Parametric Equations Flashcards Preview

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Flashcards in Parametric Equations Deck (18):
1

Parametric curve

A set of points generated by a parametric equation

2

Parameter

The third variable, usually 't' upon which the independent or dependent variable depends

3

Forward orientaion

The direction in which the curve is generated as the parameter increases

4

Derivatives of Parametric curves

Written as [dy/dt]/[dx/dt]
h'(t)/g'(t)
h(t)- function that outputs the y-value
g(t)- function that outputs the x-value

5

Parametric equations for an ellipse/circle

x(θ)=cos(θ)*'r'
y(θ)=sin(θ)*'r'

6

Parametric equations for a hyperbola

x(θ)=sec(θ)*'r'
y(θ)=tan(θ)*'b'

b= √(c^2-a^2)
a= vertices of (0,±a) or (±a,0)
c= foci at (0,±a) or (±a,0)

7

Parametric equations for a parabola

x(θ)=2θ*r
y(θ)=θ^2*r

8

Parametric equations in colloidal dispersion/concentration

S

9

Translations and rotations of axis

A

10

Celestial orbit in Parametric equations

S

11

Length of the polar curve

L= ∫ √(f(θ)^2+f'(θ)^2)dθ

12

Arc Length with time

s(t)=∫|v(u)|du
from a to t

13

Curvature

How much the tangent vector changes given time

14

Curvature (given arc-length)

k=|d(r'/|r'|)/ds|

15

Curvature (given time)

k=|d(r'/|r'|)/dt|/|v|
Also
=|T'(t)/r'(t)|

16

Curvature (given a point)

k=(r"xr')/(|v|^3)

17

T-value of parametric equations

T=(r'/|r'|)

18

Parametric equation

An equation that either specifies x or y in terms of a third variable (usually 't')