[upon losing the use of his right eye] "Now I will have less distraction."
Leonhard Euler

"If you come to a fork in the road, take it."
Yogi Berra

Class time and location: Tuesday and Thursday 12:30-1:50 in MCS B31

Discussion section: Tuesday 3:30-4:20 in PSY B53

Text: Blanchard, Devaney, and Hall: Differential Equations (third edition, purple sunrise and Zakim bridge on cover), Brooks/Cole Publishing Company, 2006. ISBN number 0-495-01265-3.

In this course, we study 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 as such 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 three in-class exams during the semester, all at the normal class time. They will be held on October 1, November 5, and December 10. The final exam will be held 9-11 on Saturday, December 19. 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. Your most significant written work will consist of two group projects due periodically throughout the semester.

Grades for the course will be determined by applying the most favorable of the following two weighting schemes:

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 (H1N1 but 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.

Homework: Assignments from the text will be made at the end of each class, and you are expected to work these exercises before the next class. In addition, you will be expected to submit your homework for review by the end of discussion section each week, i.e., by 4:20 pm on Tuesday. No late homework will be accepted for any reason.

Office: MCS Room 255.

Phone number: 617-353-9555.

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: Tuesday and Thursday 4:30-6. 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.

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. A copy of the code is available in CAS Room 105 if you cannot access it on the web, and it is your responsibility to know and follow the provisions of the 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 group projects as well as the text of your reports must be original to your group, and all group members are responsible for all aspects of the group projects. Any case of suspected academic misconduct will be referred to the CAS Student Academic Conduct Committee.

Class conduct: See the course web page for a discussion of conduct that is inappropriate during class or discussion section.

Last drop date: Students cannot withdraw from a course after the tenth week of the semester. In other words, if you are in this course after November 12, you will receive an academic grade (A-F) for your work at the end of the semester. I will not let students who are doing poorly avoid a failing grade by granting an incomplete.