I wonder - would it be possible to automate the following way of adding a legend to plots? If so - how?

plot([f(x), g(x), 7], legend = ['f(x)' = f(x), 'g(x)' = g(x), y = 7]);

In my opinion such a legend makes the plot much more readable - but most students (and others) will usually be too lazy to type this out, hence the wish for it be to automated.

Any help will be much appreciated.

In Maple 17, the following expression needs to be integrated with respect to q3, p3 and q. Here, mu is a real, positive scalar. 

a := 1/(sqrt(mu^2+(px-p3x-q3x)^2)*sqrt(mu^2+(-p3x+qx-q3x)^2)*sqrt(mu^2+q3x^2)*(sqrt(mu^2+(-p3x+qx-q3x)^2)+sqrt(mu^2+q3x^2)))

However, the integration will not work with the "int" command (e.g. wrt q3). The indefinite integration will work if the integral is evaluated using the steps: highlight expression -> right click -> Integrate -> wrt q3 command.

The output of the integral (using the above method) is very long, it's impossible to manipulate the answer (on my i5, 8GB machine running Maple 17) because it is very tough to copy such a long output. Also, there is no way to specify that mu is a positive scalar. 

Is there a better way to perform the integration, e.g. between 0 and lambda, -1 through 1, or -infinity to +infinity?  

Assume I had a 2D line

how to put and draw this line into a new geometric world defined by patch?

I have gotten an expression:

eq21 := collect(eq20, [exp(-sqrt(s)*x/sqrt(Dp)), exp(sqrt(s)*(-lh+x)/sqrt(Dp)), exp((-2*lh+x)*sqrt(s)/sqrt(Dp)), exp((lh-x)*sqrt(s+thetac)/sqrt(Dc))], simplify);

q(x, s) = exp(-sqrt(s)*x/sqrt(Dp))*_F1(s)+sqrt(Dp)*(-Dp*sqrt(s+thetac)*alpha1*pinf*s^2-2*Dp*sqrt(s+thetac)*alpha1*pinf*s*thetac-Dp*sqrt(s+thetac)*alpha1*pinf*thetac^2+A2*Dp*sqrt(s+thetac)*alpha1*s+A2*Dp*sqrt(s+thetac)*alpha1*thetac+Dc*sqrt(s+thetac)*alpha1*pinf*s^2+Dc*sqrt(s+thetac)*alpha1*pinf*s*thetac+A1*Dc*alpha1*s^2+A1*Dc*alpha1*s*thetac+A1*sqrt(Dc)*sqrt(s+thetac)*s^2+A1*sqrt(Dc)*sqrt(s+thetac)*s*thetac-A2*Dc*sqrt(s+thetac)*alpha1*s)*exp(sqrt(s)*(-lh+x)/sqrt(Dp))/((s+thetac)^(3/2)*(-sqrt(Dp)*alpha1+sqrt(s))*s*(Dc*s-Dp*s-Dp*thetac))+(sqrt(Dp)*alpha1+sqrt(s))*_F1(s)*exp((-2*lh+x)*sqrt(s)/sqrt(Dp))/(-sqrt(Dp)*alpha1+sqrt(s))+Dc*A1*exp((lh-x)*sqrt(s+thetac)/sqrt(Dc))/((Dc*s-Dp*s-Dp*thetac)*sqrt(s+thetac))-(-pinf*s-pinf*thetac+A2)/((s+thetac)*s)

I need to further simplify the coefficient of

exp(sqrt(s)*(-lh+x)/sqrt(Dp))

Would you like to give some tips?

Thanks.

how to calculate potential energy in terms of gauss curvature?

how to find back a patch in maple from Pi+GaussCurvature*Area(triangle) = Pi

restart:
with(LinearAlgebra):
EFG := proc(X)
local Xu, Xv, E, F, G;
Xu := <diff(X[1],u), diff(X[2],u), diff(X[3],u)>;
Xv := <diff(X[1],v), diff(X[2],v), diff(X[3],v)>;
E := DotProduct(Xu, Xu, conjugate=false);
F := DotProduct(Xu, Xv, conjugate=false);
G := DotProduct(Xv, Xv, conjugate=false);
simplify([E,F,G]);
end proc;

UN := proc(X)
local Xu,Xv,Z,s;
Xu := <diff(X[1],u), diff(X[2],u), diff(X[3],u)>;
Xv := <diff(X[1],v), diff(X[2],v), diff(X[3],v)>;
Z := CrossProduct(Xu,Xv);
s := VectorNorm(Z, Euclidean, conjugate=false);
simplify(<Z[1]/s|Z[2]/s|Z[3]/s>,sqrt,trig,symbolic);
end:

lmn := proc(X)
local Xu,Xv,Xuu,Xuv,Xvv,U,l,m,n;
Xu := <diff(X[1],u), diff(X[2],u), diff(X[3],u)>;
Xv := <diff(X[1],v), diff(X[2],v), diff(X[3],v)>;
Xuu := <diff(Xu[1],u), diff(Xu[2],u), diff(Xu[3],u)>;
Xuv := <diff(Xu[1],v), diff(Xu[2],v), diff(Xu[3],v)>;
Xvv := <diff(Xv[1],v), diff(Xv[2],v), diff(Xv[3],v)>;
U := UN(X);
l := DotProduct(U, Xuu, conjugate=false);
m := DotProduct(U, Xuv, conjugate=false);
n := DotProduct(U, Xvv, conjugate=false);
simplify([l,m,n],sqrt,trig,symbolic);
end proc:

