Maple 18 Questions and Posts

These are Posts and Questions associated with the product, Maple 18

Hi I have the following ln function that I want to differentiate wrt variable c:

 

I2 := -sqrt(-c^2+1)*ln(abs((.9*sqrt(-c^2+1)-c*sqrt(1-.9^2))/(-.9*sqrt(-c^2+1)-c*sqrt(1-.9^2))))

 

When I differentiate I obtain an expression that involves 

...abs(1, (.9*sqrt(-c^2+1)-.4358898944*c)/(-.9*sqrt(-c^2+1)-.4358898944*c))...

Why does it give a comma at the abs expression? how to get rid of that.

Hello everyone,

I have a function of 5 variables, A, P, N, k. I want to solve and express as a power series of 'k'

w=F*k+G+H/k+...

and gather the coefficients of each power.

However, the result I obtain in my code differs from the analytical value I found. What am I doing wrong?

Thanks!

collect_mp.mw

How to get a plot for different values of Mh.

like Mh=[1 2 3 4]

Code:

restart;
with(DEtools,odeadvisor);

m:=10;H:=1;Mh:=1;b:=0.02; a:=0.05;V:=array(0..m); V[0]:=1-exp(-t);

for k from 1 to m do

if k=1 then chi:=0;

 chi:=1;

 fi;

 p:=0;

 for j from 0 to k-1 do

   p:=p+(V[k-1-j]*diff(V[j],t$2)-diff(V[k-1-j],t)*diff(V[j],t)-a*(2*diff(V[k-1-j],t)*diff(V[j],t$3)-diff(V[k-1-j],t$2)*diff(V[j],t$2)-V[k-1-j]*diff(V[j],t$4)));  od;

p:=(p+diff(V[k-1],t$3)-b*(diff(V[k-1],t$2)+t*diff(V[k-1],t$3))-Mh*diff(V[k-1],t))*h*H;

p:=factor(p);

V[k]:=(-int(p,t)+0.5*exp(t)*int(exp(-t)*p,t)+0.5*exp(-t)*int(exp(t)*p,t)+chi*V[k-1]+C1+C3*exp(-t));

v:=unapply(V[k],t);

V[k]:=frontend(expand,[V[k]]);  V[k]:=subs(C3=solve(eval(subs(t=0,diff(V[k],t))),C3),V[k]); V[k]:=frontend(expand,[V[k]]);

V[k]:=subs(C1=solve(eval(subs(t=0,-V[k]-diff(V[k],t))),C1),V[k]);

od:

appr:=0;

for k from 0 to m do

 appr:=appr+V[k];

od:

u_appr:=unapply(appr,(h,t)):

u_appr_1:=unapply(diff(u_appr(h,t),t),(h,t)):

evalf(u_appr_1(-0.4,t)):

with(plots);

plot([u_appr_1(-0.4,t)],t=0..4,0..1.2,color=[black],axes=frame):

 

 

this plot for Mh=1:

 

How to apply two for loops to solve ode problem.

code:

restart; with(plots); fcns := {T(eta), f(eta)};
m := .5; bet := 1; na := 1/6; N := 5;
eq1 := (diff(f(eta), `$`(eta, 3)))*pr+m-m*(diff(f(eta), `$`(eta, 1)))+((m+1)*(1/2))*(diff(f(eta), `$`(eta, 2)))*f(eta) = 0;
eq2 := diff(T(eta), `$`(eta, 2))+((m+1)*(1/2))*(diff(T(eta), `$`(eta, 1)))*f(eta) = 0;
bc := f(0) = 0, (D(f))(0) = 0, (D(f))(N) = 1, (D(T))(0) = -bi*(1-T(0)), T(N) = 0;
bi:= [seq(1..4,0.1)];  NN := nops(bi);  
pr:=[seq(1..2,0.1)];  NN1 := nops(pr);
for i  from 1 to NN do    
for j from 1 to NN1 do  

R := dsolve(eval({bc, eq1,eq2}, bi[i],pr[j]), fcns, type = numeric, method = bvp[midrich], maxmesh=2400):  
X1||[i,j]:=rhs(-R(0)[3]):
end do:  
end do:  

Have a good day.
 

I am trying to expand a multivariable (more specifically 4 variables) function in powers of one of its variables when it goes to infinity.

However, the result I get is always zero, even if I input (or not) values for some of the other variables.

Can anybody help?

series_expansion.mw

P.s.: I want to do the same for the other two functions I defined in the worksheet as well.


 

restart; _local(gamma); _local(I); m := 3; A := 10; delta := .112; rho := .23; beta := 1.4; alpha := 2.1; gamma := 1.02; q := 2.3; b1 := 50; b2 := 10; b3 := 5; b4 := 20; S(0) := b1; B(0) := b2; V(0) := b3; R(0) := b4; mu := .13; i = 1; for k from 0 to m do S(k+1) := (A*delta*k-(rho+mu)*S(k)-beta*(sum(S(m)*B(j-m), j = 0 .. m)))/(k+1); B(k+1) := -(-(mu+alpha+gamma)*B(k)+beta*(sum(S(m)*B(j-m), j = 0 .. m)))/(k+1); V(k+1) := (rho*S(k)-(1-q)*S(k)-mu*V(k))/(k+1); R(k+1) := (gamma*B(k)-mu*R(k))/(k+1) end do; s := sum(S(kk)*t^kk, kk = 0 .. m); b := sum(B(kk)*t^kk, kk = 0 .. m); v := sum(V(kk)*t^kk, kk = 0 .. m); r := sum(R(kk)*t^kk, kk = 0 .. m); SS(0) := s; BB(0) := b; VV(0) := v; RR(0) := r; S(0) := subs(t = T(i), s); B(0) := subs(t = T(i), b); V(0) := subs(t = T(i), v); R(0) := subs(t = T(i), r)

I

 

Warning, The imaginary unit, I, has been renamed _I

 

3

 

10

 

.112

 

.23

 

1.4

 

2.1

 

1.02

 

2.3

 

50

 

10

 

5

 

20

 

50

 

10

 

5

 

20

 

.13

 

i = 1

 

-18.00-1.4*S(3)*B(-3)-1.4*S(3)*B(-2)-1.4*S(3)*B(-1)-14.0*S(3)

 

32.50-1.4*S(3)*B(-3)-1.4*S(3)*B(-2)-1.4*S(3)*B(-1)-14.0*S(3)

 

75.85

 

7.60

 

3.800000000-.4480000000*S(3)*B(-3)-.4480000000*S(3)*B(-2)-.4480000000*S(3)*B(-1)-4.480000000*S(3)

 

52.81250000-2.975000000*S(3)*B(-3)-2.975000000*S(3)*B(-2)-2.975000000*S(3)*B(-1)-29.75000000*S(3)

 

-18.70025000-1.071000000*S(3)*B(-3)-1.071000000*S(3)*B(-2)-1.071000000*S(3)*B(-1)-10.71000000*S(3)

 

16.08100000-.7140000000*S(3)*B(-3)-.7140000000*S(3)*B(-2)-.7140000000*S(3)*B(-1)-7.140000000*S(3)

 

.2906666667-.4129066667*S(3)*B(-3)-.4129066667*S(3)*B(-2)-.4129066667*S(3)*B(-1)-4.129066667*S(3)

 

55.85709723-1.296018889*S(3)*B(-3)-1.296018889*S(3)*B(-2)-1.296018889*S(3)*B(-1)-12.96018889*S(3)-.4666666667*(.2906666667-.4129066667*S(3)*B(-3)-.4129066667*S(3)*B(-2)-.4129066667*S(3)*B(-1)-4.129066667*S(3))*B(-3)-.4666666667*(.2906666667-.4129066667*S(3)*B(-3)-.4129066667*S(3)*B(-2)-.4129066667*S(3)*B(-1)-4.129066667*S(3))*B(-2)-.4666666667*(.2906666667-.4129066667*S(3)*B(-3)-.4129066667*S(3)*B(-2)-.4129066667*S(3)*B(-1)-4.129066667*S(3))*B(-1)

 

2.748344167-.1820700000*S(3)*B(-3)-.1820700000*S(3)*B(-2)-.1820700000*S(3)*B(-1)-1.820700000*S(3)

 

17.25940667-.9805600000*S(3)*B(-3)-.9805600000*S(3)*B(-2)-.9805600000*S(3)*B(-1)-9.805600000*S(3)

 

-.2034933335+1.482334934*S(3)*B(-3)+1.482334934*S(3)*B(-2)+1.482334934*S(3)*B(-1)+14.82334934*S(3)-.3500000000*(.2906666667-.4129066667*S(3)*B(-3)-.4129066667*S(3)*B(-2)-.4129066667*S(3)*B(-1)-4.129066667*S(3))*B(-3)-.3500000000*(.2906666667-.4129066667*S(3)*B(-3)-.4129066667*S(3)*B(-2)-.4129066667*S(3)*B(-1)-4.129066667*S(3))*B(-2)-.3500000000*(.2906666667-.4129066667*S(3)*B(-3)-.4129066667*S(3)*B(-2)-.4129066667*S(3)*B(-1)-4.129066667*S(3))*B(-1)

