Math 53
Autumn 2024

Page Table of Contents

• Course Description
• Teaching team
• Office hours
• Textbook
• Attendance
• General guidance
• Pre-class reading assignments
• Grade breakdown
• Homework overview
• Exam conflicts
• OAE accommodations
• Academic Integrity Working Group
• Course disruptions
• Additional course policies

Course Description

Differential equations arise in quantitive modeling throughout the natural sciences, engineering, finance, computer graphics, machine learning, and much more. This course explores many approaches to understanding the behavior of solutions to such equations. In some cases there are explicit solution formulas, but usually there are no formulas for solutions yet we want to understand what happens (e.g., do solutions approach some limiting value as time evolves, or does "chaos" emerge?).

There are many visual and computational tools that can be brought to bear on this topic, such as linear algebra (e.g., eigenvectors and matrices), power series, numerical methods, and derivative matrices. We will learn about all of these methods, and then see how some ideas adapt to multivariable settings (with the aid of Fourier methods) to unlock the mysteries of partial differential equations. Along the way, we will encounter a vast array of sources of real-world motivation and utility for the results and concepts that are discussed.

By the end of this course, you should be able to:

• use visual tools to analyze solutions of low-order differential equations,
• apply insights from linear algebra to describe solutions to both linear and non-linear systems of differential equations,
• carry out a variety of numerical methods and be aware of their advantages and disadvantages, and
• compute Fourier series and Fourier transforms in many cases and use such computations to solve some important partial differential equations.

For a more detailed syllabus see the schedule page. Per University policy, your decision to take the course implies that you agree to these requirements and to the grading policies spelled out here; so be sure to read everything on these pages.

Instructors

• John Anderson
  Office: Building 380, 382-A
  Email: jrlander(at)stanford(dot)edu
  Office hours: 12:30 - 2:30 on Mondays and 12:30 - 1:30 on Wednesdays in Building 380, 382-A,
  
• Jae Hee Lee
  Office: Building 380, 382-J
  Email: jhlee18(at)stanford(dot)edu
  Office hours: 10:30 - 11:30 on Wednesdays and 12:30 - 2:30 on Fridays in Building 380, 382-J,
  

Teaching Assistants

• Zhihan Li
  Office: 381-A
  Email: zhli21(at)stanford(dot)edu
  Office hours: 10:30 - 11:30 on Mondays, 3:30 - 4:30 on Tuesdays, and 3:30 - 4:30 on Thursdays in Building 380, 381-A
  


• Dmitrii Skvortsov
  Email: skvod03(at)stanford(dot)edu
  Office hours: 4:30 - 6:30 on Tuesdays and 3:00 - 4:00 on Fridays in Huang basement

Office Hours

You are encouraged to attend anyone's office hours, regardless of what lecture or TA section you are enrolled in. No appointment is necessary, just drop in at the scheduled office hours with your questions!

If the class prefers to have some office hours online instead, we may have some on Zoom. In that case, the Zoom link for office hours would be found on Canvas.

Textbook

The course textbook can be found here. The textbook was designed by the math department with input from several other departments. It is filled with interesting applications of all kinds. Please read the introduction! It contains an overview of the class and a guide for how to read the rest of the book. You will also find an email there for sending any feedback you may have. The book has been made with all of you in mind, so giving feedback can be very constructive!

Attending Lecture and Section

Attendance is not required at lecture, but regular attendance is important to your success in this class. A student who misses class is responsible for finding out what was discussed and learning the material that was covered on that day.

Discussion sessions are a great additional resource we have in Math 53. Held at various times on Tuesdays and Thursdays this term, they will provide opportunities to see more guided examples and try your hand at exercises with a member of the teaching team present. Although the problems are not graded, the additional exposure to and practice with the material will greatly aid to your learning. Note that the discussion sessions will begin on Tuesday, September 24.

In the (hopefully unlikely) case that a class has to be held online, we will notify you and a Zoom link will be provided on Canvas.

