Here is a schedule
of the topics and sections
we will cover, as well as the timing of the tests.
The test dates are firm, but we will expand or contract class discussions
of the topics in accordance with the class's rate of learning.
The tests will cover only the material we have finished at the time
of the test.
F = Fundamentals of Differential Equations,
M = Matrix Operations
| Introduction | F, Chap. 1 and 2 | 9/6 - 9/16 | |
| Modelling | F, Chap. 3 | 9/19 - 9/21 | |
| Linear Algebra | M, Chap. 1-6 | 9/22 - 10/4 | |
| Test 1 | Wed, Oct. 5 | ||
| Second order equations | F, Chap. 4 | 10/7 - 10/21 | |
| Higher order equations | F, Chap. 6 | 10/24 - 10/26 | |
| Test 2 | Fri, Oct. 28 | ||
| Linear Algebra (cont.) | M, Chap. 7 | 10/31 - 11/4 | |
| Systems | F, Chap. 9 | 11/7 - 11/21 | |
| Test 3 | Wed, Nov 23 | ||
| Thanksgiving Break | 11/24 - 11/27 | ||
| Laplace Transforms | F, Chap. 7 | 11/28 - 12/6 | |
| Power series | F, Chap. 8 | 12/7 - 12/14 | |
| Final Exam | Friday, Dec. 16 | 8:00 - 10:30 AM |
This is a payoff course, where everything you have learned up to this point will come together to allow you to solve much more sophisticated problems.
Linear equations can be solved quickly and efficiently, and lead to notions like the number of degrees of freedom of a system, or the number of independent constraints on a system.
In algebra and in much of calculus, solutions to problems consist of single numbers: the maximum volume, or minimum perimeter, or an area or speed. In contrast, the solution to a differential equation is a function which might express the trajectory of an object or the response of a system to a varying input. An enormous amount of insight into the behavior of systems can be gained from studying the differential equations these systems obey.
The two subjects interact strongly because the differential equations we understand best are the linear ones, and tools from linear algebra help in their solution, while their solutions display the meaning of some of the ideas from linear algebra. Nonlinear problems are often studied by their linear approximations, so that understanding the linear equations is a key step in the analysis of all differential equations.
First, READ THE BOOKS . You should read each section before we talk about it in class, then again after class, before doing the homework for the section. If you have any trouble understanding it, read it several times, first, quickly for an overall idea what the section is about, then in detail, working out the examples the book uses to make sure you know why each statement is true. Only after this should you start the homework. You may be pleasantly surprised how much easier the homework is with this sort of preparation. You will certainly understand the material and retain more of it, if you study in this way.
Second, regular attendance will be expected. Some topics may be covered more thoroughly in class than in the texts, and you will be resonsible for this material.
There will be weekly quizzes each Wednesday, of about 10 minutes duration, which will help you assess your understanding of the material. The best 10 of these (out of 14) will be counted toward your final grade. If a test is given on a Wednesday, the quiz will be on Monday that week.
Grades will be computed as follows:
| Test 1 | 20 % |
| Test 2 | 20 % |
| Test 3 | 20 % |
| Quizzes | 10 % |
| Final | 30 % |
Cell phone policy: phones should not interrupt the class. Please make certain they will not make noise before class starts.