 

44.36655818+.3921579862*S(3)*B(-3)+.3921579862*S(3)*B(-2)+.3921579862*S(3)*B(-1)+3.921579862*S(3)-.7291666668*(.2906666667-.4129066667*S(3)*B(-3)-.4129066667*S(3)*B(-2)-.4129066667*S(3)*B(-1)-4.129066667*S(3))*B(-3)-.7291666668*(.2906666667-.4129066667*S(3)*B(-3)-.4129066667*S(3)*B(-2)-.4129066667*S(3)*B(-1)-4.129066667*S(3))*B(-2)-.7291666668*(.2906666667-.4129066667*S(3)*B(-3)-.4129066667*S(3)*B(-2)-.4129066667*S(3)*B(-1)-4.129066667*S(3))*B(-1)

 

0.2185881458e-1-.1520195250*S(3)*B(-3)-.1520195250*S(3)*B(-2)-.1520195250*S(3)*B(-1)-1.520195250*S(3)

 

13.68262908-.2986166168*S(3)*B(-3)-.2986166168*S(3)*B(-2)-.2986166168*S(3)*B(-1)-2.986166168*S(3)-.1190000000*(.2906666667-.4129066667*S(3)*B(-3)-.4129066667*S(3)*B(-2)-.4129066667*S(3)*B(-1)-4.129066667*S(3))*B(-3)-.1190000000*(.2906666667-.4129066667*S(3)*B(-3)-.4129066667*S(3)*B(-2)-.4129066667*S(3)*B(-1)-4.129066667*S(3))*B(-2)-.1190000000*(.2906666667-.4129066667*S(3)*B(-3)-.4129066667*S(3)*B(-2)-.4129066667*S(3)*B(-1)-4.129066667*S(3))*B(-1)

 

50+(-22.06933333-1.4*(.2906666667-.4129066667*S(3)*B(-3)-.4129066667*S(3)*B(-2)-.4129066667*S(3)*B(-1)-4.129066667*S(3))*B(-3)-1.4*(.2906666667-.4129066667*S(3)*B(-3)-.4129066667*S(3)*B(-2)-.4129066667*S(3)*B(-1)-4.129066667*S(3))*B(-2)-1.4*(.2906666667-.4129066667*S(3)*B(-3)-.4129066667*S(3)*B(-2)-.4129066667*S(3)*B(-1)-4.129066667*S(3))*B(-1)+5.780693334*S(3)*B(-3)+5.780693334*S(3)*B(-2)+5.780693334*S(3)*B(-1)+57.80693334*S(3))*T(i)+(2.497813333-.4480000000*(.2906666667-.4129066667*S(3)*B(-3)-.4129066667*S(3)*B(-2)-.4129066667*S(3)*B(-1)-4.129066667*S(3))*B(-3)-.4480000000*(.2906666667-.4129066667*S(3)*B(-3)-.4129066667*S(3)*B(-2)-.4129066667*S(3)*B(-1)-4.129066667*S(3))*B(-2)-.4480000000*(.2906666667-.4129066667*S(3)*B(-3)-.4129066667*S(3)*B(-2)-.4129066667*S(3)*B(-1)-4.129066667*S(3))*B(-1)+1.849821867*S(3)*B(-3)+1.849821867*S(3)*B(-2)+1.849821867*S(3)*B(-1)+18.49821867*S(3))*T(i)^2+(-.9095153783-.4129066667*(.2906666667-.4129066667*S(3)*B(-3)-.4129066667*S(3)*B(-2)-.4129066667*S(3)*B(-1)-4.129066667*S(3))*B(-3)-.4129066667*(.2906666667-.4129066667*S(3)*B(-3)-.4129066667*S(3)*B(-2)-.4129066667*S(3)*B(-1)-4.129066667*S(3))*B(-2)-.4129066667*(.2906666667-.4129066667*S(3)*B(-3)-.4129066667*S(3)*B(-2)-.4129066667*S(3)*B(-1)-4.129066667*S(3))*B(-1)+1.704919154*S(3)*B(-3)+1.704919154*S(3)*B(-2)+1.704919154*S(3)*B(-1)+17.04919154*S(3))*T(i)^3

 

