MATHEMATICS 464

Differential Equations II

 

Spring 2001

 

Instructor:

 

Steven E. Rigdon, Ph.D.

1325 Science Building

Phone: 618-650-2193

e-mail: srigdon@siue.edu

web: www.siue.edu/~srigdon.html

Office Hours:

Tuesday: 3:20-5:00

Thursday: 1:00-2:00 and 5:00-6:00

 

 

Textbooks:

 

Fourier Series and Boundary Value Problems, by J. W. Brown and R. V. Churchill, McGraw-Hill

 

Differential Equations and Boundary Value Problems: Computing and Modeling, 2nd 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 first-order 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 First-Order 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 First-Order 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 Second-Order 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 Steady-State Temperature and Laplace's Equation

14

April 17 & 19

Í 9.7 Continued

Student Presentations

B&C Sections 10-16

15

April 24-26

B&C Sections 17-21, 24

B&C Sections 26-28

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.