# Math 141 - Week 8 Notes Monday, March 1, 1999

Topics for this week -

1. Double integrals in polar coordinates
2. moments and centers of mass
3. moment of inertia
4. surface area
5. differential equations
• covers: sections 13.4, 13.5, 13.6, 8.1
• Topics for next week -

1. Separable differential equations
2. Direction Fields
3. Homogeneous differential equations
4. Orthogonal Trajectories
5. First-order linear differential equations
6. Electric Circuits
7. Exact equations
8. Complex numbers
• covers: sections 8.1, 15.1,15.2,15.3,15.4 and Appendix H

Examples -

1. Evaluate the double integral of f(x,y)=srqt(x2+y2) over the region bounded by the cardioid r=1+cos(theta).
2. Evaluate int(exp(-x^2),x=0..infinity);
3. Find the mass and the center of mass: D={(x,y) | x=-1..1,y=0..1} and the density rho(x,y)=x2
4. Find the moments of inertia Ix,Iy,I0, where D is bounded by x=y2 and y=x-2, and rho(x,y)=3.
5. Find the area z=4-x2-y2 thatlies above the xy-plane.
6. Find an equation of the curve that passes through the point (1,1) and whose slope at (x,y) is y2/x3.
7. Logistic Growth.
8. Direction fields.

Eighth Homework Assignment - due on FRIDAY, March 19.