Differential Equations and Linear Algebra
Math 2150, Winter 2003

Here are the solutions to the sample final exam.

Table of Contents


Class:


Professor:


Schedule:

The first class is Thursday, January 9, 2003 and the last class is Tuesday, April 22, 2003.

Here is a schedule, subject to change, of the topics and sections we will cover, as well as the timing of the tests.
F = Fundamentals of Differential Equations,
M = Matrix Operations

Introduction F, Chap. 1 and 2 2 weeks
Modelling F, Chap. 3 1/2 week
Linear Algebra M, Chap. 1-6 2 and 1/2 weeks
Test 1 Thur, Feb 13 (subject to change)
Higher order equations F, Chap. 4 and 6 3 weeks
Test 2 Thur, Mar 6 (subject to change)
Spring Break Mar 10-15
Systems F, Chap. 9 1 and 1/2 weeks
Linear Algebra (cont.) M, Chap. 7 1 week
Test 3 Thur, Apr 3 (subject to change)
Laplace Transforms F, Chap. 7 1 and 1/2 weeks
Power series F, Chap. 8 1 week
Final Exam Thur, May 1 6:00 - 7:50 PM, 137 State Hall


Introduction

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.


Requirements and grades:

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 and class participation will be expected. The only way to learn mathematics is to do it. You should make sure you understand the homework assigned. I will answer questions about it in class, before or after class, or in office hours.

There will be weekly quizzes each Tuesday, 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 Tuesday, the quiz will be on Thursday that week.

Grades will be computed as follows:


Test 1 20 %
Test 2 20 %
Test 3 20 %
Quizzes 10 %
Final 30 %

Naturally, all work you turn in should be your own. The University has strict policies on intellectual honesty.

Assignments

(A link to the web page containing the list of assignments.)