MATH 209: Differential Equations and Vector Calculus: MWF 11 - 11:50am
Professor Steven Miller (Steven.J.Miller AT williams.edu), 202 Bronfman Science Center (413-597-3293)
Office hours: TBD and by appointment (click here for my schedule)
COURSE DESCRIPTION: Historically,
much beautiful mathematics has arisen from attempts to explain heat flow,
chemical reactions, biological processes, or magnetic fields. A few ingenious
techniques solve a surprisingly large fraction of the associated ordinary and
partial differential equations. We will start with difference equations. These
are the discrete analogues of differential equations, and have numerous
applications in both pure and applied math (for example, a generalization of the
Fibonacci numbers explains why double-plus-one will almost surely bankrupt you
if you play roulette in Las Vegas!). After studying these we’ll move on to
differential equations, describing both general existence and uniqueness
theorems as well as techniques to solve the systems (which range from complete
solutions to numerical approximations). Examples will be drawn from pure
mathematics, physics, biology, as well as from class requests. As time permits,
we will describe special functions and advanced topics. Format:
lecture/discussion. Evaluation will be based on problem sets, hour tests, and a
final exam.
Prerequisites: Mathematics 102 (or demonstrated
proficiency on a diagnostic test; see Mathematics 101). No
enrollment limit (expected: 30).
HOMEWORK / EXAMS / GRADING: I encourage you to work in groups, but everyone must submit their own HW assignment. HW is to be handed in on time, stapled and neat -- late, sloppy or unstapled HW will not be graded. Please show your work on the HW and exams (otherwise you risk getting no credit). Grades are 20% HW, 40% Midterm, 40% Final. All exams are cumulative.
SYLLABUS / GENERAL: The textbook will be the 9th edition of Boyce and DiPrima’s `Elementary Differential Equations and Boundary Value Problems’ (I will try to post the HW so you can use the 8th edition if you find it). We will follow the book closely, covering most of the first 8 chapters, occasionally supplementing with additional material from other sources. Also, please feel free to swing by my office or mention before, in or after class any questions or concerns you have about the course. If you have any suggestions for improvements, ranging from method of presentation to choice of examples, just let me know. If you would prefer to make these suggestions anonymously, you can send email from mathephs@gmail.com (the password is the first seven Fibonacci numbers, 11235813).
OBJECTIVES: There are two main goals to this course: to learn how to solve difference and differential equations, and to learn how to model real world problems and how to attack their solution. We will constantly emphasize the techniques we use to solve problems, as these techniques are applicable to a wide range of problems in the sciences.
HOMEWORK
HANDOUTS