titre = nom, date

(1) crtl_k, ctrl-j

(2) titre

(3) save

(4) print .... utiliser preview

(5) coller= F4, décoller =F5 (cf menu Edit)

(6) supprimer une cellule : Ctrl-del

sin : fonction, type procedure
sin(t) : résultat, type function

> whattype(sin);
whattype(eval(sin));
whattype(sin(t));

> plot(sin);

> plot(sin(t));

Plotting error, empty plot

> plot(sin(t), t=-5..5, color= blue, linestyle=24);

> Pi, evalf(Pi)<> evalf(pi);

> plot(sin(t), t=-5..5, y, color= blue, linestyle=24, tickmarks=[[ evalf(Pi/2)="Pi/2"], [-1,1]]);

aide = F1

missing semi-colon

> plot(sin(t), t=0..Pi, filled=true);

deux point pour ne pas afficher

> pl1:= plot(sin(t), t=-5..5, y, color= blue, linestyle=24, tickmarks=[[ evalf(Pi/2)="Pi/2"], [-1,1]]) :

> pl2:= plot(sin(t), t=0..Pi, filled=true):

> display(pl1, pl2);

>

Sections Ctrl-point

>

approximations de Taylor

> series(sin(t),t); series(sin(t),t,12); series(cos(t),t,12);

> tmp:= series(sin(t),t) + series(cos(t),t,12);

> whattype(series(sin(t),t));

> series(tmp, t,10);

> mtaylor(sin(t),t,10);

> pl1:= plot(mtaylor(sin(t),t,2), t=-10..10):

> pl2:= plot(mtaylor(sin(t),t,4), t=-10..10):

> display(pl1,pl2, view=[DEFAULT, -50..50]);

seq donne une suite càd DES objets

> sq:= seq( mtaylor(sin(t),t,2*k), k=1..4);

> plot( [sq], t=-Pi..Pi, color=[blue, red, green], view=[DEFAULT, -1..1]);

>

Newton

> tmp:= (1- z)/(z+2); whattype(%);

> f:= unapply(tmp, z);

> pl1:= plot(f(t), t=-10..10):

> pl2:= plot(t, t=-10..10, color=blue):

> x0:= -1.; li:= seq( (f@@k)(x0), k=1..5);

> pl3:= plots[pointplot]([[-1,0], [-1,2], [2,2]], style=line, color=green): %;

> pl3:= plots[pointplot]([-1,0,-1,2,2,2], style=line, color=green): %;

> pl3:= plots[pointplot]([-1,0,-1,2$4,-0.25$4,0], style=line, color=green): %;

> li;
seq(k$4, k=li);

ctrl-z pour annuler la dernière action

> pl3:= plots[pointplot]([-1,0,-1, seq(k$4, k=li[1..-2]), li[-1]$3 ], style=line, color=green): %;

> display(pl1, pl2,pl3, view=[-1..3, -1..2.5], scaling=constrained);

>

> x0:= -6.; li:= seq( (f@@k)(x0), k=0..8);

> pl4:= plots[pointplot]([li[1]$3, seq(k$4, k=li[1..-2]), li[-1]$3 ], style=line, color=green):

> display(pl1, pl2, pl4, view=[-7..4, -7..4]);

reperage de coordonnées sur le graphe

répétition ==> procedure : nom := proc() .... end

> tracer:= proc(x0, nbit) local li, pl4; li:= seq( (f@@k)(x0), k=0..nbit);

> pl4:= plots[pointplot]([li[1]$3, seq(k$4, k=li[1..-2]), li[-1]$3 ], style=line, color=green):

> display(pl1, pl2, pl4, view=[-7..8, -7..8]);

> end :

> tracer(-3.2, 15);

> alpha, beta:= solve(f(z)=z); fsolve(f(z)=z); fsolve(f(z)=z, z=-5..0);

> D(f)(alpha); evalf(%);
D(f)(beta); evalf(%);

Pourquoi sont-ils inverses ?

> map( ((z->z)=evalf)@rationalize@D(f), [alpha, beta]) ;

> phi:= unapply( (z-beta)/(z-alpha),z);

> 'theta=phi(z), Theta=phi(f(z))'; solve({%}, {z, Theta}):
map(collect, rationalize(%), theta, expand);

>

>

>

>