In spite of its less than glorious start, Fourier's paper was the impetus for major developments in mathematics and in the application of mathematics. His ideas forced mathematicians to come to grips with the definition of a function. This, together with other metamathematical questions, caused nineteenth-century mathematicians to rethink completely the foundations of their subject, and to put it on a more rigorous foundation. Fourier's ideas gave rise to a new part of mathematics, called harmonic analysis or Fourier analysis.
We will study harmonic analysis in three settings.
Fourier series and its applications to partial differential equations are discussed in Differential Equations with Boundary Values by Polking, Boggess, and Arnold. This treatment is at a more elementary level and lacks rigor, but you might find it interesting.
There is a very interesting treatment of harmonic analysis, its applications, and its history in Fourier Analysis by Thomas Körner.
In order to use fseries you will need to download the file fseries.m.
All homework is due in class on the date announced. This will typically be about a week after the assignment is posted. Each student will be allowed to have at most one late homework assignment during the semester. The one late homework will be accepted up to seven days after the due date, with or without excuse, and without penalty. No other late homeworks will be accepted even with an excuse. There will be absolutely no exceptions to these rules.
Many of the Exercises in the book extend the material in the text. Therefore they are as important as the text itself. Many homework assignments will contain more problems to be done than are to be turned in. It should be emphasized that a person learns mathematics by doing problems. You are encouraged to at least look at all of the exercises in the book.
A homework assignment is meant to convince the grader that you understand the material. The best way to do that is to use complete sentences and to organize your work in paragraphs. In your writing, attempt to achieve the same clarity you find in textbooks. The grader has instructions that if he cannot understand your writing, he is not to grade your paper.
The homework is not pledged. You are encouraged to discuss the homework, and to work together on the problems. However each student is responsible for the final preparation of his or her own homework papers.
Most mathematicians and scientists prepare their papers using the mathematical typesetting language TeX. It is not required, but you are encouraged to use TeX for your assignments. This is especially true for the project reports.