This course is a study of Ordinary Differential Equations (ODE's), including modeling physical systems.
- Solution of first-order ODE's by analytical, graphical and numerical methods;
- Linear ODE's, especially second order with constant coefficients;
- Undetermined coefficients and variation of parameters;
- Sinusoidal and exponential signals: oscillations, damping, resonance;
- Complex numbers and exponentials;
- Fourier series, periodic solutions;
- Delta functions, convolution, and Laplace transform methods;
- Matrix and first order linear systems: eigenvalues and eigenvectors; and
- Non-linear autonomous systems: critical point analysis and phase plane diagrams.
18.02 or 18.022 or 18.023 or 18.024 (corequisite), 18.01 or 18.014 (prerequisite)
These lectures will follow an "active learning" approach. The lecture period will be used to help you gain expertise in understanding, constructing, solving, and interpreting differential equations. You must come to lecture prepared to participate actively. At the first recitation you will be given a set of flashcards. Bring these with you to each lecture. (Extras will be available in lecture in case of need.) You will use them to announce your answer to questions posed occasionally in the lecture. In case of divided opinions a discussion will follow. As a further element of your active participation in this class, you will often be asked to spend a minute responding to a short feedback question at the end of the lecture. Despite the large size of this class, I will listen and respond to this feedback.
Edwards, C., and D. Penney. Elementary Differential Equations with Boundary Value Problems. 4th ed. Upper Saddle River, NJ: Prentice Hall, September 29, 1999. ISBN: 0130113018.
Polking. Ordinary Differential Equations using MATLAB®. 2nd ed. Upper Saddle River, NJ: Prentice Hall, June 1, 1999. ISBN: 0130113816.
Students will also receive two sets of notes "18.03: Differential Equations" by Arthur Mattuck, and my "18.03 Supplementary Notes."
These small groups will meet twice a week to discuss and gain experience with the course material. Even more than the lectures, the recitations will involve your active participation. Come prepared. Your recitation leader may begin by asking for questions, so be ready if you have them. He may then hand out problems for you to work on in small groups. Ask questions early and often. Your recitation leader will also hold office hours, a resource you should not overlook.
Another resource of great value is the tutoring room. This is staffed by experienced undergraduates. Extra staff is added before hour exams. This is a good place to go to work on homework.
The final grade will be based on three components of the course, which will be given equal weight:
Problem Set Policy Statement
We will drop the problem set with the lowest per-problem average score, and multiply up the remaining problem sets to give a total problem set score. There will be 8 problem sets, therefore, seven of the eight will constitute your PS grade component.
I will try to be very precise about what I expect you to learn in the course of this semester. You should plan to achieve a real mastery of a few Essential Skills (PDF), which are spelled out in the attached document. These are the skills courses at MIT with 18.03 as a prerequisite will expect you to have down cold, and the faculty teaching these next courses are aware of this list.
Assignments will be due at the end of each week. Each homework assignment will have two parts: a first part drawn from the book or notes, and a second part consisting of problems which will be handed out. Both parts will be keyed closely to the lectures, and you should form the habit of doing the relevant problems between successive lectures and not try to do the whole set on the night before they are due. Your recitation leader should have the graded problems sets available for you at the next recitation.
I encourage collaboration in this course, but I insist on honesty about it. If you do your homework in a group, be sure it works to your advantage rather than against you. Good grades for homework you have not thought through will translate to poor grades on exams. You must turn in your own writeups of all problems, and, if you do collaborate, please write on your solution sheet the names of the students you worked with. Because the solutions will be available immediately after the problem sets are due, no extensions will be possible.
Hour exams will be held during the lecture hour on three Fridays during the term. Examination rooms will be announced in lectures. If you must miss an exam, contact the Undergraduate Mathematics Office before the exam to arrange for a make-up which can be granted under certain limited circumstances such as illness or family emergency.
There will be a three hour comprehensive examination, during the Final Exam Period, at a time and place to be announced.
ODE Manipulatives ("Mathlets")
We will employ a series of specially written computer toys, or demonstrations, called "Mathlets." You will see them used in lecture occasionally, and each problem set will contain a problem based around one or another of them. (Note: Mathlets not currently available to OCW users.)