Did you get here from lemonade? If you're lost, click here to go back...

See all sketches...

Sketch 8

A Review of Introductory PDE Theory

Huh...

I was motivated to make this note because I feel like I didn't learn PDEs as thoroughly as I wanted to the semester I took it. Also, I want my study of PDEs in this sketch to contain many many more pictures than a book like Evans, which I felt could have used many more pictures (although I guess it did have a few). Finally, I want this summary to supplement the material covered in many PDEs courses by giving examples of the application of the theory of PDEs to study things in

(I might slip in some applications of ODEs as well, but don't hate me for it). Finally, I want to talk about a philosophical remark I vaguely remember my physics teacher making in freshman year:
Most physical phenomena can be modeled very nearly by a second-order differential equation.

- May or may not have been said by Prof. Benjamin Safdi

I honestly might be remembering it a bit (or completely) wrong, but we can maybe try in this sketch to see if we can reconstruct his message from my painfully bad memory. 😃😜 I'll even see if I have a picture from the class he said it! I really enjoyed his lab class!

Date Started: June 25, 2024
Date Finished: June 25, 2024

Some History and A List of Problems

Distributions and Fourier Analysis

As Strichartz put it in his amazing book, sometimes it doesn't make so much sense to worry about individual points x. Read the first few pages of his book for a more thorough explanation, but the idea is that we can better understand these functions by "testing" them with test functions.

Bonus Section: Discretizations that Show Up in Time Series Modeling

References