第十八單元 平面上之參數方程式.

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1 第十八單元 平面上之參數方程式

2 Parametric Equations A plane curve is determined by a pair of parametric equations t, Called the parameter, as measuring time

3 Example Eliminate the parameter in Solution

4 Example Example Solution

5 Example

6 Example

7 Differentiation for parametric curve
Theorem

8 Example

9 Area

10 Example

11 Some Famous Curves

12 Some Famous Curves

13 Some Famous Curves

14 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= ],color=black,numpoints=400,frames=40, > scaling=unconstrained): g3:=animatecurve([3*t/(1+t^3),3*t^2/(1+t^3),t= ],color=blue,numpoints=400,frames=40,scaling=unconstrained): display(g1,g2,g3);

15 Swallowtail Catastrophe Curve

16 graph

17 Ovals of Cassini

18 Ovals of Cassini

19 Witch of Agnesi

20 Newton’s Parabola

21 Newton’s Parabola (animator)

22 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 進入函數圖形，那裡有更動畫圖形和微積分相關的分析。