Math 141 - Week 11 Notes Monday, March 29, 1999
Topics for this week -
- nonhomogeneous linear equation:methods of undetermined coefficients
- nonhomogeneous linear equations: Methods of variation of parameters
- Applications of second-order differential equations
- Series solutions
- sequence
- series
Covers: sections 15.6,15.7,15.8,10.1,10.2
Topics for next week -
- The integral test and estimates of sums
- The comparison test
- Alternating series
- Absolute Covergence
- Ratio test
- Root test
Covers: sections 10.3,10.4,10.5,10.6
Examples
- Solve the initial value problem y"-y=xe^{3x}, y(0)=0,y'(0)=1.
- Solve the initial value problem y"+y=1/cos(x).
- 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.
- Solve the initial value problem:
y''+x^{2}y=0,y(0)=1,y'(0)=0.
- Find the limits: a)
a_{n}=(n^{2}-1)/(n^{2}+1); b)
a_{n}=(-1)^{n}n^{2}/(1+n^{3}); c)
a_{n}=(-1)^{n}(n+1)/n.
- Find the limit of (1+1/n)^{n}.
- Problem #59, pp.607.
- Problem #16,22,36, pp.616.
Homework Assignment - Homework #11 Due Fri,April 9
- Reading: In Chapter 15, read sections
15.6,15.7,15.8. In Chapter 10, read sections 10.1,10.2.
- 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:
- Section 15.6, p.1002, #10,25;
- Section 15.7, p.1009, #2,3,5;
- Section 15.8, p.1014, #9 (list first 5 non-zero terms of the power
series);
- Section 10.1,p.607, #6,10,29,30,32,34,49,60,63;
- Section 10.2, p.616, #17,18,29,34,41,45,47,54 a),68.