Math 20: Differential Equations

Instructor	Tanya Leise
Email	tleise at amherst dot edu
Phone	542-5411
Office	SMudd 503
Office hours	Feel free to drop in whenever my door is open, or make an appointment Regular hours: MTWF 10am-noon, Th 9am-noon
Text	Strogatz, Nonlinear Dynamics and Chaos (on reserve in Merrill Library)

Course goals:

• Understand the qualitative dynamics of linear and nonlinear differential equations
• Be able to derive bifurcation diagrams for nonlinear differential equations
• Learn general principles for analysis of DEs and other kinds of models, like finding normal forms and nondimensionalizing equations
• Through a final project, have each student study a topic or application of interest (for example, the proof of an important theorem, an application from biology or economics, or a look at chaos)

Course Topics:

• One-dimensional differential equations (first order) and basic types of bifurcations that can occur
• Dynamics on a circle
• Two-dimensional problems (second order), including stability analysis via linearization and phase plane analysis
• Introduction to chaos

Attendance: You are to be in class and to be there on time. Cooperative learning is more effective and more fun than struggling through material on your own. If you do miss a lecture, it is your responsibility to obtain the material that you missed and to get your assignments handed in to me. Keep me informed of your status--if you are ill or will be going on a sports-related trip, for example, please send me an email as soon as possible letting me know the situation. I am much more willing to be lenient in extensions and such if you have kept me notified of your situation.

Questions: If you have a question during lecture, please raise your hand and ask it right away. Chances are that other students are wondering the same thing. If a question arises later, feel free to visit my office and we'll work through sample problems until you are comfortable with the mathematics. Always feel free to ask me to slow down as well.

Grading: Your course grade will be based on three exams (50% total), homework/worksheets/labs (25%), and a final project (25%). There will not be a final exam.   I will try to keep your grades entered in the Blackboard Gradebook in a timely manner; please check them occasionally and let me know if you find any discrepencies.

Intellectual Responsibility

• Exams. Your work must be entirely your own, so please follow the guidelines of the honor code. Unless I explicitly allow other aids, you are only allowed whatever implements you need to read and write (no notes or calculators).  Please turn off your cell phone in kindness to your fellow test-takers during in-class exams.
• Labs. Sending or receiving a copy of a Mathematica file that contains student work violates the honor code and will be treated as plagiarism. You may talk with others about strategies for solving a problem in Mathematica, but please do not share files.
• Homework. You may study with other students following these guidelines:

1. If you worked with or received help from any source other than me, you should put a note on the front of your homework saying, "I worked with <names>." Make sure your name stands out as the author of your homework.
2. Working together does not mean that one of you does the first half of the homework set and the other does the second. Everyone should work on every problem.
3. Each student must hand in his or her own problem set. You may not hand in a single packet as the work of multiple people.
4. Do not copy someone else's solution—you will not learn anything and it is plagiarism. You may discuss problems with others, but then you must be able to work out the solution on your own again and write it down yourself.
5. If you are unsure what agrees or does not agree with the precepts of intellectual responsibility in this course, feel free to talk to me about it.

Homework Guidelines

• All problem sets are due at THE START OF CLASS. Late homework will receive half credit for homework handed in after start of class but within 2 class days (e.g., homework due Monday will get half-credit if handed in after the start of class on Monday through Wednesday start of class, and will not accepted after that).
• If you are unable to attend class due to illness or an emergency, let me know as soon as you can and we will work out an appropriate schedule for assignments.
• Your name should be written on all sheets handed in.
• Problem solutions must be written out in the order they were assigned.
• Multiple pages must be stapled or clipped together.
• Homework should be neat. No dog ears. No messy edges from notebook paper.
• Where appropriate, please box or highlight final answers. In general, try to make your answers readable and easy to find. Always keep the grader happy!
• As mentioned elsewhere, no copying!

Course Resources:

Don't struggle alone! You have many options for getting help with this course.

• Me. Feel free to come to my office hours, make an appointment by email or phone, or simply try stopping by my office—you are welcome whenever my door is open. If you have some anxiety about taking math exams, please come see me and we can work together on building your math confidence.

• Homework. Although the practice problems are not graded, please work through them. Mathematics is learned ACTIVELY, not passively. You can't absorb math through listening or reading, even if you think you understand it all.
• Textbook. I won't go over everything that is contained in the text, and I will try to avoid doing the same examples. Hence your textbook in an important independent source of information and you should read it!
• Lecture notes. Reviewing the notes you take in lecture will give you a chance to see the material again after you have had some time to assimilate it.
• Your classmates. Discussing math with others can help you think through the concepts. Explaining an idea you already understand will deepen your comprehension, and for the concepts that you don't understand well, the explanation of a peer may be more helpful than mine or the textbook's.
• Mathematica is available for all college-owned computers, and is already installed in all of the public labs, e.g. in on the first floor of Seeley Mudd.  Mathematica isn't available for student-owned computers for free, but you can access Mathematica by connecting remotely to remus or romulus via the Gnome Desktop (see https://cms.amherst.edu/offices/it/help/software/unix/gnome/node/23577).

To the Math 20 Homework Schedule