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.

    1. Reading: In Chapter 13, read sections 13.4,13.5,13.6. In Chapter 8, read section 8.1,8.4.
    2. 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: