The problem sets listed below we be graded pass/fail. Their purpose is to offer students ample opportunity to learn and practice the mathematical techniques introduced in the lectures. Homework problems , in contrast, will be assigned numerical grades as described in the syllabus. Their purpose is to offer students some detailed feedback on their progress. Roughly speaking, the problem sets test breadth of understanding, while the homework problems test depth.
The following sets of practice problems will be examined for completeness:
Review of linear algebra [PDF], due Tuesday, September 7.
Variational calculus [PDF], due Thursday, September 16.
Hilbert space and Fourier series [PDF], due Tuesday, September 28.
These problem sets are entirely optional. They involve prerequisite material that will not be covered in the lectures. Their purpose is to help students review this material as they prepare for the course. Students should at least examine each problem to ensure that they would feel comfortable solving it, even if they do not write out a full solution.
The instructor will be available during the office hours listed in the syllabus, or by appointment, to discuss these problems during the last two weeks prior to the start of the course.
Elementary calculus [PDF]
Matrices and determinants [PDF]
Vector algebra and geometry [PDF]
Vector calculus [PDF]
Matrix algebra [PDF]
Complex numbers [PDF]
Its usually a good idea to have a handbook of formulas and so forth. This one is priced nicely.
Here are several other texts that might be useful. The first is the book we used last year and quite readable. The second is enormous and comprehensive. The third has, in my opinion, a slightly more engineering approach. The last is a classic, but probably more of a graduate-level text. The fifth is an outline with a large number of solved problems.
This site was last updated Thursday, September 9, 2010 1:45 PM EDT.