Math 241 Ordinary Differential Equations Syllabus

This is the course syllabus for Winter 2020 Math 241 Ordinary Differential Equations.

Instructor Info

Rob Thompson
rthompson@carleton.edu
Anderson 238 x4366
Office hours: see here

Course Description

This class is an introduction to ordinary differential equations (ODE), mathematical modeling and applied mathematics in general. We'll study some methods for solving ODE explicitly, but our focus will be on the "language" of ODE in applied math and ways we can get qualitative information about the way that solutions to ODE behave. Major topics will include: separation of variables, phase portraits, equilibria and their stability, non-dimensionalization, and bifurcations of many kinds. We'll look at using ODE to model physical, biological, chemical, and social processes.

Classroom climate

Our classroom is a community where everyone should feel respected and empowered to succeed. We are here to learn (myself included), and learning means cooperating, asking lots of questions, taking risks, and making mistakes! Please be kind to one another and help make our classroom a place where everyone is encouraged to participate.

Readings

We will follow the (really great) textbook:

The class will cover Chapters 1-3, 5-8, omitting some sections. There will be regular assigned readings from this book, so you'll want to purchase it or get access to a copy. Several copies will be available in the Math Skills Center for use 24 hours a day.

Mathematica

We will write code in Mathematica to solve differential equations, work with data and create visualizations. You can install Mathematica on your computer for no cost, use it in the Carleton computer labs. If your computer will run it, you should install Mathematica. To install it, follow the instructions at Carleton's Mathematica portal.

Note-taking duties

I will ask for two volunteers every class period to be note-takers. On a day that you are a volunteer, you will take extra careful notes, then promptly scan them into a single pdf document and email them to me. I will post them in our Notes directory for everyone to access.

Assessment

Your grade in this class will be based on weekly problem sets, participation, three take-home exams, two labs and a final project in the proportions below.

Problem Sets 15%
Participation 5%
Exams (3) 20% each
Labs (2) 5% each
Final Project 10%

Problem Sets
Every week you will need to submit written homework. This homework will be posted on the course webpage, and due the week after it is posted on Tuesdays at 5pm. Please put your completed problem sets in the Math Skills Center box labeled “Rob Thompson Math 241 Section X” (where X is your section, either 3a or 4a) before the deadline. Late assignments might not be accepted unless arrangements are made with me in advance of the deadline. I will drop your lowest problem set score from your final grade.

Participation
This is a miscellaneous category, based on completion of occasional reading quizzes, in class activities, willingness to volunteer for note-taking and other factors at my discretion.

Exams
You will have three take-home exams. These exams will be distributed in the third, sixth, and ninth week of class, and you will have a week to complete them. These exams will be done without collaboration. Exam content and allowed time and resources will be announced ahead of time. These exams are meant to be just like in-class exams, except done on your own schedule in order to alleviate test anxiety and pressures of in-class exams. I will state the rules of the exam clearly on the cover page; breaking these rules is academic dishonesty and will be referred to the Academic Standing Committee.

Labs
You will complete two lab assignments, done in small groups. These labs will give you a chance to investigate questions that are more open-ended than typical homework problems and to practice communicating your results.

Final Projects
There will be a final project for this course, done with a partner. This final project will consist of reading a research level article on differential equations, and recording a video presentation on the contents of the article. I will suggest many possible articles, or let you choose your own (with my approval).