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第十八單元 平面上之參數方程式
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Parametric Equations A plane curve is determined by a pair of parametric equations t, Called the parameter, as measuring time
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Example Eliminate the parameter in Solution
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Example Solution
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Example
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Differentiation for parametric curve Theorem
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Example
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Area
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Example
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Some Famous Curves www.chit.edu.tw/mathmet
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Some Famous Curves
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> with(plots): > g1:=animatecurve([3*t/(1+t^3),3*t^2/(1+t^3),t=0..40],numpoints=400,frames=40, scaling=unconstrained): g2:=animatecurve([3*t/(1+t^3),3*t^2/(1+t^3),t=-0.6..-0.1],color=black,numpoints=400,frames=40, > scaling=unconstrained): g3:=animatecurve([3*t/(1+t^3),3*t^2/(1+t^3),t=-100..-1.6],color=blue,numpoints=400,frames=40,scaling=unconstrained): display(g1,g2,g3);
![> with(plots): > g1:=animatecurve([3*t/(1+t^3),3*t^2/(1+t^3),t=0..40],numpoints=400,frames=40, scaling=unconstrained): g2:=animatecurve([3*t/(1+t^3),3*t^2/(1+t^3),t=-0.6..-0.1],color=black,numpoints=400,frames=40, > scaling=unconstrained): g3:=animatecurve([3*t/(1+t^3),3*t^2/(1+t^3),t=-100..-1.6],color=blue,numpoints=400,frames=40,scaling=unconstrained): display(g1,g2,g3);](http://images.slideplayer.com/12/3373995/slides/slide_14.jpg "> with(plots): > g1:=animatecurve([3*t/(1+t^3),3*t^2/(1+t^3),t=0..40],numpoints=400,frames=40, scaling=unconstrained): g2:=animatecurve([3*t/(1+t^3),3*t^2/(1+t^3),t=-0.6..-0.1],color=black,numpoints=400,frames=40, > scaling=unconstrained): g3:=animatecurve([3*t/(1+t^3),3*t^2/(1+t^3),t=-100..-1.6],color=blue,numpoints=400,frames=40,scaling=unconstrained): display(g1,g2,g3);")
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Swallowtail Catastrophe Curve
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graph
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Ovals of Cassini
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Witch of Agnesi www.chit.edu.tw/mathmet
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Newton’s Parabola
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Newton’s Parabola (animator)
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單元結語 曲線以參數式來表示，在計算上及表示上 更加明顯和方便。 還有許多曲線的例子，在此無法一一介紹， 同學可進入本校網站 www.chit.edu.tw/mathmet 進入函數圖形，那裡有更動畫圖形和微積 分相關的分析。 www.chit.edu.tw/mathmet
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