Math 141 - Week 2 Notes Monday, January 18, 1999

Topics for this week -
  1. Polar coordinates in the plane -- polar curves can be viewed as a special kind of parametric curves. Calculus of polar curves (tangents, areas, arclength etc)
  2. Beginning of 3D calculus -- (x,y,z) coordinates, vectors in 2 and 3 dimensions, dot product and cross product.
Examples -
  1. Polar curves -- circles (r = 1, r = sin(theta)), flowers (r = sin(n theta) etc..), cardioids (r = 1+cos(theta)), spirals etc..
  2. Find the areas of the two parts of the "limacon" r = 1 - 2 cos(theta).
  3. Where on r = 1 - cos(theta) is the tangent line vertical?
  4. Find the length of r = 1 - cos(theta).
  5. Find equation of sphere of radius 3 centered at (3,2,4).
  6. Find the angle between the vectors (-3,1,-1) and (1,-1,0).
  7. 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.
  8. 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.

  1. Reading: Chapter 9, sections 9.3-9.5.
  2. More reading: From the Lab Manual, the section on polar plotting (pp 111-112) and solved problems on pp 161-162.
  3. 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 and 78.

    Section 9.5, p.578: # 12, 20, 26, 46.