Pre-class reading assignments

There will be a short assignment due on Mondays and Fridays at 9 am just before lecture. This will involve answering a few questions pertaining to either the previous lecture or a selection of reading. These questions are meant to 1. reinforce and gauge your understanding of the previous lecture, and 2. to encourage you to engage a bit with the material of the next lecture beforehand. This will help you get more out of the lecture! The questions will take the form of a quiz posted on Canvas. Only the question pertaining to the previous lecture is graded for correctness. The other questions are graded for effort.

The selection of reading can be found on the assignment.

General Guidance

In order to learn the material, attending lecture is not enough. Struggling with the material yourself is a very important (probably the most important!) part of the process, so don't get discouraged if something is confusing!

The weekly homeworks, pre-class reading assignments, and worksheet sections will give you practice with the material yourself. Meanwhile, in lecture, the instructor will describe the material and work through examples. You will get much more out of lectures if you are engaging with the material, and the pre-reading assignments encourage you to do so! You are also encouraged to attend office hours for help with the homework, additional information about topics from lecture, etc.

Grade breakdown

Your grade will be based on the following components:

• Homework: 20% (lowest two scores dropped)
• Pre-class assignments: 10% (graded out of 80% of total points, with a maximum of 100%)
• Midterm exams: 20% each (there are two midterms)
• Final exam: 30%

Homework

There will be weekly homework posted on the course Canvas. For details about handing in your homework, see the homework page.

No late homework will be accepted.

The lowest two homework grades will be dropped in final average calculations.

Homework and the Honor Code

You are bound by the Stanford Honor Code for all work submitted for Math 53, including the homework assignments. For homework, we encourage you to use your book and all your notes, come to office hours, talk with any tutor(s) you have, and collaborate with your peers. We believe that thinking about math and conversing about math is an important part of the learning process.

However, we expect that the work you submit is work you have written yourself and reflects your understanding of the problem and how to solve it. If you work on a problem with someone else, DO NOT copy their solution and instead, write it up on your own.

Finding a solution on of the internet, copying it without thought onto your homework, and then submitting it for credit is a violation of the Stanford Honor Code and will be treated as such.

Exam conflicts

Please determine if you have any exact conflicts as quickly as possible! The exam information can be found under the Exams tab. If you have exam conflicts, please email your instructor and fill out the form found here to schedule an alternate exam sitting on the same day. In order to make sure that the logistics can be properly handled, this should be done at least two weeks before an exam!

Access and Acommodations

Stanford is committed to providing equal educational opportunities for disabled students. Disabled students are a valued and essential part of the Stanford community. We welcome you to our class.If you experience disability, please register with the Office of Accessible Education (OAE). Professional staff will evaluate your needs, support appropriate and reasonable accommodations, and prepare an Academic Accommodation Letter for faculty. To get started, or to re-initiate services, please visit  the OAE website.

If you already have an Academic Accommodation Letter, please use the Google form found here to upload it and detail the specific accommodations you will need in this course. Letters are preferred by the end of week 2, and at least two weeks in advance of any exam, so we may partner with you and OAE to identify any barriers to access and inclusion that might be encountered in your experience of this course. New accommodation letters, or revised letters, are welcome throughout the quarter; please note that there may be constraints in fulfilling last-minute requests.

Academic Integrity Working Group

This course is participating in the proctoring pilot overseen by the Academic Integrity Working Group (AIWG). The purpose of this pilot is to determine the efficacy of proctoring and develop effective practices for proctoring in-person exams at Stanford. To find more details on the pilot or the working group, please visit the AIWG’s webpage.

Course disruptions

Stanford as an institution is committed to the highest quality education, and as your teaching team, our first priority is to uphold your educational experience. To that end we are committed to following the syllabus as written here, including through short- or long-term disruptions, such as public health emergencies, natural disasters, or protests and demonstrations. However, there may be extenuating circumstances that necessitate some changes. Should adjustments be necessary, we will communicate clearly and promptly to ensure you understand the expectations and are positioned for successful learning.

Other important policies

• Calculator policy: Calculators are not needed (nor permitted) on any exam (numbers are kept simple on exams), and no coding is required in this course (but we will provide some software widgets to explore examples). Occasionally, homework problems may call for the use of a scientific or graphing calculator, and it is fine to use them for this purpose.
• Honor code policy: By Math Department policy, any student found to be in violation of the Honor Code on any assignment or exam in this course will receive a final course letter grade of NP.