# 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