Maple Questions and Posts

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Please explain the logic used to construct the plot below.

plots:-implicitplot(r >= cos(theta), r = 0 .. 1/3, theta = 0 .. 2*Pi, filledregions, coords = polar, numpoints = 5000, scaling = constrained)

I found that while using maple gui cases of corruption, stuck while typing etc. Hope this problem will get solved in coming version

Dear Users!

Hoped everything going fine with you. I want to make animation of ten solutions as given bellow but fail to do that. Please see it fix the problem. I shall be very thankful to u.
SOLNSuy[1, 1] := 2.5872902469406659197*10^(-20)-.65694549571241255901*y+1.9708364871372376767*y^2-1.3138909914248251176*y^3-1.6010739356637904911*10^(-19)*y^4;
SOLNSuy[2, 1] := -4.002204462000*10^(-20)-1.7879176897079605225*y+5.3637530691192141414*y^2-3.5758353794044226250*y^3-6.8309939211286845440*10^(-12)*y^4;
SOLNSuy[3, 1] := -1.1953264450000*10^(-19)-3.2481690589079594122*y+9.7445071767154794599*y^2-6.4963381177952273213*y^3-1.2292726248071398400*10^(-11)*y^4;
SOLNSuy[4, 1] := -2.6720465500000*10^(-19)-4.9239979672954025921*y+14.771993901873204315*y^2-9.8479959345587718955*y^3-1.9029826928878336000*10^(-11)*y^4;
SOLNSuy[5, 1] := 3.416928541000*10^(-20)-6.7268498492441931137*y+20.180549547714413714*y^2-13.453699698443639810*y^3-2.6580790570532587008*10^(-11)*y^4;
SOLNSuy[6, 1] := -2.554122292000*10^(-20)-8.5884528335125514887*y+25.765358500514014457*y^2-17.176905666966875698*y^3-3.4587270427710613504*10^(-11)*y^4;
SOLNSuy[7, 1] := -9.206107680000*10^(-20)-10.456823708331499352*y+31.370471124965259849*y^2-20.913647416590986491*y^3-4.2774005353527132160*10^(-11)*y^4;
SOLNSuy[8, 1] := 1.9644186790000*10^(-19)-12.293003938471349390*y+36.879011815379230436*y^2-24.586007876856948223*y^3-5.0932823222176363520*10^(-11)*y^4;
SOLNSuy[9, 1] := -3.775112769000*10^(-19)-14.068404975282556550*y+42.205214925807397100*y^2-28.136809950465931724*y^3-5.8908824448577377280*10^(-11)*y^4;
SOLNSuy[10, 1] := 1.146281780000*10^(-19)-15.762658869974768890*y+47.287976609878780960*y^2-31.525317739837422477*y^3-6.6589592851037286400*10^(-11)*y^4;
plots[animate](plot, [SOLNSuy[A, 1], y = 0 .. 1], A = 1 .. 10);

Special request:
@acer @Carl Love @Kitonum @Preben Alsholm

Simple example to illustrate the desired functionality:
Say we have a 2D vector function which describes the position of a particle

r := t -> <5*cos(Pi*t), 5*sin(Pi*t)>

We want to define the velocity and acceleration as functions, so we could do something like

v := t -> <diff(r(t)[1], t), diff(r(t)[2], t)>

The problem now is that we cannot call our velocity function with numeric arguments.
A simple solution is to call the function via "subs", as in

subs(t = 2, v(t))

but IMHO, this is not very elegant and I guess inefficient. Is there a command that enables for pulling out the evaluated result from diff such that it can be used directly as a functional expression ? I.e., I want to be able to call

v(2)

directly, without having to do substitutions.

 

EDIT:

I found that you can do

v := <diff(r(t)[1], t, diff(r(t)[2], t)>
v := unapply(v, t)

but please provide your recommendations. Thanks

Hi everyone:

I want to earn f(zeta) and zeta=x/a while the f(x) is: 

f:=(x)->A1*sin(k*x)+A2*cos(k*x)+A3*sinh(k*x)+A4*cosh(k*x)

zeta=x/a and a, k, A1..A4 are constants. 

f(zeta)=? 

 

 

Hello,

 

I have problem with usage of diff function. I need to compute partial derivative over  diff(varphi__l(t),t) in that equation.

T__ln := (1/2)*(diff(varphi__l(t), t))^2+((1/2*(m))*v__l+(1/2*(I))*(diff(varphi__l(t), t))^2)+((1/2*(m))*v+(1/2*(I))*(diff(varphi__l(t), t))^2)

If I am trying to use:

diff(T__ln, diff(varphi__l(t), t))

I get the error:

Error, invalid input: diff received diff(varphi__l(t), t), which is not valid for its 2nd argument
 

Hi all, this is my first post here, I'm finding Maple super interesting so far.

I had a little problem with plots, whenever I update my underlying function and re-run my cells it won't update the curve at all whether automatically or after selecting the entry and pressing `execute ! `.

I'd have the select and delete the plot and then re-plot again.

Is this how it is or there is something I'm missing?

LeadingTerm(y^2-x^2/y, plex(x, y));
 

(in Groebner:-LeadingTerm) the input is not polynomial in, {x, y}

how to do when fraction in it ?

it return error

plot(x mod 3, x=-5..5);

 

plots exactly the same as

 

plot(x, x=-5..5);

 

and

 

plot(floor(x) mod 3, x=-5..5);

 

The mod function is doing nothing, why?

 

If I do 5 mod 4 I get 1, as expected.

n := 0
u[0] := x^3+(1/2)*A*x^2
for k from 0 to n do
A[k] := sum((Diff(u[i], x))*(Diff(u[k-i], x)), i = 0 .. k);
A[k] := sum((diff(u[i], x))*(diff(u[k-i], x)), i = 0 .. k)
end do;
 

it gives A[0]:=0 which is incorrect. why? and how it will give correct answer?

Need the code of the following:

 

h is the step size could be 0.1 or 0.01 etc

Dear experts

I am trying to study linear version of the Navier-Stokes (NS) equation. I define NS equations in a way suggested in this page

restart;

with(PDEtools): with(Student[VectorCalculus]):

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

V:= VectorField(< v[1](x,z,t),0,v[3](x,z,t)>);

NavierStokes:= diff(V,t) - nu*Laplacian(V) +1/rho* Gradient(p(x,z,t)) - VectorField(< 0,0,-g>)=0;

the velocity components are intriduced as following

v[1]:=(x,z,t)->diff(f(z),z)*exp(I*k*x+(-1)*I*omega*t);

v[2]:=(x,z,t)->0;

v[3]:=(x,z,t)->(-1)*I*k*f(z)*exp(I*k*x+(-1)*I*omega*t);

So the problem is 2D model so that v[1] and v[3] satisfy incompresibility condition. It is clear that substituting velocity components into NS leads to differential equations for f(z). The general form of f(z) is

f(z) = a1*cosh(k*z)+a2*sinh(k*z)+a3*cosh(kappa*z)+a4*sinh(kappa*z).

my problems are

1) apply v[1], v[3] and find f(z) with Maple. then apply boundary conditions to find coeffs a[i] with Maple

2) In addition, Substituting the f(z) into BCs leads to a linear homogeneous system of equations for the coefficients. The vanishing of the determinant of this system which is the condition for the existence of a nontrivial solution is interested. How can I do that?

3) f(z) is for the case that the bottom is z=0 and surface is z=h. in my case bottom is z=-h and surface is z=0. how to do this in the solution. I dont know how to apply it.

4) calculate pressure

this file is what I did.

NSE.mw

The function evalf(  ) will encounter a critical bug when doing the following evaluation:

restart;
P1 := 1007;
P2 := 1014;
P3 := 1014.1;
evalf(P2 - P1, 2);
evalf(P3 - P1, 2);

The first evalf( ) returns a correct value, while the second one returns a wrong value.
This is really unbelievable!

Here is a little animation to wish all of you a Merry Christmas

FireWorks.mw


hello,

How I can remove this error for dsolve equation.

Thanks

2023.mw


 

"restart:Digits :=15: upsilon:=0.3:E(x):=E0*((x)/((b)))^(beta):rho(x):=rho0*((x)/((b)))^(beta):alpha(x):=alpha0*((x)/((b)))^(beta):a:=0.2:b:=1:omega:=100:E0:=390e9:rho0:=3900:T(x):=Ta+(Tb-Ta)/(ln(b/(a)))*(ln(x)-ln(a)):Ta:=373:Tb:=273:upsilon:=0.25:alpha0:=7e-6:  h(x):=(1-n*(x/(b)))^(k):n:=0.415196:k:=3:beta:=1:    dsys5 := {(1/(b))*( diff(u(x),x,x) )+(1/(b*h(x))*(diff(h(x),x))+1/(b*E(x))*(diff(E(x),x))+1/(b*(x)))*(diff(u(x),x))+((upsilon)/((b^(2)*x))*1/(h(x))*(diff(h(x),x))-1/((b*x)^(2))+(upsilon)/(b^(2)*(x))*1/(E(x))*(diff(E(x),x)))*b*u(x)+(1+upsilon)*((rho(x)*x*b*(omega^(2)))/(E(x))*(1-upsilon)-(alpha(x)*Ta)/(b)*(diff(T(x),x))-((diff(alpha(x),x))/(b)+(alpha(x)*diff(E(x),x))/(b*E(x))+(alpha(x)*diff(h(x),x))/(b*h(x)))*Ta*T(x) ),u(a) = 0,(E(b))/((1-upsilon^(2)))*(D^((1))(u)(b)+upsilon/(x)*D^((0))(u)(b))-(E(b)*alpha(b)*T(b)*Ta)/((1-upsilon^())) =-1}:dsol5 := dsolve(dsys5,abserr=1e-1, 'maxmesh'=900, numeric, method=bvp[middefer],output=listprocedure):fy := eval(u(x),dsol5)"

Error, invalid input: eval received dsol5, which is not valid for its 2nd argument, eqns

 

``


 

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