Transcript Vector Valued Functions - TCC: Tidewater Community College

Vector Valued Functions
Section 1
Written by Richard Gill
Associate Professor of Mathematics
Tidewater Community College: Norfolk Campus
Example 1: Sketch the curve represented by
r (t )  cost i  3 sin t j
Solution: If x = cost and y = 3sint then
y2
9sin 2 t
y2
2
2
2
2
x 
 cos t 
 cos t  sin t  1  x 
1
9
9
9
2
This will be a vertical ellipse centered at the origin.
Example 2: Sketch the curve represented by
2
r(t)  t, t 2 , t 3
3
Solution: Begin with a table.
Example 3: Sketch the space curve represented by the intersection of the
surfaces x2  y 2  4 and z  x 2 Then represent the curve by a vector valued
function using the parameter x = 2sin(t).
Solution: The first surface can be represented as:
The intersection as:
The second as:
Example 3: Sketch the space curve represented by the intersection of the
surfaces x2  y 2  4 and z  x 2 Then represent the curve by a vector valued
function using the parameter x = 2sin(t).
Solution Continued:
x  2 sin t and x 2  y 2  4 
4 sin 2 t  y 2  4  y 2  4  4 sin 2 t 
y 2  4(1  sin 2 t )  y 2  4 cos2 t  y  2 cost
x  2 sin t and z  x 2  z  4 sin 2 t
http://www.youtube.com/user/EducatorVids?v=WZ6psE6qwo&feature=pyv&ad=8642525948&kw=parametric
You Tube Video on Parametric Equations
The link below takes you to a site constructed by Paul
Dawkins of Lamar University. As the course progresses we
would like to know whether the links that we provide are
helpful. By the same token, if you find links on your own
that you find helpful please share them with the class.
http://tutorial.math.lamar.edu/Classes/CalcIII/VectorFunctions.aspx#ThreeD_VecFcn_Ex2b
For comments on this
presentation you may email the
author Professor Richard Gill at
[email protected] or the publisher to
the VML at [email protected]