Class time and location: Tue, Thu 12:30-2:00 in MCS B23

Text: Blanchard, Devaney, and Hall: Differential Equations (first edition), Brooks/Cole Publishing Company, 1998. ISBN number 0-534-34550-6.

In this course, we study the solutions of ordinary differential equations using a three-pronged approach. Solutions are obtained using analytic, geometric, and numerical techniques. All three approaches have their advantages, and we will learn when to use the appropriate technique. We begin by deriving a few classical examples with an emphasis on the phenomena that they model. We then discuss first-order equations using all of the techniques mentioned above. Next we study first-order systems. Using techniques from linear algebra, we derive a systematic approach to the solution of linear systems. Unfortunately, nonlinear systems are more difficult to investigate, but we learn how to apply what we know from the linear case to the nonlinear case. The course concludes with a discussion of Laplace transforms.

Our goal is to be able to say as much as possible about the solutions of a differential equation even if those solutions cannot be expressed in terms of the standard elementary functions (polynomial, rational functions, trigonometric functions, etc.)

This is an honors-level course in mathematics, and consequently it differs from the standard introduction to differential equations in two ways. First, the discussion of the mathematics will be more rigorous. Some class time will be devoted to proofs of fundamental theorems, and students will be expected to prove some of their assertions in their written work. Second, we will study certain topics that do not fit in the standard curriculum.

Course web page: http://math.bu.edu/people/paul/MA231.html

Exams, projects, and grading: We will have two in-class exams during the semester, both at the normal class time. They will be held on October 19 and November 28, and the final exam will be held 12:30-2:30 on Monday, December 18. Please note the date of the final and make your travel plans now! University policy states that you must take the final at the scheduled time.

In addition to the in-class exams, you will be required to submit a substantial amount of written work during the semester. This work will include solutions to the homework and Mac Lab worksheets. Your most significant written work will consist of four projects due periodically throughout the semester

Your final course grade will be determined using the following percentages:

Make-up exams: I have an absolutely firm policy of not giving make-up exams. If you miss an exam, then you must provide an acceptable, written excuse (not an email message) for your absence or you will receive a grade of zero. A valid reason for missing an exam would be something serious like illness (not a slight cold) or a family emergency. Neither poor preparation nor sleeping through an exam are acceptable. If possible (particularly if you want to be sure that your excuse is an acceptable one), contact me before missing an exam. Students who miss more than one exam should probably withdraw from the course.

Homework: Assignments from the text will be made at the end of each class, and you are expected to read the text and work these exercises before the next class. In addition, you will be expected to submit your homework for review once each week. Your homework will play a role in your discussion section grade. No late homework will be accepted for any reason.

Office: MCS Room 255.

Phone number: 353-9555. You can leave a message if I am not available.

Email address: paul@bu.edu. I find that email is a good way to leave messages, but it is not a good way to get help on your homework. For help with the mathematics in this course, I encourage you to visit me in my office. If you miss class, do not send me email asking for answers to questions that were covered in class.

Office hours: T 2:30-4:00, R 3:00-4:30. I will be available in my office during these hours for consultation on a first-come-first-served basis. You do not need an appointment in advance. In addition, many brief matters can be handled directly after class, and in special cases, we can schedule appointments at other times.

MA 231 Discussion hour: Thursday 2-3 has been scheduled as the discussion hour for this course. This hour will be devoted entirely to questions you may have on the homework and the projects.

Additional help: There will frequently be at least one teaching assistant available to give you some help with your homework in MCS 147. We will provide more information as soon as tutoring begins.

Academic Conduct: Your work and conduct in this course are governed by the CAS Academic Conduct Code. This code is designed to promote high standards of academic honesty and integrity as well as fairness. Copies of the code are available in CAS Room 105, and it is your responsibility to know and follow the provisions of that code. In particular, all work that you submit in this course must be your original work. For example, the computations that you do for your projects as well as the text of your reports must be original. With group projects, all group members are responsible for all aspects of the project. Any cases of suspected academic misconduct will be referred to the CAS Student Academic Conduct Committee.