Table of Contents
Math 527: Differential Equations with Linear Algebra
Lecture: McConnell 208, MWF 8:10a-9:00am
Instructor: John F. Gibson. Office hours M 3-4pm, W 4-5pm, N309E Kingsbury Hall
Teaching assistants:
- Eric Laflamme (sections 1-3). Office hours M 10-11am, Tues 2-3pm, Kingsbury W353
- Evan Brand (sections 4-6). Office hours W 4-5pm, Thur 2-3pm, Kingsbury N316
Suggested text: Zill, A First Course in Differential Equations with Modeling Applications, 9th edition. Other options
Announcements
Homeworks
| homework | due | solutions | topic | notes |
|---|---|---|---|---|
| HW1 | 9/2 | HW1 solns | calculus review | includes table of Greek letters |
| HW2 | 9/9 | HW2 solns | separation of variables | problem 10 has typos and is too hard, please ignore |
| (HW #3) | HW3 solns | 1st order linear, exact eqns | will not be collected, do as exam prep | |
| HW4 | 9/23 | HW4 solns | 2nd order const coeff homog | |
| HW5 | 9/30 | HW5 solns | damped oscillations, judicious guessing | |
| (HW6) | HW6 solns | judicious guessing, variation of parameters | will not be collected, do as exam prep | |
| HW7 | 10/14 | HW7 solns | Basics of Laplace transforms | v2, fixed mistake in prob 1 |
| HW8 | 10/21 | HW8 solns | Laplace transforms, s and t translation | |
| (HW9) | HW9 solns | Laplace transforms, Heaviside and Dirac delta | will not be collected, do as exam prep | |
| HW9 solns (version 2) | another version of hw9 solutions | |||
| HW10 | 11/10 | HW10 solns | power series | |
| HW11 part 1 | 11/23 | hw11_part_1_solns.pdf | gaussian elimination and determinants | |
| HW11 part 2 | 11/23 | hw11_part_2_solns.pdf | linear systems | fixed typo in problems 6 and 7 |
| (HW12, v2) | HW12 solns | linear systems and power series | will not be collected, do as exam prep |
Exams
The Final exam is scheduled for 8-10am Wednesday Dec 14, 2011. The exam room follows the first letter of your last name
- A-J: McConnell 208
- K-Z: DeMeritt 112
You will be allowed a cheat sheet of any material you want, in your own handwriting, on one side of an 8.5 x 11 inch sheet of paper. I advise you to use the cheat sheet for Laplace transforms and general prescriptions about the classification and methods of solution of ODEs, rather than copying worked-out examples.
The approximate format of the exam will be
- one 1st order problem (linear, separable, exact)
- one or two 2nd order linear const coeff problems (homogeneous, judicious guessing, variation of parameters, reduction of order) (maybe two of these)
- one 2nd order linear const coeff problem (Laplace transforms)
- one series solution problem
- one linear system problem (matrix ODE)
- one conceptual problem
Here is a Practice Final Exam. And here are some brief solutions Practice Final Exam Solutions. Good luck!
Supplementary material
- Partial derivatives. A pretty good explanation by wikipedia. The important parts are the Introduction, the first third of the Basic Definition, and the Antiderivative Analog
- Wolfram Alpha and Wolfram Mathworld. Check your homework, deepen your knowledge.
- The Tacoma Narrows Bridge collapse: video and explanation. Note that the explanation I gave in class yesterday was wrong, according to this paper!
- The eigenvectors of a compound pendulum. This movie shows a 3-part pendulum with initial conditions set to match three linearly independent eigenvectors of the linearized dynamics. Once the pendulum bobs are released, you can see that the motion of the system in comprised of a fixed shape (the displacement of the three bobs corresponding to the three components of an eigenvector) multiplied by an oscillation in time (the complex part of the eigenvalue) and a slow decay of the magnitude of oscillation (the real part of the eigenvalue).
