Math 3410,  Spring 2019


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.

Roughly, quizzes last for around 25-30 minutes. Midterm runs for the whole 75 minutes.
Homework policy will be announced later.


The exact outline will be updated as we go along.


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.93-100)
revision on linear constant coeff 
homogeneous ODE
1/24
p.119: B1-3, 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
prey-predator 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, predator-prey, phase plane analysis.
Formula for predator-prey 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 non-zero terms in each power series.
14
10.5
Bessel equation
4/30




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