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); |
| > | plot([sin,cos],TRG, TINTS, POLAR); |
| > | plot([cos,sin,TRG], TINTS); |
Lissajous and Other Parametric Curves (3.2)
| > | S := 2: C := 1: |
| > | plot([cos(C*t),sin(S*t),t=TRG], TINTS); |
| > | plot([exp(2*t), exp(2*t), t=-1..1]); |
Fun with Polar Plots (3.4 - a Maple rewrite)
| > | S :=5: |
| > | plot(sin(S*t), t=TRG, POLAR, scaling=CONSTRAINED); |
| > | tyee := 1/(3-2*cos(t)); |
| > | plot( tyee, t=TRG, POLAR, scaling=CONSTRAINED); |
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); |
| > | f := t -> t^2; |
| > | BLIST := [ seq( disk([k, f(k)], 1/2), k=0..25) ]: |
| > | display(BLIST, insequence=true); |
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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) |
| > | animate( plot, [s, 0..TT, POLAR], TT=TRG); |
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); |
| > | animate( plot, [[c,s, 0..TTT]] , TTT=TRG); |
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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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