1340ForShowA20X.mws

ForShowA20.mws
Thu Oct 20 08:18:16 MDT 2005

Housekeeping

>    restart:
with(plots,animate,display):
with(plottools, disk, arrow):

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Three Ways to Plot the Sine and Cosine

>    TRG := 0..2*Pi:

>    POLAR := coords=polar:   Maple rewrite obviate "polarplot"

>    TINTS := colour=[blue,red]:

>    plot([sin,cos],TRG, TINTS);

[Maple Plot]

>    plot([sin,cos],TRG, TINTS, POLAR);

[Maple Plot]

>    plot([cos,sin,TRG], TINTS);

[Maple Plot]

Lissajous and Other Parametric Curves (3.2)

>    S := 2: C := 1:

>    plot([cos(C*t),sin(S*t),t=TRG], TINTS);

[Maple Plot]

>    plot([exp(2*t), exp(2*t), t=-1..1]);

[Maple Plot]

Fun with Polar Plots (3.4 - a Maple rewrite)

>    S :=5:    

>    plot(sin(S*t), t=TRG, POLAR, scaling=CONSTRAINED);   

[Maple Plot]

>    tyee := 1/(3-2*cos(t));

tyee := 1/(3-2*cos(t))

>    plot( tyee, t=TRG, POLAR, scaling=CONSTRAINED);

[Maple Plot]

Fun with Animation (not in our text -- another Maple rewrite)

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Animating Blobs

>    [disk([1,2], 1/10, colour=red),
disk([0,5/2], 1/20, colour=cyan),
disk([-1,2], 1/7)]:

>    display(%, insequence=true);

[Maple Plot]

>    f := t -> t^2;

f := proc (t) options operator, arrow; t^2 end proc

>    BLIST := [ seq( disk([k, f(k)], 1/2), k=0..25) ]:

>    display(BLIST, insequence=true);

[Maple Plot]

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Animating Cartesian, Parametric, and Polar Plots (New-style Maple)

We have

                               plot(sin(S*t), TRG, POLAR);

  above.          

>    S := 3:  s := t -> sin(S*t);    r - sin(3t)

s := proc (t) options operator, arrow; sin(S*t) end proc

>    animate( plot, [s, 0..TT, POLAR], TT=TRG);

[Maple Plot]

Above we have

    plot([c,s,TRG], TINTS);

which we redo as

>    C := 3:  S := 2:

>    c := t -> cos(C*t):  
s := t -> sin(S*t);

s := proc (t) options operator, arrow; sin(S*t) end proc

>    animate( plot, [[c,s, 0..TTT]] , TTT=TRG);

[Maple Plot]

>   

Assignment #8

The assignment is to animate something.   Choose from among these:

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(i) Animate an example of  the secants approaching the tangent line in the limit definition of the derivative.

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(ii) Animate a Newton's Method example showing the x-intercepts of the tangent lines approaching the zero.

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(iii) Animate the cycloid.  Go to page 202 and read about the cycloid.

(A) Do problem 1(b)

(B) Animate the plot you did in part (A).

(C) Add to the animation the wheel with the peripheral blob roling with the blob following the cycloid.

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(iv) Some other animation using Maple -- get your instructor's assent (in email) before you launch.

 

Google: "animate Maple"

 In-class quiz at start of class, 10/27/05.

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