylor(1/f(v_rv+x21), x21 = 0, 4):

for k to 4 do g_coeff[k] := taylor(subs(v_r = v_rv, coeff(g_exp1, x21, k-1)), epsilon = 0, 3) end do:

g0 := eval(subs(par, coeff(g_coeff[1], epsilon, 0))):

g1 := eval(subs(par, coeff(g_coeff[2], epsilon, 0))):

g2 := eval(subs(par, coeff(g_coeff[3], epsilon, 0))):

g3 := eval(subs(par, coeff(g_coeff[4], epsilon, 0))):

NULL

``

eq[1] := subs(par, diff(x[1](t), t)-x[2](t)):

eq[2] := subs(par, diff(x[2](t), t)+2*zeta*x[2](t)+x[1](t)+k_r*(x[1](t)-x[3](t))+2*kappa*(x[2](t)-x[4](t))+k_rq*(x[1](t)-x[3](t))^2+k_rc*(x[1](t)-x[3](t))^3)

diff(x[2](t), t)+.1829009955*x[2](t)+1.5*x[1](t)-.5*x[3](t)-0.2e-2*x[4](t)+.2*(x[1](t)-x[3](t))^2+.2*(x[1](t)-x[3](t))^3

(1)

eq[3] := subs(par, diff(x[3](t), t)-x[4](t))

diff(x[3](t), t)-x[4](t)

(2)

eq[4] := subs(par, diff(x[4](t), t)+2*kappa*alpha*(x[4](t)-x[2](t))+k_r*alpha*(x[3](t)-x[1](t))-k_rq*alpha*(x[3](t)-x[1](t))^2+k_rc*alpha*(x[3](t)-x[1](t))^3+alpha*(sigma_0*x[5](t)+sigma_1*v_r*(1-sigma_0*x[5](t)*(g_0+g_1*x[4](t)+g_2*x[4](t)^2+g_3*x[4](t)^3))+sigma_2*v_r))

diff(x[4](t), t)+0.4e-2*x[4](t)-0.4e-2*x[2](t)+1.0*x[3](t)-1.0*x[1](t)-.4*(x[3](t)-x[1](t))^2+.4*(x[3](t)-x[1](t))^3+220*x[5](t)+2.74*v_r*(1-110*x[5](t)*(g_0+g_1*x[4](t)+g_2*x[4](t)^2+g_3*x[4](t)^3))+.1646*v_r

(3)

eq[5] := subs(par, diff(x[5](t), t)-v_r*(1-sigma_0*x[5](t)*(g_0+g_1*x[4](t)+g_2*x[4](t)^2+g_3*x[4](t)^3)))

diff(x[5](t), t)-v_r*(1-110*x[5](t)*(g_0+g_1*x[4](t)+g_2*x[4](t)^2+g_3*x[4](t)^3))

(4)

``


 

Download question.mw

 

How to convert expression below to LaTex:  $\lim _{x \rightarrow 2} \frac{2}{x+3}$

And How to convert expression below to LaTex:  $\int_{2}^{3} \frac{1}{x^{2}+2} d x$

file test: newLaTex.mw

Hi Guys,

I am trying to intgrate a function involving hyperbolic functions in a range of 0 to 1 and it is giving me very large value of 10^94. However, on doing integration terms terms i can see that some large terms involving 10^191 cancel out with each other and I can have a fnite value of this integration. It would be really helpful if someone can help me out why it is happening with int function and how can I solve this case involving hyperbolic function. For reference maple file is attached. Thanks in advance and much appreciated.

With Regards

Sunit

question.mw

Hi Guys,

I need help regarding simplifying definite integrals. I have following expression

2*s^2*(int(Phi[1, 1](x, T[2])*(diff(Y1(x), x, x)), x = 0 .. x1))+int(Phi[1, 1](x, T[2])*(diff(Y1(x), x, x, x, x)), x = 0 .. x1)-omega_y^2*(int(Y1(x)*Phi[1, 1](x, T[2]), x = 0 .. x1))

As we can notice the limit for each integral is same, so I should be able to take these integral limit outside. I am trying to use collect and simplify, but both of these command are not working. It would be really helpful for me if I can get the solution for it.

Please find the attached example sheet also.example.mw

With Regards

Sunit

 

Hi Guys,

It might be a very basic question, but I am struggling with it for a quite a time.  I have an expression in a form of

f(x)=h(x)+g(x);

and I want to use factor operation elementwise, i.e., it can individually act on h(x) and can give me

f(x)=h1(x)*h2(x)+g1(x)*g2(x). But whenever I am putting factor operation with elementwise it is not giving me desired answer. It would be really helpful and great if someone can help me out.