10+(28.43066667-1.4*(.2906666667-.4129066667*S(3)*B(-3)-.4129066667*S(3)*B(-2)-.4129066667*S(3)*B(-1)-4.129066667*S(3))*B(-3)-1.4*(.2906666667-.4129066667*S(3)*B(-3)-.4129066667*S(3)*B(-2)-.4129066667*S(3)*B(-1)-4.129066667*S(3))*B(-2)-1.4*(.2906666667-.4129066667*S(3)*B(-3)-.4129066667*S(3)*B(-2)-.4129066667*S(3)*B(-1)-4.129066667*S(3))*B(-1)+5.780693334*S(3)*B(-3)+5.780693334*S(3)*B(-2)+5.780693334*S(3)*B(-1)+57.80693334*S(3))*T(i)+(44.16516667-2.975000000*(.2906666667-.4129066667*S(3)*B(-3)-.4129066667*S(3)*B(-2)-.4129066667*S(3)*B(-1)-4.129066667*S(3))*B(-3)-2.975000000*(.2906666667-.4129066667*S(3)*B(-3)-.4129066667*S(3)*B(-2)-.4129066667*S(3)*B(-1)-4.129066667*S(3))*B(-2)-2.975000000*(.2906666667-.4129066667*S(3)*B(-3)-.4129066667*S(3)*B(-2)-.4129066667*S(3)*B(-1)-4.129066667*S(3))*B(-1)+12.28397333*S(3)*B(-3)+12.28397333*S(3)*B(-2)+12.28397333*S(3)*B(-1)+122.8397333*S(3))*T(i)^2+(52.09000233-1.296018889*(.2906666667-.4129066667*S(3)*B(-3)-.4129066667*S(3)*B(-2)-.4129066667*S(3)*B(-1)-4.129066667*S(3))*B(-3)-1.296018889*(.2906666667-.4129066667*S(3)*B(-3)-.4129066667*S(3)*B(-2)-.4129066667*S(3)*B(-1)-4.129066667*S(3))*B(-2)-1.296018889*(.2906666667-.4129066667*S(3)*B(-3)-.4129066667*S(3)*B(-2)-.4129066667*S(3)*B(-1)-4.129066667*S(3))*B(-1)+5.351348394*S(3)*B(-3)+5.351348394*S(3)*B(-2)+5.351348394*S(3)*B(-1)+53.51348394*S(3)-.4666666667*(-.9095153783-.4129066667*(.2906666667-.4129066667*S(3)*B(-3)-.4129066667*S(3)*B(-2)-.4129066667*S(3)*B(-1)-4.129066667*S(3))*B(-3)-.4129066667*(.2906666667-.4129066667*S(3)*B(-3)-.4129066667*S(3)*B(-2)-.4129066667*S(3)*B(-1)-4.129066667*S(3))*B(-2)-.4129066667*(.2906666667-.4129066667*S(3)*B(-3)-.4129066667*S(3)*B(-2)-.4129066667*S(3)*B(-1)-4.129066667*S(3))*B(-1)+1.704919154*S(3)*B(-3)+1.704919154*S(3)*B(-2)+1.704919154*S(3)*B(-1)+17.04919154*S(3))*B(-3)-.4666666667*(-.9095153783-.4129066667*(.2906666667-.4129066667*S(3)*B(-3)-.4129066667*S(3)*B(-2)-.4129066667*S(3)*B(-1)-4.129066667*S(3))*B(-3)-.4129066667*(.2906666667-.4129066667*S(3)*B(-3)-.4129066667*S(3)*B(-2)-.4129066667*S(3)*B(-1)-4.129066667*S(3))*B(-2)-.4129066667*(.2906666667-.4129066667*S(3)*B(-3)-.4129066667*S(3)*B(-2)-.4129066667*S(3)*B(-1)-4.129066667*S(3))*B(-1)+1.704919154*S(3)*B(-3)+1.704919154*S(3)*B(-2)+1.704919154*S(3)*B(-1)+17.04919154*S(3))*B(-2)-.4666666667*(-.9095153783-.4129066667*(.2906666667-.4129066667*S(3)*B(-3)-.4129066667*S(3)*B(-2)-.4129066667*S(3)*B(-1)-4.129066667*S(3))*B(-3)-.4129066667*(.2906666667-.4129066667*S(3)*B(-3)-.4129066667*S(3)*B(-2)-.4129066667*S(3)*B(-1)-4.129066667*S(3))*B(-2)-.4129066667*(.2906666667-.4129066667*S(3)*B(-3)-.4129066667*S(3)*B(-2)-.4129066667*S(3)*B(-1)-4.129066667*S(3))*B(-1)+1.704919154*S(3)*B(-3)+1.704919154*S(3)*B(-2)+1.704919154*S(3)*B(-1)+17.04919154*S(3))*B(-1))*T(i)^3

 

