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AMATH 351 A: Introduction To Differential Equations And Applications

Meeting Time: 
MWF 10:30am - 11:20am
MUE 153
Ying-Jen Yang
Ying-Jen Yang

Syllabus Description:

1. General Course Information


Lectures: Recorded videos will be posted at the Panopto Recordings tab

(Can also find links to there at the Modules tab)

The videos can only be used for students enrolled in the course to review materials. Students should not distribute them without the consent of the instructor.

Instructor: Ying-Jen Yang


(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:

MWF 10:30-11:30 

Join Zoom Meeting:

(Go to the Zoom tab on the left)

Teaching Assistant (TA)

Teaching Assistant: Yu-Chen Cheng

TA's email:

TA's office hours: TBD (will use Zoom, starting from Week 2)

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, or discuss questions with people (even anonymously). Also, it is easy to use LaTeX command on Piazza, just use $$ $$. See this Link for introduction on the LaTeX commands for math equations. 

Please use the following Link to sign up for Piazza!


2. Course Content Information

See Modules for details.


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. Most importantly, we aim to illustrate the logic hidden behind different solution methods, not just doing tedious algebra manipulation (although sometimes it is hard to avoid).


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 a lot of linear algebra, some complex variable, and power series that are relevant to us. Exposure to linear algebra, complex variable, and Taylor series would be helpful.

Rough Outline

  1. Introduction to Differential Equations: Variables, Matrices, 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 deemphasizing Laplace transform in this first ODE course (in my opinion, better learn it after learning contour integral in complex analysis to have a more systematic way to perform the inverse Laplace transform, rather than guessing the inverse 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 slides would be provided. (I may provide lecture note as well)

For textbook references, the following two books are recommended:

  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. B&D, Chapter 1- 5 , 7-9 ).
    It is the standard textbook for undergraduate ODE class. We will focus mostly in the material within.
  2. Steven H. Strogatz, Nonlinear Dynamics and Chaos, 2nd ed. (S, 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 book and the subject.


3. Assignments and Grades

Homework Assignments

General: Homework is assigned weekly. You must submit your scanned or typed-up homework PDF file to Canvas. No late homework is allowed. 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. LaTeXing (or use LyX) is highly encouraged. The first page of your submitted homework must be your "answer sheet" where you collect and present all the answers of all the problems (except the proof problems). Format of the answer sheet will be provided with the problem sheets. For the rest of the pages, you must present all your work to justify how you got those answers. If your submission is not in the required format or you didn't show your work, you will get a 0.

Partial Credits: We have a big class. And I am asking the TA to grade all the questions because I dislike statistical grading. Therefore, most of the homework problems will NOT have partial credits (only exception is proof like question). 

Many problems in your homework will be either truth/false problems or be solving a given ODE. No-partial-credit-for-homework policy also helps you to develop the good habit of checking your answer. For solving ODE problems, I will provide the form of the answer with a lot of boxes for your convenience. 

Discussion: You are encouraged to talk to your classmates (online), discuss questions on Piazza and check answers with each other. However, your work should base on your own words. The TA will randomly go through your work. If you didn't show any 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.

Exams and Grades

We will have two take-home exams.

Midterm: starting on May 1 (Fri) (tentative), time length TBD

Final: starting on Jun 8 (Mon) (tentative), time length TBD

Both exams are open-book but no internet. You can read any textbook, our lecture notes/slides, homework solutions. But you are not allowed to search anything on the internet during the exam time.

Grade in 100% is calculated based on: 50% homework, 20% midterm, 30% final.

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 get 4.0.


4. Academic Responsibility

Students shall abide by the University of Washington Academic Responsibility policies. Violations will be reported to the appropriate Dean’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 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: 
Natural World (NW)
Last updated: 
March 23, 2020 - 10:18am