Analysis & Dynamics of Differential Equations
Math 341 Spring 2017 TuTh 8:00 - 9:15 Burruss 0355
| Instructor: |
Roger Thelwell |
Office: Roop 106 |
| Contact: |
thelwerj@jmu.edu |
tel: 568-5103 |
| Webpage: |
Check on CANVAS |
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| OFFICE |
Mon 2:30-3:30 pm, Wed 11 - noon |
| HOURS: |
Tues 11-noon, Thurs 12-1:30 pm, and by appointment |
| My Calendar: |
Schedule
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| Text: |
Nonlinear Dynamics and Chaos by Stephen Strogatz |
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Description:
Introductory study of nonlinear dynamics and chaos intended primarily for upper-level undergraduates in science and mathematics. Topics include stability, bifurcations, phase portraits, strange attractors, fractals and selected applications of nonlinear dynamics in pure and applied science. Computing will be utilized for simulations and graphics.
A qualitative, rather than quantitative, approach will be used. We will focus on geometric techniques that provide a suprising amount of information about the behavior of the solution, without the need to actually construct the soution.
Objectives
In this course students will:
- learn to apply qualitative and quantitative methods to the study of ordinary differential equations
- be familiar with phase space and Poincar ́e sections
- be able to carry out stability analysis of solutions and use bifurications to describe qualitative changes in stability
- know the characteristics of continuous and discrete systems
- know the characteristics of periodic, quasi-periodic and chaotic oribts
- explore strange attractors and learn about their fractal geometry
- be familiar with basic examples of both dissipative and conservative dynamical systems
- appreciate the limits of predictability and concepts of universality in chaotic systems
- be exposed to notions of spatiotemporal chaos, turbulence, and stochastic methods
Attendance:
You should come to every class. While I won't require attendance, the probability of
spectacular failure increases with each missed class. The lectures will supplement the material
so ably treated in the text, but will also contain jewels of information not found there. If
exceptional situtations arise that force you to miss class, contact me as soon as possible so
as to not fall behind.
Please use office hourse, and don't be afraid to send an email or give me a call.
Homework Sets:
Check CANVAS for the most current assignments.
You'll sometimes be asked to incorporate computer work as a necessary part in these assigments. Homework sets will be collected several times throughout the semester, and are a large part of the course grade. You must
SHOW your work for full credit and turn in neatly compiled problems.
As a general rule, late homework will not be accepted.
Make it easy for me follow your work - you won't get
credit by making me guess!
You are strongly encouraged to work with classmates on homework, but copying another's work will result in zeros for all. The
homework sets are pledged, and some problems may be restricted to no outside help.
Beware: your chances of passing the course are poor if you consistently find that you can't
complete the homework yourself. Some of the homework score may reflect completeness
of the assignment (i.e., reasonable attempts at all problems in the set) while the
remainder will be determined from your detailed solutions to randomly selected
problem(s) from the homework set.
Project
You'll work in a group of 2 to 3 to explore a dynamical system.
I'll keep track of your progress via weekly meetings that will begin after spring break. Near the end of the semester, your group will present your work in-class and also submit a written report.
Grading:
The standard scale will be used. 90-100: A- to A range; 80-89: B- to B+ range; 70-79: C- to C+ range;
60-69: D- to D+ range; below 60: F. An exceptional job on the final exam or
excellent class attendance and participation could bump borderline cases up to the
higher grade. Grades will be calculated in the following manner:
- Homework: 60%.
- Project: 10%. Pick a dynamical system to explore before spring break!
- Midterm: 10%. Take home (due Thursday, March 2).
- Final: 20%. Open note, and scheduled for Thursday May 4th from 8:00 am to 10:00 am in Burruss 0355, per the registrar (full SP17 schedule here).