m23f07 at math.dartmouth.edu
There beautiful water waves are described by PDEs
ifferential equations relate variables and their (possibly higher or partial)
These are universal in the sciences, with applications from mechanics
through quantum physics, ecology, biology, engineering, finance and
statistics, to name a few! We will learn solution techniques,
building on calculus from Math 3, 8, and 13, such as separation
of variables, constant-coefficient methods, application of linear
algebra to systems of equations, and Fourier series and transforms.
One goal of the course will be to apply these methods to differential
equations arising in modeling the natural world.
We will culminate with partial differential equations such as Laplace's
equation, the wave and heat equations, and eigenvalue problems.
These days, computers enable accurate numerical solution and visualization, and this course has a small but key computer component (using Matlab, or any other equivalent package that you may know). As well as improving your understanding, this will teach you valuable tools that have become the bread-and-butter of science and engineering.
Lectures: MWF 10-11:05am, Kemeny room 105, important to attend since we'll often do worksheets. I recommend you read the book section in advance of lecture. X-hour is 12-12:50pm Thurs, and we'll use intermittently for: Matlab sessions, review, problem-solving, catch-up lectures, etc. Do not schedule anything regular in this X-hr. I encourage you to come to office hours: 3-4pm Mon, 5-6pm Tues, 3-4pm Fri
Required book: Elementary Differential Equations and Boundary Value Problems (8th edition) by Boyce and DiPrima (Wiley, 2004), available at Wheelock Books. Expensive but worth it! There's a Student companion site with reviews, quizzes, Matlab, etc, by chapter.
Grade weighting: Your overall grade will be computed according to HW 20%, Quizzes 15%, Midterm 25%, Final 40%. Note that although HW has a low weighting, it is the main chance you get to practise the material and get feedback. Practise is key so that you can tackle exams confidently.
Exams and quizzes: Quizzes are 25 mins, will be about 4 total. Exams count more (also read this):
Homework: 9 weekly HW's due Wednesday at start of lecture. I strongly encourage you to try the relevant homework problems before the next lecture (leaving it all for Tues night risks being left behind in this fast-paced course.) Also, getting together in a study group is good. Late homework will not be accepted (unless by prior arrangement for a valid, and exceptional, reason). Your lowest HW score will be dropped.
Honor principle. Exams: no help given or received. Homework: no copying, however collaboration on approaches to problems is encouraged. Write-ups must be done individually.
Special needs: Let me know if you have any, by the first 2 weeks. Also stop by the Academic Skills Center in 301 Collis to register for support services.
Private tutoring: Tutor Clearinghouse may have private one-on-one tutors available for Math 23. The tutors are recruited on the basis that they have done well in the subject, and are trained by the Academic Skills Center. If a student receives financial aid, the College will pay for three hours of tutoring per week. If you would like to have a tutor, please go to 301 Collis and fill out an application asap.
Religious observance: Some students may wish to take part in religious observances that occur during this academic term. If you have a religious observance that conflicts with your participation in the course, please meet with me before the end of the second week of the term to discuss appropriate accommodations.