Math 141 - Week 2 Notes Monday, January 18, 1999
Topics for this week -
Polar coordinates in the plane -- polar curves can
be viewed as a special kind of parametric curves.
Calculus of polar curves (tangents, areas,
- Beginning of 3D calculus -- (x,y,z) coordinates,
vectors in 2 and 3 dimensions, dot product and
Polar curves -- circles (r = 1, r = sin(theta)),
flowers (r = sin(n theta) etc..), cardioids (r =
1+cos(theta)), spirals etc..
- Find the areas of the two parts of the "limacon" r
= 1 - 2 cos(theta).
- Where on r = 1 - cos(theta) is the tangent line
- Find the length of r = 1 - cos(theta).
- Find equation of sphere of radius 3 centered at
- Find the angle between the vectors (-3,1,-1) and
- Find the equation of the plane through the points
(0,1,), (-1,1,2) and (2,1,-1). Then find the
distance from (5,5,5) to the plane.
- If the cross product of V and W is zero, what can
you say about V and W? What about the dot product?
What if both are zero?
Maple - Not too much this week.You can see some polar
curves on pp 161-162 of the Lab Manual.
Second Homework Assignment - due on
FRIDAY, January 29.
- Reading: Chapter 9, sections 9.3-9.5.
More reading: From the Lab Manual, the section on
polar plotting (pp 111-112) and solved problems on
Make certain that you can do
all of the
Core problems for sections 9.4 and 9.5.
But write up only the following to be handed in:
Section 9,4, p. 572: # 24, 28, 34, use Maple
to do problems 44, 48 and 52, then do 68, 72
Section 9.5, p.578: # 12, 20, 26, 46.