5+75.85*T(i)+(-21.81329000-1.071000000*(.2906666667-.4129066667*S(3)*B(-3)-.4129066667*S(3)*B(-2)-.4129066667*S(3)*B(-1)-4.129066667*S(3))*B(-3)-1.071000000*(.2906666667-.4129066667*S(3)*B(-3)-.4129066667*S(3)*B(-2)-.4129066667*S(3)*B(-1)-4.129066667*S(3))*B(-2)-1.071000000*(.2906666667-.4129066667*S(3)*B(-3)-.4129066667*S(3)*B(-2)-.4129066667*S(3)*B(-1)-4.129066667*S(3))*B(-1)+4.422230400*S(3)*B(-3)+4.422230400*S(3)*B(-2)+4.422230400*S(3)*B(-1)+44.22230400*S(3))*T(i)^2+(2.219127367-.1820700000*(.2906666667-.4129066667*S(3)*B(-3)-.4129066667*S(3)*B(-2)-.4129066667*S(3)*B(-1)-4.129066667*S(3))*B(-3)-.1820700000*(.2906666667-.4129066667*S(3)*B(-3)-.4129066667*S(3)*B(-2)-.4129066667*S(3)*B(-1)-4.129066667*S(3))*B(-2)-.1820700000*(.2906666667-.4129066667*S(3)*B(-3)-.4129066667*S(3)*B(-2)-.4129066667*S(3)*B(-1)-4.129066667*S(3))*B(-1)+.7517791681*S(3)*B(-3)+.7517791681*S(3)*B(-2)+.7517791681*S(3)*B(-1)+7.517791681*S(3))*T(i)^3

 

20+7.60*T(i)+(14.00564000-.7140000000*(.2906666667-.4129066667*S(3)*B(-3)-.4129066667*S(3)*B(-2)-.4129066667*S(3)*B(-1)-4.129066667*S(3))*B(-3)-.7140000000*(.2906666667-.4129066667*S(3)*B(-3)-.4129066667*S(3)*B(-2)-.4129066667*S(3)*B(-1)-4.129066667*S(3))*B(-2)-.7140000000*(.2906666667-.4129066667*S(3)*B(-3)-.4129066667*S(3)*B(-2)-.4129066667*S(3)*B(-1)-4.129066667*S(3))*B(-1)+2.948153600*S(3)*B(-3)+2.948153600*S(3)*B(-2)+2.948153600*S(3)*B(-1)+29.48153600*S(3))*T(i)^2+(14.40924560-.9805600000*(.2906666667-.4129066667*S(3)*B(-3)-.4129066667*S(3)*B(-2)-.4129066667*S(3)*B(-1)-4.129066667*S(3))*B(-3)-.9805600000*(.2906666667-.4129066667*S(3)*B(-3)-.4129066667*S(3)*B(-2)-.4129066667*S(3)*B(-1)-4.129066667*S(3))*B(-2)-.9805600000*(.2906666667-.4129066667*S(3)*B(-3)-.4129066667*S(3)*B(-2)-.4129066667*S(3)*B(-1)-4.129066667*S(3))*B(-1)+4.048797611*S(3)*B(-3)+4.048797611*S(3)*B(-2)+4.048797611*S(3)*B(-1)+40.48797611*S(3))*T(i)^3

(1)


 

Download badSums2.mw

Dear friends,

Greetings.

How to get the second solution.

how to change the guess value in maple.

figure 1 plot in Matlab with two different initial guesses.

 

TWOSOLUTION.mw

 



 

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.

 

restart;
T := -S(xi)*S(xi)+mu*R(xi)-lambda;
                        2                    
                  -S(xi)  + mu R(xi) - lambda
Q := -S(xi)*R(xi);
                          -S(xi) R(xi)
u := a[0]+a[1]*S(xi)+b[1]*R(xi);
                 a[0] + a[1] S(xi) + b[1] R(xi)
diff(u, xi);
                  / d        \        / d        \
             a[1] |---- S(xi)| + b[1] |---- R(xi)|
                  \ dxi      /        \ dxi      /
Fr := Q*b[1]+T*a[1];
                         /      2                    \     
     -S(xi) R(xi) b[1] + \-S(xi)  + mu R(xi) - lambda/ a[1]
diff(Fr, xi);
       / d        \                    / d        \     
      -|---- S(xi)| R(xi) b[1] - S(xi) |---- R(xi)| b[1]
       \ dxi      /                    \ dxi      /     

           /         / d        \      / d        \\     
         + |-2 S(xi) |---- S(xi)| + mu |---- R(xi)|| a[1]
           \         \ dxi      /      \ dxi      //     
d := -T*R(xi)*b[1]-S(xi)*Q*b[1]+(-2*S(xi)*T+mu*Q)*a[1];
 /      2                    \                   2           
-\-S(xi)  + mu R(xi) - lambda/ R(xi) b[1] + S(xi)  R(xi) b[1]

