Review guide for the second exam
|The exam on Thursday, November 18, will cover|
what we've done on linear algebra
and introductory Fourier series (12.1-12.3).
What's below is copied from the syllabus:
Goals Students should know
principal definitions of linear algebra and recognize and work
with these ideas. Students should know how to
compute the rank of a matrix, the determinant of a matrix, and be able
to invert and diagonalize simple matrices "by hand".
Students should be able to compute the Fourier coefficients of
simple functions "by hand". They should know what orthogonality means
for functions. Given a function's graph on [0,A] they should be able to
graph the sum of the Fourier sine and cosine series on [-A,A]. They
should have some qualitative understanding of what partial sums of
Fourier series look like compared to the original function, including an
idea of the Gibbs phenomenon.
The following resources may be helpful to students when preparing for
the second exam.
- Draft formula sheet
Here is a draft of a formula
sheet covering Fourier series which I would include with the exam.
You may send me comments or corrections or suggested additions.
- Material from the spring 2004 version of the course
The second exam last spring covered only linear algebra. With that in
mind, you might want to look at the following material. There are review problems and answers. See especially problem 14 and its answers. That problem
asks for very brief definitions of common terms in linear algebra. I
think students in this semester's class should be able to answer that
sort of question, also. A version of the second exam I gave
and answers to that exam
are available. I
believe most of the material is quite similar to what we have done
this semester, and therefore can be useful to you. Most of the spring
2004 review problems were copied from past exams in this course.
The first seven review problems here
cover material to be tested on this exam, and here
are answers. Problems 1 and 2 and 3 on this
exam could be asked here.
- A sample second midterm exam
These problems are from another section, which just gave an exam at
approximately the same logical time in the course. Thus there are
linear algebra questions and some
Fourier series problems.
email@example.com and last modified 11/10/2004.