Anyone know Maple ?

[akya]

Well, it's worth 10% of my year in Maths...

So here's the things...

The surface of a hill is given with the following equation f(x,y)= exp(-3*x^2-y^2); . A "THING" is located at the initial point P(1, 3/2) and wants to make the ascension while maintaining at each point of its trajectory, the direction of the maximum variation rate.

The thing is I have to find and represent it on the same figure :

a ) the surface;

b ) the ascension trajectory (gradients, differential equation of the trajectory and the particular solution, parametric equations)

c ) the projection of the traject on the domain (parametric equations)

d ) the trajectory at the same altitude h = 0,4 (parametric equations),

Instructions:

The window in which it is displayed must be -2 <= x <= 2 ; -2 <= y <= 2 et 0 <= z <= 1, axes are of the type framed and the style of the surface, wireframe

The curves must be of different colors and large=3.

Can anyone help me ?

[chichigrande]

I have no clue what to do. Maybe some one else might be able to help.

[Klaas]

I'm afraid I can't help you, but I have a question

Do you know of any online information regarding Maple? I'll be using it next year, so maybe I can try it out already when I have some free time.

[akya]

no online info unfortunatly...and the labs I do in class are in french... care to try ?

A friend gave me clues and I was finally able to do the problem...want to know how ?

>restart: with(plots): with(linalg):
>f:=(x,y)->(-3*x^2-y^2);
>bla:=plot3d(f(x,y),x=-2..2,y=-2..2,view=[-2..2,-2..2,0..1],axes=framed,style=wireframe):
>display(bla);
>gradient:=((diff(f(x,y),x),diff(f(x,y),y)));
>subs(x=1,y=3/2,vector[gradient]]);
>trajectory:=diff(y(x),x)=gradient[2]/gradient[1];
>dsolve(diff(y(x),x)=y(x)/(3*x),y(x));
>dsolve({diff(y(x),x)=y(x)/(3*x),y(1)=3/2},y(x));
>x[a]:=t;
>y[a]:=3*t^(1/3)/2;
>plot([x[a],y[a],t=0..1]);
>ble:spacecurve([x[a],y[a],f(x[a],y[a])],t=0..1,color=pink,thickness=3):
>bli:spacecurve([x[a],y[a],0],t=0..1,color=orange,thickness=3):
>blo:spacecurve(sqrt(ln(1/0.4)/3)*cos(t),sqrt(ln(1/0.4))*sin(t),0.4],t=0..2*Pi,color=blue,thickness=3):
>display(bla,ble,bli,blo);

I you need any explanations, tell me

[Wijitmaker]

Sorry akya, if you were using mathmatica I could help, but I don't have maple.

[King Tutankhamun]

What is Maple? Is it a special language of math?

[chichigrande]

THat is what I was wondering. What excactly is the purpose of maple?

[akya]

Sorry akya, if you were using mathmatica I could help, but I don't have maple.

I told you I posted the solution

Found it finally

Maple is a program used to simplify the calculations and display 3d graphs...it can serve for all sorts of mathematical problems..

[Yiuel]

Beurk, Maple... I had to use it years before now (when I was 15) and all I can say is that it may be somehow powerful, I just hate Maple. Hope that I'll never use it again.