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 |
|
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 |
|
|
|
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 |
Manual Chapter 13, P212-217 |
Sec 8.4 #4,6,14,21, Sec 8.5 #2,13,16,17,19,23 |
|
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 |