I am attaching maple sheet for reference also.

Thanks in advance and regards

Sunit.
example.mw
Download example.mw

 

How do I find integer solutions to this non-linear equation:

 

8= 7(x^2+y^2+z^2)+2x+4y-8z.

 

Tried isolve and it wasn't working. (I guess too many variables?)

 

Also, if f(x,y,z) is the RHS, how do I write a loop that finds integer solutions to f(x,y,z)=c for |x|,|y|,|z|< N, say?

Hello,

I don't understand why Maple gives me the following error:

Error, (in fsolve/Iterators) unrecognized form

The full maple file:


 

restart

mbal := 0.28e-2:

rbal := 0.2e-1:

Cw := .47:

g := 9.81:

A := Pi*rbal^2:

beta := 3.33*Pi*(1/180):

s0x := .2:

s0y := .25:

rho := 1.293:

l := 2:

vx := diff(sx(t), t);

diff(sx(t), t)

(1)

vy := diff(sy(t), t);

diff(sy(t), t)

(2)

ax := diff(sx(t), `$`(t, 2));

diff(diff(sx(t), t), t)

(3)

ay := diff(sy(t), `$`(t, 2));

diff(diff(sy(t), t), t)

(4)

v0x := cos(beta)*v0;

cos(0.1850000000e-1*Pi)*v0

(5)

v0y := sin(beta)*v0;

sin(0.1850000000e-1*Pi)*v0

(6)

`&Sigma;Fx` := -Fdx = mbal*ax;

-Fdx = 0.28e-2*(diff(diff(sx(t), t), t))

(7)

`&Sigma;Fy` := -Fz-Fdy = mbal*ay;

-Fz-Fdy = 0.28e-2*(diff(diff(sy(t), t), t))

(8)

Fz := mbal*g;

0.27468e-1

(9)

Fdx := .5*rho*vx^2*A*Cw;

0.1215420e-3*(diff(sx(t), t))^2*Pi

(10)

Fdy := .5*rho*vy^2*A*Cw;

0.1215420e-3*(diff(sy(t), t))^2*Pi

(11)

ics1 := sx(0) = s0x, (D(sx))(0) = v0x;

sx(0) = .2, (D(sx))(0) = cos(0.1850000000e-1*Pi)*v0

(12)

ics2 := sy(0) = s0y, (D(sy))(0) = v0y;

sy(0) = .25, (D(sy))(0) = sin(0.1850000000e-1*Pi)*v0

(13)

verplaatsingx := dsolve({ics1, `&Sigma;Fx`}, sx(t));

sx(t) = (1400000/60771)*ln((60771/1400000)*cos((37/2000)*Pi)*v0*exp((60771/7000000)*Pi)*t*Pi+exp((60771/7000000)*Pi))/Pi

(14)

verplaatsingy := dsolve({ics2, `&Sigma;Fy`});

sy(t) = (1/243084)*(60771*Pi+2800000*ln((1/92736546000)*(20257*Pi^(1/2)*sin((37/2000)*Pi)*v0*sin((3/70000)*231841365^(1/2)*Pi^(1/2)*t)+20*231841365^(1/2)*cos((3/70000)*231841365^(1/2)*Pi^(1/2)*t))^2))/Pi

(15)

eindy := rhs(verplaatsingy) = rbal;

(1/243084)*(60771*Pi+2800000*ln((1/92736546000)*(20257*Pi^(1/2)*sin((37/2000)*Pi)*v0*sin((3/70000)*231841365^(1/2)*Pi^(1/2)*t)+20*231841365^(1/2)*cos((3/70000)*231841365^(1/2)*Pi^(1/2)*t))^2))/Pi = 0.2e-1

(16)

eindx := rhs(verplaatsingx) = l;

(1400000/60771)*ln((60771/1400000)*cos((37/2000)*Pi)*v0*exp((60771/7000000)*Pi)*t*Pi+exp((60771/7000000)*Pi))/Pi = 2

(17)

t := solve(eindy, t);

RootOf(1397733*Pi+70000000*ln((1/92736546000)*(20257*Pi^(1/2)*sin((37/2000)*Pi)*v0*sin((3/70000)*231841365^(1/2)*Pi^(1/2)*_Z)+20*231841365^(1/2)*cos((3/70000)*231841365^(1/2)*Pi^(1/2)*_Z))^2))

(18)

t := evalf(t[1]);

RootOf(1397733*Pi+70000000*ln((1/92736546000)*(20257*Pi^(1/2)*sin((37/2000)*Pi)*v0*sin((3/70000)*231841365^(1/2)*Pi^(1/2)*_Z)+20*231841365^(1/2)*cos((3/70000)*231841365^(1/2)*Pi^(1/2)*_Z))^2))[1]

(19)

v0 := fsolve(eindx, v0)

Error, (in fsolve/Iterators) unrecognized form

 

``

``


 

Download ttbuddymaple.mw

 

Thank you!

