# Math 141 - Week 4 Notes Monday, February 1, 1999

Topics for this week -

1. Lines, planes and quadric surfaces in three-dimensional space
2. Curves in 3-space, arclength
3. Functions of two or more variables (domains, range, limits)
4. Partial derivatives (first and higher, equality of "mixed partials")

Examples -

1. Find equation of sphere of radius 3 centered at (3,2,4).
2. 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.
3. What is the surface 4x = y^2 -2z^2?
4. Describe the curve given by x=6t, y=3sqrt(2) t^2, z=2t^3. Find its length for t = 0..1.
5. Describe the domain and graph of the function f(x,y) = ln(1-x^2-y^2).
6. Find the partial derivatives of that function up to second order.
7. 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.
1. Reading: Chapter 11, section 11.6. In Chapter 12, read sections 12.1, 12.2, 12.3.
2. 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).
3. 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.
4. 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