第十八單元 平面上之參數方程式
Parametric Equations A plane curve is determined by a pair of parametric equations t, Called the parameter, as measuring time
Example Eliminate the parameter in Solution
Example Example Solution
Example
Example
Differentiation for parametric curve Theorem
Example
Area
Example
Some Famous Curves www.chit.edu.tw/mathmet
Some Famous Curves
Some Famous Curves
Some Famous Curves > 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);
Swallowtail Catastrophe Curve
graph
Ovals of Cassini
Ovals of Cassini
Witch of Agnesi www.chit.edu.tw/mathmet
Newton’s Parabola
Newton’s Parabola (animator)
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。