Fourier Analysis, Math
Instructor Info: Larry
Guth, E17-314, email@example.com
Class times: MWF 2-3, E17-129
Office hours: Mon 3-4 and Tues 3-4.
Office hours in the first two weeks. I will have office hours on Friday Sep. 11 after class (3 pm). I'll have office hours on Monday Sep. 14 at the usual time, but I won't have office hours on Tues. Sep. 15.
Midterm: The midterm will be Tuesday Oct. 27, 7:30 - 9:30 pm, in our usual classroom, E17-129.
Course description: In Fourier
analysis, we study how to decompose a complicated function
as a sum of many simple pieces. In particular, we will
prove that an arbitrary function can be written as a
linear combination of sine waves. This decomposition has a
remarkable range of applications, including partial
differential equations, number theory, geometry, and some
topics in applied math. We will rigorously study this
decomposition, and we will look at many applications. Here
is a description of the things we will study: Course
description. Here is a course syllabus with exam
dates and basic logistical information: Course
Textbooks: We will use two textbooks
from the Princeton Lectures in Analysis sequence, written
by Stein and Shakarchi: Fourier Analysis: An
Introduction, and Real Analysis: Measure
theory, Integration, and Hilbert Spaces.
I think that these are really good books, and that you'll
enjoy owning both of them. We will cover Chapters 1 - 7 of
Fourier Analysis and most of Chapters 1 and 2 of Real
Course work: We will have weekly problem sets.
There will be a midterm halfway through the semester and a final exam.
Formula list . This is a list of formulas from our class that you will be able to use during the midterm.
Practice Midterm. You can work on these problems to study for the midterm. This practice test also shows the format of the actual midterm.
Solutions to the practice midterm.
Practice Final. This was last year's final exam. You can work on these problems to study for the final. This practice test also shows the format of the actual exam.
Solutions to the practice final. .
Problem Set 1, due Wednesday Sep. 16 in class.
Problem Set 2, due Wednesday Sep. 23 in class.
Problem Set 3, due Wednesday Sep. 30 in class.
Problem Set 4, due Wednesday Oct. 7 in class.
Problem Set 5, due Wednesday Oct. 14 in class.
Problem Set 6, due Wednesday Oct. 21 in class.
Problem Set 7, due Monday Nov. 9 in class.
Problem Set 8, due Wednesday Nov. 18 in class.
Problem Set 9, due Friday Dec. 4 in class.
Optional Open-Ended Projects :
Fourier analysis and probability .