Math 141 - Week 4 Notes Monday, February 1, 1999
Topics for this week -
- Lines, planes and quadric surfaces
in three-dimensional space
- Curves in 3-space, arclength
- Functions of two or more variables (domains, range, limits)
- Partial derivatives (first and higher, equality of "mixed partials")
Examples -
- Find equation of sphere of radius 3 centered at (3,2,4).
- 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.
- What is the surface 4x = y^2 -2z^2?
- Describe the curve given by x=6t, y=3sqrt(2) t^2, z=2t^3. Find its
length for t = 0..1.
- Describe the domain and graph of the function f(x,y) = ln(1-x^2-y^2).
- Find the partial derivatives of that function up to second order.
- What is the limit of x^2y^3/(2x^2+y^2) as (x,y) -> (0,0)?
Maple - To plot curves in three dimensions, use "spacecurve"
(pretty much like parametric plotting in 2D). For graphs of functions of
two variables, use "plot3d", for implicitly defined functions use
"implicitplot3d" -- Note that "spacecurve" and "implicitplot3d" are in the
"plots" library.
Fourth Homework Assignment - due on
FRIDAY, February 12.
- Reading: Chapter 11, section 11.6. In Chapter 12, read sections
12.1, 12.2, 12.3.
- More reading: From the Lab Manual, the sections on 3d
plotting and implicit 3d plotting (pp 117-124). Also look at the solved
problems on pp 166-169).
- Chapter 11 problems:
Make certain that you can do
all of the
Core problems for section 11.6.
But write up only the following to be handed in:
- Section 11.6, p. 722: # 6, 14, all of 17-24 (matching), 36, 38 (use
Maple to draw pictures for 6, 14, 36 and 38 -- you will need to
use.
- Chapter 12 problems: Make sure you can do all of the Core
problems for sections 12.1, 12.2, and 12.3. But write up
only the
following to be handed in:
- Section 12.1, p. 768: # 6, 12, 22, 36, 48, 52 (for all six of the
preceding, use Maple to draw the graphs, too), and all of 59-64
(matching)
- Section 12.2, p. 777: # 4, 24, 36, 46, 50 (use Maple for the last
one)
- Section 12.3, p. 784: # 8, 16, 32, 38, 56, 62, 72, 85