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Author: Juan Carlos Bustamante
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Exercice n. 23, section 3.2

On condisère la fonction f(x)=2x2+3xy+4y23x2+5y2f(x) = \frac{2x^2+3xy+4y^2}{3x^2 + 5y^2}

var('x,y') cm = colormaps.Blues def f(x,y) : return (2*x^2 + 3*x*y+4*y^2)/(3*x^2 + 5*y^2) def c(x,y): return f(x,y) S=plot3d(f,(x,-2,2),(y,-2,2),color = (c,cm), opacity=1, mesh=1) show(S, aspect_ratio = [1,1,3]) C=contour_plot(f, (x,-2, 2), (y,-2, 2), cmap='Blues',linestyles='solid', colorbar=True) show(C,figsize=4)
(x\displaystyle x, y\displaystyle y)
3D rendering not yet implemented
%md ## Exerice n. 42, section 3.2

Exerice n. 42, section 3.2

var('x,y') cm = colormaps.Blues def f(x,y) : return sin(x^2 + y^2)/(x^2 + y^2) def c(x,y): return 0.4+0.8*f(x,y) S=plot3d(f,(x,-pi, pi), (y,-pi, pi),color = (c,cm), opacity=1, mesh=1) show(S, aspect_ratio=[1,1,2]) C=contour_plot(f, (x,-3*pi, 3*pi), (y,-3*pi, 3*pi), cmap='Blues',linestyles='solid', colorbar=True) show(C,figsize=4)
(x\displaystyle x, y\displaystyle y)
3D rendering not yet implemented