## 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 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.

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.
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