AMATH 383 A: Introduction to Continuous Mathematical Modeling

Winter 2022
TTh 2:30pm - 3:50pm / OTB 014
Section Type:
Syllabus Description (from Canvas):

1. Course Information:


Introductory survey of applied mathematics with emphasis on modeling of physical and biological problems in terms of differential equations. Formulation, solution, and interpretation of the results.

System of interest: Complex Systems (or this webpage by Sante Fe), which includes most systems in real life

Math Used: Algebra, Calculus, Linear Algebra, Differential Equations (+dynamical systems), and Probability

Modeling Philosophy: There are fundamentally two kinds.

      1. "Mechanistic" modeling (gives the phenomena a mechanistic cause), e.g. Newton's Classical Mechanics
      2. Data-driven modeling (uses data to represent the phenomena mathematically), e.g. Kepler's law

We will be focusing on the first type.

General Information:

Instructor: Ying-Jen Yang


Lectures:    T Th 2:30-3:50 at OTB 014 (the original scheduled GLD 322 is having a heating issue)

                  Lectures will be streamed and recorded on Zoom as well

Office Hours: WF 2-3 pm (go to Zoom tab)

TA: Saba Heravi

TA's Office Hours: Th 6-8 pm (go to Zoom tab)


2. Course Material:

Textbook and References:

  • Lecture note will be provided.
  • (Suggested) Topics in Mathematical Modeling, by K.K. Tung, Princeton University Press

Ebook available at UW library:

Click on the Online access>

Then click on JSTOR ebooks purchased

Here you will be on publisher's webpage, and you will see downloadable .pdf for each and every chapter of the text book.  

Many exercises are directly from the book or modified from there.

  • (Suggested) Nonlinear Dynamics and Chaos, by Steven H. Strogatz, 2nd ed.

Ebook available at UW libraryClick on Online Access

Many exercises are directly from the book or modified from there.

  • (Optional) Mathematical Biology I: An Introduction, by J. D. Murray, 3rd ed.
  • (Optional) More paper to come


Outline (Tentative):

Week 1 (1/03-1/07): Introduction of mathematical modeling and Kepler's law as an example

Week 2 (1/10-1/14): Formulating ODE and Numerical Method for ODE

Week 3 (1/17-1/21): Concepts of Invariant, Stability Analysis, and Bifurcation

Week 4 (1/24-1/28): 1-D Bifurcation

Week 5 (1/31-2/04): 2-D Systems and Interactions

Week 6 (2/07-2/11): Multi-Stability and Coexistence

Week 7 (2/14-2/18): Oscillation

Week 8 (2/21-2/25): Special Types of Dynamics: Reversible, Conservative, Dissipative,...etc

Week 9 (2/28-3/04): Intro to Stochastic Processes and Markov Chain

Week 10 (3/7-3/11): Stochastic Thermodynamics of Markov chains


From week 7-10, some lectures may have quest speakers, or become a work-in-class day for students to work on their projects.


3. Assignments and Grade

Join Piazza by this link to ask questions about homework and term project.


General: Homework is assigned weekly. Homework will be posted on Friday and due at 9 pm on the Friday next week. You must submit your scanned or typed-up homework PDF file to Gradescope. Remember to label your work with corresponding questions. No late homework is allowed. If for some reasons that you need extension, please email the instructor.

Format: Submitted files must be portrait, letter-size, and easy-to-read. LaTeXing (or use LyX) is highly encouraged. You must present all your work to justify how you got those answers. If you didn't show your work, you will get a 0.

Discussion: You are encouraged to talk to your classmate, discuss questions on Piazza and check answers with each other. However, your work should base on your own words. 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.

Proposal and Term Paper

One of the main learning goal of this course is to have a first taste on how to do a theoretical/mathematical research. You will form a group of 2-4 people and study one topic that interests all of the group members. The group would submit

  • a proposal on the topic of your final project is due by the end of Week 8
    (about 2-5 pages long including some preliminary work; font size 11~12, 1.5 to double spaced text) 
  • a term paper is due by the end of Week 10
    (about 10 pages if not including figures and about 15 pages including figures; font size 11~12, 1.5 to double spaced text)

The project can be original or a review from journal papers or book sections. A potential project topic list will be provided but you can (and are encouraged) also come up with your own topic (talk to the instructor either way). A guide on how to write a term paper will also be provided soon. Many of the term papers would turn out to be a critical and careful review of some part of journal papers and/or book sections+some extensions/work of your own. Of course, synthesize the several papers you review on the same topic and present them in one single coherent story. Reproduce and discuss the papers' the assumptions, simplifications, analysis, and their discussion,...etc, how they did it and how to improve.


  1. Six weekly assigned homework for the 2/3 of the quarter 
  2. a term paper proposal with a group (2-4 people)
  3. a term paper with the same group

Details percentage: (tentative) 65% homework; 10% proposal; 25% term paper.


4. Academic Responsibility

Students shall abide by the University of Washington Academic Responsibility policies (Links to an external site.). 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 applied mathematics with emphasis on modeling of physical and biological problems in terms of differential equations. Formulation, solution, and interpretation of the results. Prerequisite: either AMATH 351, MATH 136, or MATH 207. Offered: AWS.
GE Requirements Met:
Natural Sciences (NSc)
Last updated:
May 24, 2024 - 9:18 pm