There will be a midterm and a final, plus 4 quizzes.
Tentatively, homework 10%, each
quiz 10%, midterm 20%, final 30%
Tentative dates: 2/5 (quiz), 2/19 (quiz), 3/12 (midterm),
4/9 (quiz), 4/30 (quiz), final exam
All of them on Tuesday.
Week  Section  Topic  Lecture date 
Homework Exercises (turn in the red color ones) 
H/W Due date 
Quiz/exam date Study guide 

1 
Read Chapter 4; theorems 4.1.2, 4.1.3, 4.2.1, 4.2.2. 
revision on existence and uniqueness of ODE 
1/22 

Read section 5.5 (p.93100) 
revision on linear constant coeff homogeneous ODE 
1/24 
p.119: B13, 8,14, 18, 24 

5.1 
linear homogeneous equations 
1/24 

2 
5.2 
linear independence and
Wronskian 
1/29 
p.119: A2, A3, A10, A11 
2/5 
2/5 Quiz Constant coeff linear homogeneous ODE, definitions of linearly independence and Wronskian, use Abel's Theorem. 
5.3 
reduction of order 
1/31 

3 
5.4.1 
variation of parameter 
2/5, 2/7 
p.119: use variation of parameter to solve: C7 (cf example 5.4.5), 13, 17 

5.5.1 
Euler equation 
2/7 
p.119: D18, 19 
2/12 

5.6 
Will skip that. But I expect
you already know method of undetermined coeff. Do some revision and reading. 

4 
5.7 
oscillatory
behavior 
2/12, 2/14 
p.119: D1,
5, 6 
2/19 

5 
5.8 
nonlinear 2nd order eqn 
2/19 
p.119: D11 
2/26 
2/19 Quiz Reduction of order, Euler equation, variation of parameter 
7.3 
Wronskian of a system 
2/21 

6 
7.4 
revision on 1st order linear constant coeff
homogeneous system and phase plane. Read 7.4 (for 2 by 2 systems) or your old text 
2/21, 2/26 
p.163: A4, B2, 3,
4, B11, D1 
3/5 

7 
8.1 
planar Hamiltonian system 
2/28, 3/5 
p.185: 6,
8, 10 
3/14 

8.2 
preypredator system 
3/7 
p.185: 14 
3/14 

8.3 
phase plane analysis 
3/7 

8 
3/12 
3/12 Midterm. Covers Ch 5 and 7. Mainly on material after 2nd quiz, i.e. 5.7, 5.8.1, 5.8.2, 7.3, 7.4 Definition of oscillating solutions; Definitions of linearly independence and Wronskian for vector functions; 

8.4 
On x''=f(x) 
3/14 

3/17 3/23 
Spring Break 

9 
8.4 
On x''=f(x) 
3/26 
p.185: 11, 20, 21, 30  3/28 

more examples on x''=f(x); motivation of eigenfunction problem 
3/28 

10 
Example 9.2.1 
We deviate from the text.
Basically we study 1 important example in depth. 
4/2 
p.196: 10, 11 
4/4 

Not in the text 
numerical series; series of
functions 
4/2 

Not in the text 
brief discussion of Sturm Liouville Theorem 
4/4 

11 
9.3 
heat equation 
4/9, 4/11 
p.196: 16 
4/16 
4/9 Quiz Covers all of Ch 8. That is, Hamiltonian systems, predatorprey, phase plane analysis. Formula for predatorprey is given in the revised formula sheet. Expect at least 1 problem for phase plane. 
Not in the text 
wave equation 
4/11 

12 
10.2 
power series 
4/16 

10.3 
ordinary point 
4/18, 4/23 
p.223: 4 
4/25 

13 
10.4 
Frobenius method 
4/23 

10.4 
4/25 
p.223: 1, 7, 8 
5/2 
4/30 Quiz One question on the heat equation, the other on ordinary point. Calculate at least 3 nonzero terms in each power series. 

14 
10.5 
Bessel equation 
4/30 

10.5 
last date of class 
5/2 
p.223: 9, 10 
