Math 141 - Week 7 Notes Monday, February 22, 1999
Topics for this week -
- Lagrange Multiplier
- Double integrals over rectangles
- Iterated Integrals
- Double integrals over general regions
- Double integrals in polar coordinates
Topics for next week -
- Double integrals in polar coordinates
- Applications of double integrals
- Surface area
- Separable and homogeneous differential equations
- First-order linear differential equations
Examples -
- Find the maximum and minimum values of x2-2*y2 on the unit disk.
Include checking the boundary!
- Classify all critical points of (x2+2y2) exp(-(x2+y2)).
- A pentagon is composed of a rectangle surmounted by an isosceles
triangle (so parameters are the
length/width of the rectangle and the base angle(s) of the
triangle) -- given a fixed perimeter P, maximize
the area.
- Find shortest distance from (1,2,0) to the elliptic cone z2 = x 2 + 2y2
- Minimize x4+y4+z4 on the plane x+y+z=1.
- Evaluate the double integral of ye^{x} on the triangular
region with vertices (0,0),(2,4),(6,0).
- Evaluate int(int(y*cos(x^2),x=y^2..9),y=0..3);
- Evaluate int(exp(-x^2),x=0..infinity);
Seventh Homework Assignment - due on FRIDAY, March
5.
- Reading: In Chapter 12, read sections
12.7,12.8. In Chapter 13, read sections 13.1, 13.2, 13.3, 13.4.
- Make sure you can do all of the Core
problems for sections 12.7,12.8, 13.1, 13.2, 13.3 and 13.4. But write up
only the
following to be handed in
(
from the old final exams):
- Section 12.7, p. 819, #8, 12, 26, 30, 42, 48 (it's ok to use Maple
to help with the algebra!)
- Section 12.8, p. 826, # 8, 16, 20, 30, 40.
- Section 13.1, p.837, #5,
- Section 13.2, p.842, #6,10,18,28,33
- Section 13.3, p.850, #5,8,12,16,22,28,36,40,45
The idea behind Lagrange Multiplier