Math 141 - Week 11 Notes Monday, March 29, 1999

Topics for this week -

  1. nonhomogeneous linear equation:methods of undetermined coefficients
  2. nonhomogeneous linear equations: Methods of variation of parameters
  3. Applications of second-order differential equations
  4. Series solutions
  5. sequence
  6. series
  • Covers: sections 15.6,15.7,15.8,10.1,10.2

    • Topics for next week -

    1. The integral test and estimates of sums
    2. The comparison test
    3. Alternating series
    4. Absolute Covergence
    5. Ratio test
    6. Root test
  • Covers: sections 10.3,10.4,10.5,10.6

    • Examples

    1. Solve the initial value problem y"-y=xe3x, y(0)=0,y'(0)=1.
    2. Solve the initial value problem y"+y=1/cos(x).
    3. A spring with a 3-kg mass is held stretch 0.6 m beyond its natural length by a force of 20 N. If the spring begins at its equilibrium position but a push gives it an initial velocity of 1.2 m/s, find the position of the mass after t seconds.
    4. Solve the initial value problem: y''+x2y=0,y(0)=1,y'(0)=0.
    5. Find the limits: a) an=(n2-1)/(n2+1); b) an=(-1)nn2/(1+n3); c) an=(-1)n(n+1)/n.
    6. Find the limit of (1+1/n)n.
    7. Problem #59, pp.607.
    8. Problem #16,22,36, pp.616.

    Homework Assignment - Homework #11 Due Fri,April 9
    1. Reading: In Chapter 15, read sections 15.6,15.7,15.8. In Chapter 10, read sections 10.1,10.2.
    2. Make sure you can do all of the Core problems for sections 15.6,15.7, 15.8,10.1,10.2. But write up only the following to be handed in: