This schedule is tentative. It will get more accurate as the semester progresses. (I will post the homework solution once the homework has been graded. The solution to problems on the manual will not be included. Also you can pick up the graded homework from my office in case you miss that in class. They will be in the box outside my office)

Reminder:

(1) I will give a final review session on the last day of class.

(2) You can pick up previous old homework assignment in the box.

(3) The final exam and final project will be handed out on the last day of class. They are both due 5:00pm of Wednesday, December 20 of 2006. Put your paper in the box if I am not in the office.

(4) I will still hold office hour until Wednesday, Dec 20. The time and place are the same. You can also make appointment if the schedule does not fit you.

P.S: Here is the grading scale I am using:

97% and up   A+; 94 - 96%     A; 91 - 93%     A-; 88 - 90%     B+; 85 - 87%     B; 82 - 84%      B-; 79 - 81%      C+

76 - 78%      C; 73 - 75%     C-; 69 - 72%      D+; 65 - 68%      D; 60 - 64%     D-; below 60%   F

 

Day

Topics

Reading

Homework

08/29

Introduction to ODEs

Manual Chapter 1,2

Sec 1.3, #2,8,17,21, Solution

08/31

ODEs and their solutions

 

Sec 2.1, #2,6,7,10,13,14,Solution

09/05

Solutions to separable equations

Manual Chapter 3 Page 28-35

Sec 2.2 #3,10,15,22, Manual Page 25 #3,4,8, Solution

09/07

Linear equations

 

Sec 2.4 #2,7,13,37, Manual Chapter 3, #2,6, Solution, Handout1

09/12

Mixing problems, Existence and uniqueness

 

Sec 2.5 #1,6, Manual Chapter 2, #19,36, Solution

09/14

Existence and uniqueness, Dependence on initial conditions

 

Sec 2.7 #1,2,9,26,30, Solution, Handout2

09/19

Autonomous equations and stability

Manual Chapter 3

Sec 2.9 #2,9,20,26(use dfield6 as your numerical solver), Solution

09/21

Modeling

Page 124-126 of the book

Sec 3.1 #2,12, Sec 3.3 #3,5,7, Solution

09/26

Numerical methods - Euler's method

Manual Chapter 4

Sec 6.1 #2,4, Solution

09/28

Runge-Kutta methods

Manual Chapter 5

Sec 6.2 #2,20, Manual Chapter 5 #2

(download eul,rk2,rk4 from http://math.rice.edu/~dfield/), Solution

10/03

Vectors and matrices

Manual Chapter 6, 8 (Page 105-118), 11(Page 154-164)

Section 7.1 #34,36,42,44,51,53, Solution

10/05

Solving systems of linear equations

 

Section 7.3 #14,16,17,23,24, Manual Chapter 8 #9, Solution, Here are the first midterm and its solution

10/10

Homogeneous and inhomogeneous systems

 

Sec 7.4 #4,6,8,24, Solution

10/12

Bases of a subspace

 

No homework

10/19

Bases of a subspace (continued)

 

Sec 7.5 #4,9,13,22,29, Solution

10/24

Determinants

Introduction to systems

Manual Chapter 11

Sec 7.7 #7,12,26,36

Sec 8.1 #7,12,13, Solution

10/26

Linear systems of ODEs
Properties of Linear Systems

Manual Chapter 13, P212-217

Sec 8.4 #4,6,14,21, Sec 8.5 #2,13,16,17,19,23

Solution

10/31

Planar systems of ODEs

 

Sec 9.1 #10,12,21,23, Solution

11/02

Planar systems of ODEs (continued)

 

Sec 9.2 #4,23,24,37,38,44, Solution

11/07

Higher dimensional systems

 

Sec 9.5 #7,21,27,40,48, Solution

11/09

The exponential of a matrix

 

Sec 9.6 #3,18,19,26,28,35,41, Solution

11/14

Higher order linear equations

 

Sec 9.8 #10,15,25,28, 31,40. Solution. Here are the second midterm and its solution

11/16

2nd order equations

Undetermined coefficients

 

Sec 4.3 #2,10,18,21,22,24, Sec 4.5 #2,6,17,19,25, Solution

11/21

Inhomogeneous systems and equations

 

Sec 4.6 #3,5, Sec 9.9 #1,7, Solution

11/28

The linearization of nonlinear systems

Manual Chapter 7

Sec 10.1 #2,4, Solution

11/30

Long term behavior of nonlinear systems

Manual Chapter 8 Page 114-118

Sec 10.2 #4,6,11, Solution

12/05

Invariant sets and the use of nullclines

 

Sec 10.3 #2,3,8, Solution

12/07

Final Review

 

Final exam, Solution, Final project, guidelines of project