Ordinary Differential Equations: Math 106A

Fall 2003

Updated 12/13/03

 

Final Projects

 

FINAL EXAM SOLUTIONS page 1, 2, 3, 4, 5 (corrected: spiral sink, not sink!), and Mathematica plots etc ( notebook and html).

 

Happy holidays!

 

IMPORTANT: If you would like, you can have your oral project presentation count as an oral final exam. However, if you choose to do so, you must have, on average, very good to excellent assessments of your homework assignments and you must have turned in something plausible for all but one of the assignments. (I.e., you can have one missing and one lousy assignment, since your average homework score is computed dropping your two worst scores.) Scout's honor that the homeworks that count towards your average are principally original work (not copied from the solutions or others in the class); it's OK to get a few problems that way, but the bulk of the assignment should be your own work. Ask me if you have any questions about that. If you qualify for and choose to make use of this option, please let me know by the Tuesday after Thanksgiving (the earlier the better, though).
If you choose to take a written exam, the project will still contribute to your grade. In that situation, the project can only influence your grade for the better. If you have more specific questions, ask.

Also, if you're missing more than two homework assignments, expect that to influence your grade. Get in any late homework ASAP!!!

 

RELATIVELY NEW: Yet another take on complex conjugate eigenvalues and the associated solutions (page 1, 2, 3).

 

Mathematica notebooks

Arnold's cat Mathematica notebook (or html `hardcopy') from class and cat sketching hints (notebook or html `hardcopy') for homework.

Mathematica notebook on matric exponentiation: notebook (executable and modifiable in Mathematica), HTML file.

 

INSTRUCTOR INFORMATION

Instructor: Debra Lewis
Office: 213 Kerr
Phone: 459-2718
E-mail: lewis@math.ucsc.edu
Office hours: M 10:30-12:00, W 7:00-8:30 PM, and by appointment
 

TEXT

Differential Equations, second edition, by P. Blanchard, R. Devaney, G. Hall. Brooks/Cole.
 

COURSE WEBPAGE

Math 106A home
 

OPTIONAL GRAPHING SOFTWARE

Some simple numerical and graphics software is provided with the textbook. (Windows and Macs machines only, sorry!)

A phase portrait plotting Java applet.

A graphing utility called DPGraph is available for free to all UCSC students, faculty and staff. For further information, go to DPGraph information.

Mathematica, Maple, and Matlab are excellent multipurpose mathematical software packages, but cost money.

Supposed instructional computing lab software availability: DPGraph: BE 109; Mathematica 3.0: all instructional computing PC labs; Matlab 6.5: BE 109, Oakes, and Social Sciences I PC labs.
WARNING: The computing lab installations of mathematical software tend to be unstable. ``The PC lab ate my homework'' is not a valid justification for an incomplete assignment.
 

HOMEWORK POLICIES

There will be weekly homework assignments, given in class.
Homework assignments and solutions are available online, but assignments are not `locked in' until they've been given in lecture.

Late homework will not be accepted.
Your homework should be neatly written, with the pages securely fastened together and your name on every page.
 

EXAMS

 

GRADING

Your overall score in the course will be the best of three weighted averages of your homework, midterm, final exam, and final project scores.
Your two lowest homework scores will be dropped.
 

TENTATIVE LECTURE SCHEDULE:

Tuesday Thursday
September 25: 1.1-3   Review from a dynamical systems perspective
September 30: 1.5-7   Equilibria, bifurcations in 1-D October 2: 2.1-2   Modeling dynamical systems, 2-D vector fields
October 7: 2.2-3   Some special systems October 9: 2.4-5   Approximating solutions: Euler's method
October 14: 3.1   Linear systems October 16: 3.2   Eigenvectors and straight-line solutions
October 21: 3.3   Linear systems with real eigenvalues October 23: 3.4   Linear systems with complex eigenvalues
October 28: 3.6   Second-order linear systems, harmonic oscillators October 30: MIDTERM
November 4: 3.7   Trace-determinant plane, bifurcations November 6: 4.1-2   Forced harmonic oscillators
November 11:   HOLIDAY November 13: 4.2-3   Undamped forcing and resonance
November 18: 5.1   Equilibria of nonlinear systems November 20: 5.2   Qualitative analysis of nonlinear systems
November 25: 5.3   Hamiltonian systems (!!!) November 27:   HOLIDAY
December 2: 5.3   Existence and uniqueness of solutions December 4: 6.1   Laplace transforms