Math 141 - Week 8 Notes Monday, March 1, 1999
Topics for this week -
- Double integrals in polar coordinates
- moments and centers of mass
- moment of inertia
- surface area
- differential equations
covers: sections 13.4, 13.5, 13.6, 8.1
Topics for next week -
- Separable differential equations
- Direction Fields
- Homogeneous differential equations
- Orthogonal Trajectories
- First-order linear differential equations
- Electric Circuits
- Exact equations
- Complex numbers
covers: sections 8.1, 15.1,15.2,15.3,15.4 and Appendix H
Examples -
- Evaluate the double integral of
f(x,y)=srqt(x^{2}+y^{2}) over the region bounded by the
cardioid r=1+cos(theta).
- Evaluate int(exp(-x^2),x=0..infinity);
- Find the mass and the center of mass: D={(x,y) | x=-1..1,y=0..1}
and the density rho(x,y)=x^{2}
- Find the moments of inertia
I_{x},I_{y},I_{0}, where D is bounded by
x=y^{2} and y=x-2, and rho(x,y)=3.
- Find the area z=4-x^{2}-y^{2} thatlies
above the xy-plane.
- Find an equation of the curve that passes through the point (1,1)
and whose slope at (x,y) is y^{2}/x^{3}.
- Logistic Growth.
- Direction fields.
Eighth Homework Assignment - due on FRIDAY, March
19.
- Reading: In Chapter 13, read sections 13.4,13.5,13.6. In
Chapter 8, read section 8.1,8.4.
- Make sure you can do all of the Core
problems for sections 13.4 and 8.1. But write up
only the
following to be handed in:
- Section 13.4, p.856, #5,8,12,19,20,25,31
- Section 13.5, p.862, # 8, 13,19,20
- Section 13.6, p.864, #1,8.
- Section 8.1, p.511, #6,8,14,18,29,35.