akya Posted May 23, 2004 Report Share Posted May 23, 2004 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, wireframeThe curves must be of different colors and large=3.Can anyone help me ? Quote Link to comment Share on other sites More sharing options...

chichigrande Posted May 23, 2004 Report Share Posted May 23, 2004 I have no clue what to do. Maybe some one else might be able to help. Quote Link to comment Share on other sites More sharing options...

Klaas Posted May 23, 2004 Report Share Posted May 23, 2004 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. Quote Link to comment Share on other sites More sharing options...

akya Posted May 24, 2004 Author Report Share Posted May 24, 2004 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 Quote Link to comment Share on other sites More sharing options...

Wijitmaker Posted May 24, 2004 Report Share Posted May 24, 2004 Sorry akya, if you were using mathmatica I could help, but I don't have maple. Quote Link to comment Share on other sites More sharing options...

King Tutankhamun Posted May 24, 2004 Report Share Posted May 24, 2004 What is Maple? Is it a special language of math? Quote Link to comment Share on other sites More sharing options...

chichigrande Posted May 24, 2004 Report Share Posted May 24, 2004 THat is what I was wondering. What excactly is the purpose of maple? Quote Link to comment Share on other sites More sharing options...

akya Posted May 25, 2004 Author Report Share Posted May 25, 2004 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.. Quote Link to comment Share on other sites More sharing options...

Yiuel Posted May 27, 2004 Report Share Posted May 27, 2004 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. Quote Link to comment Share on other sites More sharing options...

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