     /         /      2                    \                 \   
   + \-2 S(xi) \-S(xi)  + mu R(xi) - lambda/ - mu S(xi) R(xi)/ a[

  1]
diff(d, xi);
 /         / d        \      / d        \\           
-|-2 S(xi) |---- S(xi)| + mu |---- R(xi)|| R(xi) b[1]
 \         \ dxi      /      \ dxi      //           

     /      2                    \ / d        \     
   - \-S(xi)  + mu R(xi) - lambda/ |---- R(xi)| b[1]
                                   \ dxi      /     

                        / d        \        2 / d        \        /
   + 2 S(xi) R(xi) b[1] |---- S(xi)| + S(xi)  |---- R(xi)| b[1] + |
                        \ dxi      /          \ dxi      /        \
   / d        \ /      2                    \
-2 |---- S(xi)| \-S(xi)  + mu R(xi) - lambda/
   \ dxi      /                              

             /         / d        \      / d        \\
   - 2 S(xi) |-2 S(xi) |---- S(xi)| + mu |---- R(xi)||
             \         \ dxi      /      \ dxi      //

        / d        \                  / d        \\     
   - mu |---- S(xi)| R(xi) - mu S(xi) |---- R(xi)|| a[1]
        \ dxi      /                  \ dxi      //     
h := -(-2*S(xi)*T+mu*Q)*R(xi)*b[1]-(-S(xi)^2+mu*R(xi)-lambda)*Q*b[1]+2*S(xi)*R(xi)*b[1]*T+S(xi)^2*Q*b[1]+(-2*T*(-S(xi)^2+mu*R(xi)-lambda)-2*S(xi)*(-2*S(xi)*T+mu*Q)-mu*T*R(xi)-mu*S(xi)*Q)*a[1];
 /         /      2                    \                 \       
-\-2 S(xi) \-S(xi)  + mu R(xi) - lambda/ - mu S(xi) R(xi)/ R(xi) 

           /      2                    \                 
  b[1] + 3 \-S(xi)  + mu R(xi) - lambda/ S(xi) R(xi) b[1]

                         /                                2         
          3              |   /      2                    \          
   - S(xi)  R(xi) b[1] + \-2 \-S(xi)  + mu R(xi) - lambda/  - 2 S(xi

    /         /      2                    \                 \
  ) \-2 S(xi) \-S(xi)  + mu R(xi) - lambda/ - mu S(xi) R(xi)/

                                                             \   
        /      2                    \                 2      |   
   - mu \-S(xi)  + mu R(xi) - lambda/ R(xi) + mu S(xi)  R(xi)/ a[

  1]
collect(expand(h+3*Fr*Fr+(4*omega+3)*Fr), S(xi), R(xi));
     /      2         \      4
R(xi)\3 a[1]  - 6 a[1]/ S(xi) 

                                                  3        /  
   + R(xi)(6 R(xi) a[1] b[1] - 6 b[1] R(xi)) S(xi)  + R(xi)\3 

       2     2                  2                   
  R(xi)  b[1]  - 6 R(xi) mu a[1]  + 12 a[1] mu R(xi)

                  2                                        \ 
   + 6 lambda a[1]  - 8 a[1] lambda - 4 omega a[1] - 3 a[1]/ 

       2        /        2                       2        
  S(xi)  + R(xi)\-6 R(xi)  mu a[1] b[1] + 6 R(xi)  mu b[1]

   + 6 R(xi) lambda a[1] b[1] - 5 R(xi) lambda b[1]

                                      \              /      2   2 
   - 4 R(xi) omega b[1] - 3 b[1] R(xi)/ S(xi) + R(xi)\3 a[1]  mu  

       2            2      2         2                
  R(xi)  - 3 a[1] mu  R(xi)  - 6 a[1]  mu R(xi) lambda

   + 5 a[1] mu R(xi) lambda + 4 omega a[1] mu R(xi)

           2       2                                  2
   + 3 a[1]  lambda  + 3 a[1] mu R(xi) - 2 a[1] lambda 

                                        \
   - 4 omega a[1] lambda - 3 a[1] lambda/

 

 

Hello;

 I am trying to verify the analytic solution of a electric and magnetic fields created by a small dipole antenna (also called "Hertzian dipole"). The study of a small dipole is ground zero of anyone learning about antennas as calculations are "relatively" easy if a mathematical software is used. As the title suggests, the fieldplot3d returns an empty box.

