# AMATH 351 A: Introduction to Differential Equations and Applications

Spring 2021
Meeting:
MWF 10:30am - 11:20am / * *
SLN:
10216
Section Type:
Lecture
Instructor:
Syllabus Description (from Canvas):

## 1. General Course Information

### Instructor

Lectures: Synchronous lectures on MWF 10:30 am to 11:20 am
(Zoom Recording will be uploaded, Attend the lecture via Zoom ID: 952 9698 8830)

Instructor: Ying-Jen Yang

Email: yangyj@uw.edu

(Welcome to email me if you have any questions or concerns. For class material-related questions, please ask them at Piazza!)

Instructor's office hours: Thursday 5-6 pm PT and Friday 3-4 pm PT

### Teaching Assistant (TA)

Teaching Assistant: Nora Gilbertson

Email: nmg421@uw.edu

TA's office hours: Tuesdays 5-6pm and Thursdays 6-7pm PT

### Piazza Discussion board for online Q&A

We will use Piazza for online Q&A and discussion. Students are encouraged to ask questions, answer people's questions, and discuss questions with people (even anonymously).

• For each homework, I will create and pin a post for each problem as the main discussion thread of the problem. All questions on the specific problem should go to the pinned post. This way, people can easily find what questions have been asked.
• Also, it is easy to use LaTeX command on Piazza, just use two \$\$ on each side to add equations. See this Link for introduction on the LaTeX commands for math equations.

## 2. Course Content Information

See Modules for details.

### Description

This course serves as the first course in differential equations after learning Calculus from MATH 124 and 125. In this course, we will learn how to solve Ordinary Differential Equations (ODEs) with examples drawn from physical, chemical, biological sciences and engineering. We motivate most of our theoretical discussions from applications.

There are software that can get analytical solutions of ODEs for us nowadays. Thus, it is more important for us to understand the logic hidden behind different solution methods, not just being familiar with how to crank the solving machine. This way, we can understand why a solution method works and potentially develop new ways to solve ODEs in the future.

### Prerequisites

Proficiency in manipulation of algebraic equations, evaluation of limits, methods of differentiation & integration at the level of MATH 124 & 125 are assumed. We will introduce and use quite some linear algebra, a little complex variable, and power series that are relevant to us. Previous exposure to linear algebra, complex variable, and Taylor series would be helpful.

### Rough Outline

1. Introduction to Differential Equations: Variables and Classification of ODE
2. 1-D, First order, one dimensional ODE
3. n-D Autonomous linear ODEs and Diagonalization
4. More on linear ODEs: complex eigenvalues, and degenerate cases
5. Nonlinear ODE and Inhomogeneous linear ODE
6. Non-autonomous linear ODEs: series method

Note: I am de-emphasizing Laplace transform in this first ODE course. In my opinion, it is better to learn it after learning contour integral in complex analysis to have a more systematic way to perform the inverse Laplace transform. Without it, inverse Laplace transform is just reverse engineering from a table.  We will emphasize more on solving systems of ODEs (with matrices and a bit linear algebra) since it has many conceptual advantages and connections to later courses in dynamical systems. That said, no need to worry if you haven't taken linear algebra, we will start from the beginning and only focus on vectors and matrices.

### Textbook and Reference

No textbook is required. Self-contained lecture notes will be provided.

However, I do recommend the following two textbooks for references.

1. W.E. Boyce, R.C. DiPrima, and D.B. Meade, Elementary Dierential Equations and Boundary Value Problems. 11th ed. (any edition after 9th will do. We will cover Chapter 1- 5 , 7-9 ).
It is the standard textbook for undergraduate ODE class. We will focus mostly in the material in it.
2. Steven H. Strogatz, Nonlinear Dynamics and Chaos, 2nd ed.
(We will mention concepts in Chapter 1, 2, 5, and 6).
It is an awesome textbook that is used in almost all undergraduate Dynamical Systems class around the world! We will only touch a little bit of it. You can take Amath 402/502 for a thorough introduction of the subject, which almost surely uses this book.

