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The exam will cover what we have done on linear algebra and material
from sections 12.1-12.3 on Fourier series. Here, from the syllabus, is what I think the exam will ask about:
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Goals Students should know
the
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". |
Goals
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.
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The following resources will be helpful to students when preparing for
the first exam. Please also consider the draft formula sheet and,
if you wish, send me comments or corrections or suggested additions.
I will hold a review session on Wednesday, November 16, from 7 PM to 9
PM in Hill 525. This session is not intended as a substitute
for your own efforts to study, and it should not be used for a
first glance at many of the problems referenced below.
- Material from this semester
I hope to post scanned homework solutions for the textbook problems
designated by the syllabus in sections 12.1 and 12.2 done by student
volunteers. When this is done, a link will be installed here.
I will certainly ask you for the definitions of various linear algebra
terms. An effort to organize such definitions is here.
A formula sheet for Fourier coefficients will be handed out. A draft
of this formula sheet is here.
- Material from the fall 2004 version of the course
Here are
solutions to the problems suggested by the syllabus in section 12.3.
Here is the second exam
together with answers to that
exam. The material to be tested on the exam in our course is the
same as the material tested in this exam.
- Material from the spring 2004 version of the course
The second exam that semester 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.
- Also from fall 2004: another 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.
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Maintained by
greenfie@math.rutgers.edu and last modified 11/8/2005.
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