 

How do I draw three vectors on the same axis of coordinates, I see this vector appear after the previous vector one second  and on the screen when this vector appears, the previous vector remains on the screen and on the last screen I see all three vectors with the Maple command?

Example : plottools :- arrow( [1, -2], [4, -1], 0.001, 0.05, 0.1), plottools :- arrow( [-1, 3], [2, 1], 0.001, 0.05, 0.1), plottools :- arrow( [0, 2], [-3, 0], 0.001, 0.05, 0.1).

Thanks so much for the help of everyone!

How do I draw three graphs on the same axis of coordinates and I see this graph appear after the previous graph one second with the Maple command? Example : y = x, y = x2, y = 1 - x.

Thanks so much for the help of everyone!

Lecture 4 - Problem 2
a)
> a := -2100; b := 2100; N := 8; h := (b-a)/N; C := 4491; x := [seq(h, h = -2100 .. 2100, h)]; y := proc (x) options operator, arrow; sqrt(1+((1/2)*exp(x/C)-(1/2)*exp(-x/C))^2) end proc; evalf(y(x[1])); evalf(y(x[N+1])); L := (1/3)*h*(y(x[1])+4*(y(x[2])+y(x[4])+y(x[6])+y(x[N]))+2*(y(x[3])+y(x[5])+y(x[N-1]))+y(x[N+1])); evalf(L);
                             -2100
                              2100
                               8
                              525
                              4491
     [-2100, -1575, -1050, -525, 0, 525, 1050, 1575, 2100]
         /                           2\
         |    /1    /x\   1    /  x\\ |
x -> sqrt|1 + |- exp|-| - - exp|- -|| |
         \    \2    \C/   2    \  C// /
                          1.111332350
                          1.111332350
                                           (1/2)
         /                               2\    
         |    /1    /-700\   1    /700 \\ |    
     175 |1 + |- exp|----| - - exp|----|| |    
         \    \2    \1497/   2    \1497// /     

                                               (1/2)
              /                              2\    
              |    /1    /-175\   1    /175\\ |    
        + 700 |1 + |- exp|----| - - exp|---|| |    
              \    \2    \499 /   2    \499// /     

                                                (1/2)
              /                               2\    
              |    /1    /-175\   1    /175 \\ |    
        + 700 |1 + |- exp|----| - - exp|----|| |    
              \    \2    \1497/   2    \1497// /     

                                                (1/2)
              /                               2\    
              |    /1    /175 \   1    /-175\\ |    
        + 700 |1 + |- exp|----| - - exp|----|| |    
              \    \2    \1497/   2    \1497// /     

                                               (1/2)
              /                              2\    
              |    /1    /175\   1    /-175\\ |    
        + 700 |1 + |- exp|---| - - exp|----|| |    
              \    \2    \499/   2    \499 // /     

                                                (1/2)     
              /                               2\          
              |    /1    /-350\   1    /350 \\ |          
        + 350 |1 + |- exp|----| - - exp|----|| |      + 350
              \    \2    \1497/   2    \1497// /           

                                                (1/2)
              /                               2\    
              |    /1    /350 \   1    /-350\\ |    
        + 350 |1 + |- exp|----| - - exp|----|| |    
              \    \2    \1497/   2    \1497// /     

                                                (1/2)
              /                               2\    
              |    /1    /700 \   1    /-700\\ |    
        + 175 |1 + |- exp|----| - - exp|----|| |    
              \    \2    \1497/   2    \1497// /    
                          4354.742601
> L := (1/3)*h*(y(x[1])+4*add(y(i), i = y(x[2]) .. y(x[N]), 2)+2*add(y(i), i = y(x[3]) .. y(x[N-1]), 2)+y(x[N+1])); evalf(L);
Error, invalid input: add expects 2 arguments, but received 3
                          4354.742601
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