### Homework Assignments

General: Homework is assigned weekly. In principal, homework is assigned on Friday and due the next Friday. You must submit your scanned or typed-up homework PDF file to Gradescope (and label your work based on the problems). In principle, no late homework is allowed. If you need extension due to some reasons, please contact the instructor privately. At the end of the quarter, the homework assignment with the lowest grade will be dropped.

Format: Submitted files must be portrait, letter-size, and easy-to-read in a single pdf file. LaTeXing (or using a more user friendly version of LaTeX, LyX) is highly encouraged. You must Box your final answer and  present all your work clearly to justify how you got the answers. If you didn't show your work, you could get a 0.

Partial Credits: We have a big class. I hope we can "grade" all the homework questions because I personally dislike statistical grading. Therefore, many of the homework problems will NOT have a lot of partial credits (except for proof-like questions or really-long problems).

Tentative Grading Plan: Except for 1-2 randomly selected questions that will be graded with some partial credits, all other questions will be graded partially by completion.

You got ~60% of the credit if you complete the problem but didn't get the correct final answer.
You got 100% of the credit if you complete the problem and get the correct final answer.

Many problems in your homework will be either truth/false conceptual questions or problem like solving a given ODE. By completion, it means one must show full justification. If your answer is not consistent with your justification, the grader has the right to give you 0% for the particular problem.

Discuss with others: You are encouraged to talk to your classmates, discuss questions on Piazza and check answers with each other. However, your work should base on your own work and your own words. We will randomly go through your work. If you didn't show not enough work or were caught copying people's work (it's fairly obvious from a grader point of view), you will receive a 0 on that particular assignment.

We are aiming at two take-home exams. The following are the tentative dates:

Midterm:  Assigned W5 4/30 (Fri), Due W6 5/7 (Fri)

Final:  Assigned on 6/7 (Mon) 8 am. Due  6/10 (Thurs) 5 pm. Time limit: 2 days

Both exams are open-book but no internet search. And of course, you will have to work on your own. You can use the listed textbooks, our lecture notes/slides, and homework solutions provided by our class (basically everything on Canvas+textbooks). But you are not allowed to search anything related to the exam online or consult with anyone during the exam time.

Grade in 100% is calculated based on: 60% homework, 40% exam

The conversion to 4.0 GPA will be made at the end of the quarter. I will refer to historic record to determine the conversion formula. Historically, the median is around 3.5 and about 5~10% of the students could get 4.0.

Students shall abide by the University of Washington Academic Responsibility policies. Violations will be reported to the appropriate Deanâ€™s Representative and through the web-page for Community Standards and Student Conduct. The instructor reserves the right to assign a failing grade for the course for serious violations of student conduct.
Note: Use of websites or online forums which provide solutions for class assignments is not allowed. You are also not allowed to distribute course materials to any individual or corporation outside of this course without the instructor's consent.
Collaboration and study groups are highly encouraged! Copying or submitting work that is identical to a classmate's work or online solution is academic misconduct and will be reported according to the policies communicated by Community Standards & Student Conduct (CSSC). Any form of dishonesty in an assignment will lead to a zero on the assignment. Other consequences, including a failing grade in the course, will be determined based on the seriousness of the offense or multiple offenses at the instructor's discretion.

## 5. Access and Accommodations

If you have already established accommodations with Disability Resources for Students (DRS), please communicate your approved accommodations to me at your earliest convenience so we can discuss what we will do for this course. If you have not yet established services through DRS, but would like to have one, you are welcome to contact DRS at 206-543-8924 or uwdrs@uw.edu. DRS offers resources and coordinates reasonable accommodations for students with disabilities and/or temporary health conditions. Reasonable accommodations are established through an interactive process between you, your instructor(s) and DRS. It is the policy and practice of the University of Washington to create inclusive and accessible learning environments consistent with federal and state law.
Catalog Description:
Introductory survey of ordinary differential equations; linear and nonlinear equations; Taylor series; and. Laplace transforms. Emphasizes on formulation, solution, and interpretation of results. Examples drawn from physical and biological sciences and engineering. Prerequisite: MATH 125 or MATH 135. Offered: AWSpS.
GE Requirements Met:
Natural Sciences (NSc)
Credits:
3.0
Status:
Active
Last updated:
June 12, 2024 - 12:48 pm