GK := proc(X)
local E,F,G,l,m,n,S,T;
S := EFG(X);
T := lmn(X);
E := S[1];
F := S[2];
G := S[3];
l := T[1];
m := T[2];
n := T[3];
simplify((l*n-m^2)/(E*G-F^2),sqrt,trig,symbolic);
end proc:

sph := <f(u,v)|g(u,v)|h(u,v)>;
cur := GK(sph);
X := sph;
Xu := <diff(X[1],u), diff(X[2],u), diff(X[3],u)>;
Xv := <diff(X[1],v), diff(X[2],v), diff(X[3],v)>;
Z := CrossProduct(Xu,Xv);
AreaTriangle := int(int(Z[1]^2+Z[2]^2+Z[3]^2,v=-Pi/2..Pi/2),u=0..2*Pi);
dsolve(Pi+cur*AreaTriangle = Pi, [f(u,v),g(u,v),h(u,v)]);
 

I have a package of routines meant to help Danish highschool students use Maple. I would like to use MapleCloud to distribute this but have run into a major stumbling block:

While Maple is perfectly happy to use non-latin letters such as the Scandinavian letters æ, ø and å it seems that MapleCloud can't handle that. Specifically, strings containing such letters is displayed in garbled form (the non-latin letters are shows as squares), and symbolic names containing such characters seems not to be recognized. The latter problem in particular makes MapleCloud quite useless to me.

I have attached a simple workbook demonstrating the problems to this message.

 i need a help on how to find the local truncation error of a hybird block method of three order IVP. here is the one of the discrete methods i need to find the local truncation error. please any solution should put here thanks 

Please can someone help with maple comand to obtain Jacobian elliptic functions particularly in code editing region?

this equation is complicated

how to dsolve for this equation for function f ?

f(t,x,diff(x,t)) - f(t,x,p) - (diff(x,t)-p)*diff(f(t,x,p), p) = tan(t)
 

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> restart; with(PDETools), with(plots);
> n := .3; Pr := 7; Da := 0.1e-4; Nb := .1; Nt := .1; tau := 5;
> Eq1 := (1-n)*(diff(f(x, y), `$`(y, 3)))+(1+x*cot(x))*f(x, y)*(diff(f(x, y), `$`(y, 2)))-(diff(f(x, y), y))/Da+(diff(f(x, y), y))^2+n*We*(diff(f(x, y), `$`(y, 2)))*(diff(f(x, y), `$`(y, 3)))+sin(x)*(theta(x, y)+phi(x, y))/x = x*((diff(f(x, y), y))*(diff(f(x, y), y, x))+(diff(f(x, y), `$`(y, 2)))*(diff(f(x, y), x)));
> Eq2 := (diff(theta(x, y), `$`(y, 2)))/Pr+Nt*(diff(theta(x, y), y))^2/Pr+Nb*(diff(phi(x, y), y))*(diff(theta(x, y), y))/Pr+(1+x*cot(x))*f(x, y)*(diff(theta(x, y), y)) = x*((diff(f(x, y), y))*(diff(theta(x, y), x))+(diff(theta(x, y), y))*(diff(f(x, y), x)));
> Eq3 := Nb*(diff(phi(x, y), `$`(y, 2)))/(tau*Pr)+Nt*(diff(theta(x, y), `$`(y, 2)))/(tau*Pr)+(1+x*cot(x))*f(x, y)*(diff(phi(x, y), y)) = x*((diff(f(x, y), y))*(diff(phi(x, y), x))+(diff(phi(x, y), y))*(diff(f(x, y), x)));
> ValWe := [0, 5, 10];
> bcs := {Nb*(D[2](phi))(x, 0)+Nt*(D[2](theta))(x, 0) = 0, f(0, y) = ((1/12)*y)^2*(6-8*((1/12)*y)+3*((1/12)*y)^2), f(x, 0) = 0, phi(0, y) = -.5*y, phi(x, 12) = 0, theta(0, y) = (1-(1/12)*y)^2, theta(x, 0) = 1, theta(x, 12) = 0, (D[2](f))(x, 0) = Da^(1/2)*(D[2, 2](f))(x, 0)+Da*(D[2, 2, 2](f))(x, 0), (D[2](f))(x, 12) = 0};
> pdsys := {Eq1, Eq2, Eq3}; for i to 3 do We := ValWe[i]; ans[i] := pdsolve(pdsys, bcs, numeric) end do;
> p1 := ans[1]:-plot(theta(x, y), x = 1, color = blue); p2 := ans[2]:-plot(theta(x, y), x = 1, color = green); p3 := ans[3]:-plot(theta(x, y), x = 1, color = black);
> plots[display]({p1, p2, p3});

I would like to publish a technical paper about a renewable energy with you. I use Maple 2016. What i need?. Thanks!

im stuck here also still produces output but yeah  oh well :

Download MAPLE_BITTY.mw

I have a very large set of equations that calculates for a long time. Up until now, I have designated the second derivatives and copied the finished equation to another program to do the simulation. But with this file I can hardly do anything because the equations are too long. Even saving a file after computation is not easy. Export to PDF takes 20 minutes and the file has 120 MB and 1000 pages. Recording to .mw has not gone yet due to the occurrence of a write error message. I have 16 GB of RAM and after calculation is 14 GB in use.

5._Równanie_z_5_niewiadomymi.mw
Any suggestions?