MATHEMATICS 464
Differential Equations II
Spring 2001
Instructor:
Steven E. Rigdon, Ph.D. 1325 Science Building Phone: 6186502193 email: srigdon@siue.edu web: www.siue.edu/~srigdon.html 
Office Hours: Tuesday: 3:205:00 Thursday: 1:002:00 and 5:006:00 
Textbooks:
Fourier Series and Boundary Value Problems, by J. W. Brown and R. V. Churchill, McGrawHill
Differential Equations and Boundary Value Problems: Computing and Modeling, 2^{nd} Edition, by C. H. Edwards and D. E. Penney, Prentice Hall
Optional Books:
Computing Projects: Differential Equations and Boundary Value Problems, by C. H. Edwards and D. E. Penney, Prentice Hall [available in Textbook Rental]
Solutions Manual: Differential Equations and Boundary Value Problems, by C. H. Edwards and D. E. Penney, Prentice Hall [available in Bookstore]
Grading:
Points 

Midterm Exam 
100 
Notebooks and homework 
50 
4 Projects @ 25 points each, including at least 2 presentations 
100 
Final Exam 
150 
TOTAL 
400 
Notebooks and Homework:
After each class, I want you to rewrite and rework your notes in the notebook provided. In class we will often skip an example or a proof, but I will ask you to fill it in when you rework your notes. As you rework your notes, write in complete English sentences and give full explanations. I will also ask you to do specific homework problems at specific points in the notes. For example, in the first night of class I will ask you to work through Example 2 on p. 243 and work Exercise 24 from p. 252 before continuing on to the material on firstorder systems. Do not write in your "good" notebook during class. I will collect the notebooks a few times during the semester, sometimes at random, and sometimes with sufficient notice.
Projects:
Each student should do 4 projects during the term, and at least two of these must be presented before the class. Choose 2 projects from Group A, 1 project from group B, and 1 project from group C. Before you proceed with the work on a project, check with me. I would like to have all 12 projects done and presented before the class. You will have 15 for your presentation.
Group A 
Group B 
Group C 
4.1 Gravitation & Kepler's Laws of Planetary Motion 
8.2 Automatic Computation of Series Coefficients 
9.5 Heated Rod Investigations 
4.3 Comets and Spacecraft

8.3 Automating the Frobenius Series Method 
9.6 Vibrating Spring Investigations 
5.2 Automatic Calculation of Eigenvalues

9.2 Computer Algebra Calculation of Fourier Coefficients 

5.3 Earthquake Induced Vibrations of Multistory Buildings 
9.3 Fourier Series of Piecewise Smooth Functions 

6.1 Phase Portraits and FirstOrder Equations 

6.2 Phase Portraits of Almost Linear Systems 

6.3 Your Own Wildlife Preserve


Project 4 The Lorenz Attractor (p. 444)

Course Outline:
Week 
Dates 
Tuesday 
Thursday 
1 
January 9 & 11 
Í 4.1 FirstOrder Systems and Applications 
Í 4.2 The Method of Elimination 
2 
January 16 & 18 
Í 4.3 Numerical Methods for Systems 
Í 5.1 Matrices and Linear Systems

3 
January 23 & 25 
Í 5.1 Continued Student Presentations 
Í 5.2 The Eigenvalue Method for Homogeneous Systems 
4 
Jan 30 & Feb 1 
Í 5.3 SecondOrder Systems and Mechanical Applications

Í 6.1 Stability and the Phase Plane 
5 
February 6 & 8 
Í 6.1 Continued Student Presentations 
Í 6.2 Linear and Almost Linear Systems 
6 
February 13 & 15 
Í 6.3 Ecological Models: Predators and Competitors

Í 6.5 Chaos in Dynamical Systems 
7 
February 20 & 22 
Review Student Presentations 
MIDTERM EXAM 
8 
Feb 27 & Mar 1 
Í 8.1 Introduction and Review of Power Series

Í 8.2 Series Solutions Near Ordinary Points 
9 
March 6 & 8 
Í 9.1 Periodic Functions and Trigonometric Series 
Í 9.2 General Fourier Series & Convergence Student Presentations 
Spring Break ! ! 

10 
March 20 & 22 
Í 9.2 Continued Í 9.3 Fourier Sine and Cosine Series

Í 9.3 Fourier Sine and Cosine Series Student Presentations 
11 
March 27 & 29 
Í 9.4 Applications of Fourier Series 
Í 9.5 Heat Conduction and Separation of Variables 
12 
April 3 & 5 
Í 9.5 Continued Student Presentations 
Í 9.6 Vibrating String 
13 
April 10 & 12 
Í 9.6 Continued

Í 9.7 SteadyState Temperature and Laplace's Equation 
14 
April 17 & 19 
Í 9.7 Continued Student Presentations 
B&C Sections 1016 
15 
April 2426 
B&C Sections 1721, 24 
B&C Sections 2628 Student Presentations 
16 
Final Exam: Tuesday, May 1, 2001

Important Notes:
A grade of I (incomplete) can be given only under the following circumstances:
(1) the student is prevented by a medical or similar emergency from completing a small portion of the course requirements,
(2) the student presents valid documentation of the emergency, and
(3) the student is passing the course at the time of the emergency.
A grade of I cannot be given as an alternative to an E or UW.
Computing Projects:
We will use Mathematica in the classroom PH0304. I recommend Mathematica for the projects, but some of the projects may be done with Matlab. If you do not know Mathematica, let me know and we can schedule some time where you can get started with Mathematica. The lab reports may be written up using Mathematica as the word processor. Follow the directions in the tutorial handed out in the first week. Write your reports in complete English sentences. Justify your assertions by using clear and concise arguments. You may refer to Mathematica output (algebraic, numerical, or graphical) in your arguments. Deadlines for written project reports and oral presentations will be announced throughout the semester.
Homework Assignments:
Homework will be assigned during each class period. The homework assignments should be merged into your reworked class notes that you put in your notebook.