Suggestion: Work ahead. If you have looked at the section and the corresponding problems before the lecture, then you will usually have two opportunities to ask questions (and at least a couple days) before we move on.
Date Chapter.Section/Topics or Page/Problems
M May 23 Introduction: What is an ODE? What kinds of ODEs are there, and
what do solutions look like?
HW: 1.1.1,7,11,15,22,23; 1.2.1,4,6,13
W 25 More ODEs and Euler's Method
HW: 1.3.2,8,9,14,16; 1.4.1-6,8,10,12,15-21
M 30 First Order Equations (Linear, Separable, Exact, Slope Fields)
HW: 2.1.2,4,11,14,16,20 (solve in three different ways)
22,28,34,37
Separable equations, Implicit solutions, and Exact Differentials
HW: 2.2.2,6,7,12,21,25,31
2.6.2,4,10,13,16
W June 1 2.3 Modeling
HW: 2.3.2,4,(6),9,11,13,19,23,27,30
F 3 Existence and Uniqueness
HW: 2.4.1-5,7-10,14,16,18,22,28-30
Autonomous ODE and equilibria
HW: 2.5.3,7,10,11,14-16,18,23
HW: 2.6.17,19,23,32
M 6 holiday
W 8 Numerical Methods
HW: 2.7.3,4,10,21(a-c),22(a)
2.8.3,4,10
Introduction to Nonlinear Systems (Chapters 3,7, and 6)
HW: 7.1.1,2,3,4
7.2.1
Review for first exam
M 13 Midterm Exam (tentative)
W 15 Nonlinear Systems: Linearization, straight line solutions
Review of Linear Algebra (Eigenvalues and Eigenvectors)
Linear Existence and Uniqueness Theorem for Systems
The Basis Theorem for Solution Space of Linear Homogeneous Systems
General Assignment: Analyze any linear transormation on R^2
e.g., Problems 3.1.13-32
HW: 3.2.1,3,5,9,13,15,18
3.3.17-24
3.4.1-4
NOTE: When I taught this course last semester there were
several non-Georgia Tech students who had not had any linear
algebra. So I did a full review of linear algebra. I am not
going to do that this semester. If you need to review linear
algebra, see the assigned problems from the Appendices below
(and read the Appendices).
M 20 Change of Basis, inverses, determinants, etc.
See the "General Assignment" above.
W 22 Last (full) Day in Tianjin
Isoclines and Separatrices
Catalog of diagonalizable systems
Complex ODEs
HW: 7.4.1,2
3.2.19,20,21,24
3.3.1,4,12,25,27
3.4.7,11,13
Th 23 Last Recitation in Tianjin
M 27 First Lecture in Shanghai
Solving All Constant Coefficient Systems
HW: 3.5.6,10,15,16
3.6.3,10,13-16
3.7.8
W 29 Summary of Linearization and Constant Coefficient Systems
HW: 7.1.5,6,12,19,20
READ section 7.2
7.2.5,6,8,21,22,23
7.3.3,4,6
7.4.3,4,6
READ Theorem 7.5.3
7.5.16
M July 4 Other techniques for nonlinear systems
Remember: You have three extra homwork tasks to present in
class today.
Describe as fully as you can the following topics:
1. Jordan form systems with zero eigenvalue
2. Oscillations for critically damped and overdamped oscillators
3. Phase plane diagram for a simple pendulum
Suggestion: Some people have asked about their grade. If you
are concerned about your grade, you should definitely work the
six assigned problems in sections 7.3 and 7.4 and present one of
them at the board in class or during office hours.
W 6 Second order linear ODE (introduction 4.1-4.5)
HW: Read sections 4.1,2, and 3
4.1.4,5,11,14-16,17,20,25,26
4.2.2-4,7,10,13-16,20,22
4.3.2,10,17,18,30,32
4.4.6,10,12,22,28-32
4.5.5,10,12,14,19
M 11 More details and discussion of oscillators (forcing)
HW: 4.6.2,4,7,9-11,15,16,28
W 13 More details and discussion of oscillators with forcing
Resonance
HW: 4.7.8,10,12,14,15,17,23
Introduction to Laplace Transforms
HW: 5.2.26
5.4.8,10,11,12
5.6.2-6
5.7.1-6,13
M 18 Laplace Transforms
Practice Final
W 20
F 23 Final Exam
=================
Last Semester's Schedule (for reference only):
W 16 2.7-8 Runge-Kutta methods
M 21 Spring Break
W 23
M 28 More linear algebra and some first order systems
I think we pretty well tackled Appendix A1, but for the record:
HW: A1.3,5,8,9,10(a)
HW: A2.1(a),(d),2,3,6,7,10,11,12,15
A3.1,2,3,10,11,12,13,14.
HW: 7.1.1,2,3,4
7.2.1
W Mar 2 More first order systems and more linear algebra
HW: A4.1,2,3,11,14,17.
M 7 Nonlinear Systems and linearization
Change of basis and determinants, inverses, etc.
General Assignment: Analyze any linear transormation on R^2
e.g., Problems 3.1.13-32
W 9 Rabbits and Foxes
HW: 3.2.1,3,5,9,13,15,18
3.3.17-24
3.4.1-4
M 14 Solving all linear constant coefficient systems
General assignment: Analyze any linear homogeneous constant
coefficient system e.g., Problems 3.1.13-32
W 16 Solving all liner constant coefficient systems (part II)
M 21 Solving all linear constant coefficient systems (enough already!)
W 23 A Second Pass through linear constant coefficient systems (And
you thought you were experts!)
M 28 Chapter 7: Hamiltonians, Liapunov Functions, and Pendula
W 30 Review
M April 4 Second Order Linear ODE (Chapter 4)
W 6 Second Midterm (Test 2)
M 11 Second order linear ODE (introduction 4.1-4.5)
HW: 4.1.4,5,11,14-16,17,20,25,26
4.2.2-4,7,10,13-16,20,22
4.3.2,10,17,18,30,32
4.4.6,10,12,22,28-32
4.5.5,10,12,14,19
W 13
W 20 Final remarks on forcing.
Laplace Transforms
M 25 Holiday
W 27 Review
Final Exam: Thursday May 5, 2011. 13:00.