Here is some introduction for the problem in question:

 The procedure is relatively straightforward, first, current density vector is defined, from there, magnetic vector potential (named "vector A") is calculated. The curl of vector A gives the magnetic field (named "B-field") produced by the antenna. From B-field, H field is deduced as it is only a multiplication of the B-field by a constant.

 At this point, I try to plot the H-field, and it works like a charm. No problem at all.

The electric field (named "E-field") then, may be calculated by taking the curl of the H-field and multiplying by a constant.

 At this second point, I try to plot the E-field, however, Maple returns an empty box. 

First, I thaught, maybe it was a problem of division by 0, however, after redefining the axis ranges, the problem still persists. I am attaching the code and the images. Any help will be greatly appreciated.

PS: This is my first post and I am very new to maple, please indulgde me if I make some formatting and/or post mistakes

 

KB

First step: Verify calculations for Hertzian dipole

 

restart;

with(plots):

with(LinearAlgebra):

with(VectorCalculus):

#IMPORTANT: R is constant for the calculation of A

 

 

 

J:=Vector[column]([ 0 ,
                 0 ,
                 I_0/s ]);

J := I_0*e[z]/s

(1)

 

A := VectorCalculus:-`*`(VectorCalculus:-`*`(mu_0, 1/VectorCalculus:-`*`(4, Pi)), int(VectorCalculus:-`*`(VectorCalculus:-`*`(VectorCalculus:-`*`(J, exp(VectorCalculus:-`-`(VectorCalculus:-`*`(VectorCalculus:-`*`(I, k), R)))), s), 1/R), z = VectorCalculus:-`-`(VectorCalculus:-`*`(l, 1/2)) .. VectorCalculus:-`*`(l, 1/2)))

A := (1/4)*mu_0*exp(-I*k*R)*I_0*l*e[z]/(Pi*R)

(2)

A[1];

0

(3)

A[2];

0

(4)

A[3];

(1/4)*mu_0*exp(-I*k*R)*I_0*l/(Pi*R)

(5)

#Taking the curl of A:

#IMPORTANT: R is a function of x,y,z:

R:=sqrt(x^2+y^2+z^2);

(x^2+y^2+z^2)^(1/2)

(6)

 

 

 

#Defining B by taking the curl

B[1] := VectorCalculus:-`+`(diff(A[3], y), VectorCalculus:-`-`(diff(A[2], z))):

 

 

B[2] := VectorCalculus:-`-`(VectorCalculus:-`+`(diff(A[3], x), VectorCalculus:-`-`(diff(A[1], z)))):

 

 

B[3] := VectorCalculus:-`+`(diff(A[2], x), VectorCalculus:-`-`(diff(A[1], y))):

B:=Vector[column]([ B[1] ,
                 B[2] ,
                 B[3] ]):

 

 

mu_0:=4*Pi*10^(-7):

I_0:=2400:

f:=2500:

omega:=2*Pi*f:

c:=3*10^8:

k:=omega/c:

l:=3*10^(-2):

epsilon_0:=1/(mu_0*c^2):

 

 

 

B_plot:=fieldplot3d([B[1],B[2],B[3]], x=-1..1,y=-1..1,z=-1..1,fieldstrength=log,arrows=SLIM):

 

 

H:=(1/mu_0)*B:

 

H_plot:=fieldplot3d([H[1],H[2],H[3]], x=-1..1,y=-1..1,z=-1..1,fieldstrength=log,arrows=SLIM):

 

# Taking curl of H to find the E field:

 

E[1] := VectorCalculus:-`*`(1/VectorCalculus:-`*`(VectorCalculus:-`*`(I, omega), epsilon_0), VectorCalculus:-`+`(diff(H[3], y), VectorCalculus:-`-`(diff(H[2], z)))):

E[2] := VectorCalculus:-`*`(1/VectorCalculus:-`*`(VectorCalculus:-`*`(I, omega), epsilon_0), VectorCalculus:-`-`(VectorCalculus:-`+`(diff(H[3], x), VectorCalculus:-`-`(diff(H[1], z))))):

E[3] := VectorCalculus:-`*`(1/VectorCalculus:-`*`(VectorCalculus:-`*`(I, omega), epsilon_0), VectorCalculus:-`+`(diff(H[2], x), VectorCalculus:-`-`(diff(H[1], y)))):

E:=Vector[column]([ E[1] ,
                 E[2] ,
                 E[3] ]):

E_plot:=fieldplot3d([E[1],E[2],E[3]], x=1..500,y=1..500,z=1..500,fieldstrength=log,arrows=SLIM):

 

 

subs(x=1,y=1,z=1,H):

