Math 23, Winter 1998

Syllabus & Homework

On this page you will find a short syllabus for Math 23 indicating the topics and sections of the text we will cover. There is also information concerning the exams, including lists of review problems and other updates. You should check this page frequently to obtain your homework assignments.

Note on Homework

The information on this page with the exception of homework assignments is for both sections of Math 13. However, the homework assignments for Math 13 are not the same for both sections.

The homework listed on this page is for Prof. Guentner's section only. If you are in Prof. McAllister's section you should consult another web page for your homework assignments.

Course Syllabus

The topic of the course is Differential Equations. It is probably the first course you have taken on the subject, although some very simple examples of differential equations are usually discussed in a calculus course. It is also possibly the first mathematics course beyond calculus you have taken.

We will be covering the following topics in Math 23 in order:

Perhaps the most basic questions concerning a differential equation are the existence and uniqueness of its solutions. We will return to this question in various disguises throughout the course.

In Chapter 2 we will begin by discussing direction fields, and the geometry of solutions of first order equations. After this discussion, which applies to both linear and non-linear equations, we will develop the method of integrating factors for solving linear equations.

Chapter 3 treats second order equations. We will concentrate on the method of the characteristic polynomial for solving homogeneous, constant coeffecient equations. There will be a short discussion of non-homogeneous equations. The theory of 2x2 systems of first order equations closely resembles the theory of second order equations and it is therefore natural to discuss Chapter 7 immediately after Chapter 3. This theory relies heavily on some basic linear algebra which will be covered as needed.

The next topic is the Laplace transform, which is a powerful technique for solving differential equations.

Finally, we will discuss partial differential equations. We will discuss each of the three basic partial differential equations in detail; the heat, wave and Laplace equations. These will be solved using the method of Fourier synthesis. As a prerequisite for this we will discuss the convergence of Fourier series.

Homework Assignments

Chapter 2: First Order Differential Equations

Chapter 3: Second Order Linear Differential Equations

First Exam

The first exam is on Thursday, 29 January from 6:00-8:00 pm in Filene Auditorium. There are no calculators allowed on the exam, which is worth 125 points and 25% of your final grade. It covers the material above, that is, Chapter 2 and most of Chapter 3 (3.1-3.5) of the text.

The format will be approximately as follows. Note that this may change without notice.

There are two recommended methods of preparing for the exam:

When preparing keep in mind that the best way to remember the material is to understand it. Being able to work the problems is only part of this; another part is being able to check your work without consulting the back of the book. In most of the practice problems, you should be able to decide if your answer is reasonable or not. Ask yourself questions such as: Should the solution approach an equilibrium, or should it explode to infinity? Should the population be negative?

Chapter 3: Second Order Differential Equations (continued)

Chapter 7: Systems of Differential Equations

Second Exam

The second exam is on Thursday, 19 February from 6:00-8:00 pm in Filene Auditorium. There are no calculators allowed on the exam, which is worth 125 points and 25% of your final grade. It covers the material since the first exam, that is, the tail end of Chapter 3 and all of Chapter 7 (7.1-3.7) of the text.

The format will be approximately as follows. Note that this may change without notice.

There are recommended methods of preparing for the exam:

When preparing keep in mind that the best way to remember the material is to understand it. Being able to work the problems is only part of this; another part is being able to check your work without consulting the back of the book. In most of the practice problems, you should be able to decide if your answer is reasonable or not.

Chapter 6: The Laplace Transform

Chapter 10: Partial Differential Equations

Final Exam

The final exam is on Saturday, 14 March from 12:00 to 2:00 in the afternoon in Cook Auditorium. There are no calculators allowed on the exam, which is worth 175 points and 35% of your final grade. It covers the entire term, but is weighted towards the material we have covered since the second exam.

We have tried to make this exam as conceptual as possible. This means that a premium is placed on understanding or rather "feeling" the material rather than on actual calculations. So, you can expect a few problems on the order of Problem 5 on the second exam. The format will be approximately as follows. Note that this may change without notice.

There are recommended methods of preparing for the exam:

In class on Monday there was some demand for some handouts illustrating the use of Maple in the context of Fourier Series, the heat and wave equations. These, as well as some other handouts, are in a box in front of my office door:

If you try downloading the Maple files directly, you might also wish to consult Tom Shemanske's instructions for installing Maple on your Macintosh.