5/4 Monday
We covered 4.2 Weyl's equidistribution theorem.
The final exam is scheduled for Thursday, May 14, from 8:00–10:00 AM. The exam will be cumulative, with slightly greater emphasis on the more recent material. To prepare for the exam, you are encouraged to review and redo all homework problems from Homework 1 through 5, as well as revisit and work through the midterm exam questions. In addition, you should practice the extra problems at the end of each chapter. Exercises are generally more straightforward, while Problems tend to be more challenging.x ca
4/30 Thursday
We had a in-class homework session. Homework 5 solution is posted.
Next Monday 5/4 is the last day of the instruction and we will cover 4.2 Weyle's equi-distribution theorem.
4/27 Monday
We covered 4.1 The isoperimetric inequality.
On 4/30 Thursday, we will have an in-class homework session for homework 5.
4/23 Thursday
We covered 3.2 Return to pointwise convergence and proved Theorem 3.2.1. We will skip the rest of the chapter and move to Chapter 3.
On Monday 4/27, we will cover 4.1 The isoperimetric inequality.
Lecture notes for Chapter 4 are posted.
4/20 Monday
We covered 3.1.2 Proof of mean-square convergence.
On 4/23 Thursday, we will cover 3.2 Return to pointwise convergence.
4/16 Thursday
We had in-class homework session. The solution for Homework 4 is posted, and Homework 5 is due 4/30 Thursday after class.
4/13 Monday
We covered 3.1.1 Vector spaces and inner products.
On 4/16 Thursday, we will work on Homework 4 in class. The homework will be due by the end of the class. Please try the homework problems in advance so that you can use class time to ask questions about anything you find difficult.
4/9 Thursday
We started 3.1 Mean-square convergence of Fourier series.
4/6 Monday
We covered 2.5.3 Abel means and summations and 2.5.4 The Poisson kernel and Dirichlet problem in the unit disc.
Homework 4 is posted. Please work on Homework 4 until 4/16 Thursday. On 4/16, you will work on homework 4 in class and submit it for grading at the end.
4/4 Saturday
Homework 4 is posted. Please work on Homework 4 until 4/16 Thursday. On 4/16, you will work on homework 4 in class and submit it for grading at the end.
3/26 Thursday
Lecture Video on Fejér kernel.
3/23 Monday
We covered Section 2.5.1 Cesàro means and summation and 2.5.2 Fejér theorem.
Announcement: We will hold an asynchronous class on Thursday, March 26. A lecture video will be posted. Office hours on that day are canceled.
3/19 Thursday
We covered Section 2.4 Good Kernels.
Here is the solution for Midterm. Please do not distribute it.
Next week, we will cover 2.5 Cesàro and Abel summability: applications to Fourier series.
3/16 Monday
We covered Section 2.3 Convolution. I left some proof from Proposition 3.1 for you to read. Proposition 3.1-(v) uses an approximation argument from Lemma 3.2.
I'll return Midterm on Thursday.
On Thursday, we will cover 2.4 Good Kernels.
3/12 Thursday
We took Midterm.
3/9 Monday
We finished Section 2.2. Midterm will cover all materials up to Section 2.2.
Homework 3 solution is posted.
3/5 Thursday
We did in-class homework 3. You can work on the rest of problems at home as regular homeworks and hand in on Monday before the class gets started.
Homework 3
3/2 Monday
Announcement
1. Midterm will be on 3/12 Thursday.
2. Midterm will cover all materials we covered up to Section 2.2 Uniqueness of Fourier Series, and Homework 1,2, and 3.
3. We will have in-class homework session this Thursday 3/5.
Today, we covered Uniform Convergence and Uniformly Continuous Functions. We will need these facts to prove Corollary 2.3.
2/26 Thursday
We proved Theorem 2.1 The Uniqueness of Fourier Series.
Next Monday, we will prove the rest of theorems in Section 2.2.
2/23 Monday
All classes are canceled due to the inclement weather.
2/19 Thursday
We covered 2.1.1 Main Definitions and Some Examples.
Next Monday 2/23, we will cover 2.2 Uniqueness of Fourier Series. Please read and try to understand the proof of Theorem 2.1 before class.
2/16 Monday
We did in-class homework 2. The problem and solution are posted.
2/12 Thursday
We covered the heat equation and derive the stationary solution for the heat equation on unit disk.
On 2/16 Monday, we will be working on in-class homework.
2/9 Monday
We covered 1.2 Solution to the wave equation using both traveling waves and standing waves.
On Thursday 2/12, we will cover the heat equation and derive the stationary solution for the heat equation on unit disk.
2/5 Thursday
We covered 1.1 Derivation of the wave equation and started 1.2 Solution to the wave equation.
Next Monday, we will derive d'Alembert's formula for the wave equation and cover Superposition of standing waves.
2/2 Monday
We worked on in-class Homework 1. The problem and solution is posted below.
On Thursday, we will cover 1.1 Derivation of the wave equation and 1.2 Solution to the wave equation. Read textbook in advance.
1/29 Thursday
We covered the Vibrating string and standing and traveling waves.
We will have in-class homework session next Monday 2/2.
1/26 Monday
All classes are canceled due to inclement weather.
1/22 Thursday
Today is the first day of class. We went over our syllabus, introduced what the Fourier Analysis is about. Then, we derived the Euler formula.
You will need to have the textbook, Fourier Analysis by Stein and Shakarchi (ISBN 978-0691113845).
Next week, we will start covering materials from our textbook. On Monday 1/26, we will cover 1.1 The Vibrating String. Please read the material in advance.
Homework 5, due 4/30 Thursday in class, Solution
Homework 4, due 4/16 Thursday in class, Solution
Homework 3 (3/5), Solution
Homework 2 (2/16), Solution
Homework 1 (2/2), Solution