 

H_plot;

 

 

 

E_plot;

 

 

``


 

Download short_dipole_matrix_way_old_school.mw 

 

Foucault’s Pendulum Exploration Using MAPLE18

https://www.ias.ac.in/describe/article/reso/024/06/0653-0659

In this article, we develop the traditional differential equation for Foucault’s pendulum from physical situation and solve it from
standard form. The sublimation of boundary condition eliminates the constants and choice of the local parameters (latitude, pendulum specifications) offers an equation that can be used for a plot followed by animation using MAPLE. The fundamental conceptual components involved in preparing differential equation viz; (i) rotating coordinate system, (ii) rotation of the plane of oscillation and its dependence on the latitude, (iii) effective gravity with latitude, etc., are discussed in detail. The accurate calculations offer quantities up to the sixth decimal point which are used for plotting and animation. This study offers a hands-on experience. Present article offers a know-how to devise a Foucault’s pendulum just by plugging in the latitude of reader’s choice. Students can develop a miniature working model/project of the pendulum.

Hi! my name is Euge, i live in Argentina!
I´m solving a problem that ask me to find an ODE from a family of curves, 
I know this is pretty simple, I have to derive the equation two times, but i can´t find a comand in maple that helps me do that. Is there any?
Thank you! 

hi, I am trying to evaluate the following integrations (Note that; the values of alpha, lambda_1 and lambda_2) are random and they change with every iteration 

`λ1_B`[so] := 10.94:

``

W[1] := evalf[4](int(`α_B`[so]^2/((z-1+`α_B`[so])^2*(z^(`λ2_B`[so]/`λ1_B`[so])-1+`α_B`[so])), z = 1 .. infinity)); W[2] := evalf[4](int(z^(`λ2_B`[so]/`λ1_B`[so])*ln(z)/((z-1+`α_B`[so])^2*(z^(`λ2_B`[so]/`λ1_B`[so])-1+`α_B`[so])^2), z = 1 .. infinity)); W[3] := evalf[4](int(1/((z-1+`α_B`[so])^2*(z^(`λ2_B`[so]/`λ1_B`[so])-1+`α_B`[so])^2), z = 1 .. infinity)); W[4] := evalf[4](int(z^(`λ2_B`[so]/`λ1_B`[so])*ln(z)^2/((z-1+`α_B`[so])^2*(z^(`λ2_B`[so]/`λ1_B`[so])-1+`α_B`[so])^2), z = 1 .. infinity)); W[5] := evalf[4](int(1/((z-1+`α_B`[so])^3*(z^(`λ2_B`[so]/`λ1_B`[so])-1+`α_B`[so])), z = 1 .. infinity)); W[6] := evalf[4](int((z^(`λ2_B`[so]/`λ1_B`[so]))^2*ln(z)^2/((z-1+`α_B`[so])^2*(z^(`λ2_B`[so]/`λ1_B`[so])-1+`α_B`[so])^3), z = 1 .. infinity)); W[7] := evalf[4](int(z^(`λ2_B`[so]/`λ1_B`[so])*ln(z)/((z-1+`α_B`[so])^2*(z^(`λ2_B`[so]/`λ1_B`[so])-1+`α_B`[so])^3), z = 1 .. infinity)); W[8] := evalf[4](int(1/((z-1+`α_B`[so])^2*(z^(`λ2_B`[so]/`λ1_B`[so])-1+`α_B`[so])^3), z = 1 .. infinity)); W[9] := evalf[4](int(z^(`λ2_B`[so]/`λ1_B`[so])*ln(z)/((z-1+`α_B`[so])^3*(z^(`λ2_B`[so]/`λ1_B`[so])-1+`α_B`[so])^2), z = 1 .. infinity)); W[10] := evalf[4](int(1/((z-1+`α_B`[so])^4*(z^(`λ2_B`[so]/`λ1_B`[so])-1+`α_B`[so])), z = 1 .. infinity)); W[11] := evalf[4](int(1/((z-1+`α_B`[so])^3*(z^(`λ2_B`[so]/`λ1_B`[so])-1+`α_B`[so])^2), z = 1 .. infinity))

int(79.977249/((z+7.943)^2*(z^.1408592322+7.943)), z = 1 .. infinity)

 

Warning,  computation interrupted

 

Warning,  computation interrupted

 

0.1744e-1

 

Warning,  computation interrupted

 

0.3348e-2

 

Warning,  computation interrupted

 

Warning,  computation interrupted

 

Warning,  computation interrupted

 

Warning,  computation interrupted

 

Warning,  computation interrupted

 

``

``


 

Download ask_maple.mw

 

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