MATH  209:   Differential Equations and Vector Calculus:     MWF 11 - 11:50am Bronfman 106
Professor Steven Miller (Steven.J.Miller AT, 202 Bronfman Science Center (413-597-3293)

Office hours: M-F 10:05-10:50am, M-F 4-4:30pm, whenever I'm in my office (click here for my schedule)

TA Review Sessions: Sunday 9-11pm in CLARK 204 and Monday 9-11pm in BRONFMAN 106


Review sessions: Thurs May 14th from 1:30 - 3:30 in Bronfman 107;

Thurs May 21st from 2 - 4pm, Fri May 22nd from 10-11am and 1:30-2:30pm (all in Bronfman 104)

takeaways from the course        techniques for solving differential equations

course description    HW/Exams/Grading policy    HW and reading    Handouts/Programs    Project Topics    Other Links (summer research)    additional comments

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 (possibilities include Random Matrix Theory and the Calculus of Variations). 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). Grading will be: 20% homework, 40% midterms (there will be two), 40% final. You may also do a project involving differential equations, which would count for 10% of your grade (and the other categories would be reduced 10% each). All exams are cumulative.  Click here for an example on how to write up a homework (this is the solution to the first two difference equation problems).

SYLLABUS / GENERAL: The textbook will be the 9th edition of Boyce and DiPrima’s `Elementary Differential Equations and Boundary Value Problems’ (YOU MAY USE THE EIGHT EDITION FOR THIS CLASS -- IF THE HW PROBLEMS DIFFER, I WILL POST THE PROBLEM FROM THE NINTH EDITION.). We will follow the book closely, covering much of the first 8 chapters, occasionally supplementing with additional material from other sources. My lecture notes are also available online here (click here for additional comments on each lecture); note, of course, that these are rough notes to help me give each lecture and thus will not include everything mentioned in class. 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 (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 AND READING: We will cover the following sections (as well as others as time permits):





SUGGESTIONS FOR PROJECT TOPICS: Below are some possible topics; this is by no means a complete list, but rather some suggestions. Most of the links are to wikipedia to get you started; it is also worth seeing the topics listed in their differential equations section.



course description    HW/Exams/Grading policy    HW and reading    Handouts/Programs    Project Topics    Other Links (summer research)    additional comments