and Chaos
110.421, MTW 12, Room Krieger 304
Dr Mark Haskins
E-mail address: mhaskin@math.jhu.edu
Telephone: 410-516-4047
Department: Mathematics
Office: Krieger 312
Office Hours: M 3-4, T 9-10, Th 11-12
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Dynamical Systems and Chaos 110.421, MTW 12, Room Krieger 304 Dr Mark Haskins E-mail address: mhaskin@math.jhu.edu Telephone: 410-516-4047 Department: Mathematics Office: Krieger 312 Office Hours: M 3-4, T 9-10, Th 11-12 |
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HTML grade sheet A printed version is also posted on my office door. |
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A number of ideas for projects for the class and project guidelines. |
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The Matlab homepage at Mathworks has documentation about all aspects of Matlab. You may find Getting Started helpful if you have never used Matlab before. |
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HW 0 (review) : due beginning of class 09/12 HW 1: due 09/18 Postscript, HTML and PDF versions available HW 2: due 09/25 available in Postscript, HTML and PDF versions. HW 3: due 10/02 available in HTML and PDF versions. HW 4: due 10/10 available in HTML and PDF versions. HW 5: due 17/10 available in HTML and PDF versions. HW 7: due 31/10 available in HTML and PDF versions. HW 8: due 06/11 available in HTML and PDF versions. HW 9: due 13/11 available in HTML and PDF versions. HW 10: due 21/11 available in HTML and PDF versions. HW 11: due 28/11 available in HTML and PDF versions. HW 12: due 05/11 available in HTML and PDF versions. |
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This course is designed to introduce students from a variety of science and engineering backgrounds to some of the fundamental notions of nonlinear dynamics. The course does not presume a prior knowledge of differential equations although it will partly be about them (also see Prerequisites below). The approach of this course to differential equations will be quite different from those of the other differential equations courses. In general there will be an emphasis on understanding the qualitative behaviour of systems rather than learning how to "solve" some special equations. A preliminary syllabus can be found below. However, the precise details of what will be covered in the course will be determined to some extent by the background and interests of the students in the class. We will certainly discuss parts of the subject that have receive much popular attention: chaos, the Lorenz system, strange attractors, the Mandelbrot set and fractals. The goal is to sail that fine line between breadth and depth of coverage of material. Computers can be an effective tool for "experimentally" discovering properties of dynamical systems, especially discrete ones, and can lead to theoretical discoveries too. The course will include homework that involves computer work. The primary software package we will use is Matlab. A key issue will be to determine when we can rely on the computer results i.e. when does the computer lie? |
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Confusingly, Robert Devaney has written two different introductory books on chaotic dynamical systems 1. An Introduction to Chaotic Dynamical Systems 2. A First Course in Chaotic Dynamical Systems: Theory and Experiment The first book is somewhat more advanced than the second. The bookstore has copies of the first title. I expect the level of the course to fall somewhere between the two books. Both books focus exclusively on discrete dynamical systems. For the continuous dynamical systems parts of the course I will give other references and handout notes or photocopies of appropriate material. Other texts you might find helpful are: Encounters with Chaos, Denny Gulick Chaotic Dynamics: an introduction, G.L.Baker and J.P.Gollub Understanding Nonlinear Dynamics, Daniel Kaplan and Leon Glass Chaotic & Fractal Dynamics: An Introduction to Applied Scientists & Engineers, F.C. Moon. You can come and browse any of these books in my office during office hours. |
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The formal prerequisites for the class are Calculus III and Linear Algebra. Note: a course in differential equations is not a prerequisite. We will make more extensive use of notions from calculus than from linear algebra. Most notions we need from linear algebra will be recalled as needed. Students who have not taken classes recently that use calculus would benefit by reviewing the basic notions from Calculus I & II. |
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Homework, 30%: Assigned weekly and due weekly. Some problems may not be graded. No late homework accepted without a doctor's note. You may consult with classmates but be sure to do most of the work yourself. Assignments will generally be due at the beginning of class on Tuesday (beginning Oct 3). Midterm Exam, 20%: A combination in-class/take-home exam to be given in mid October, provisionally Tuesday Oct 17. Further details will be announced. Project, 20%: An opportunity to study in greater depth material of interest to you and related to the course subject. The project could be theoretical, practical (e.g. building a physical model of something), computer-related (e.g. simulating a system) or some combination of these. This project will be due before the last day of class. The subject of the project will be chosen by you with guidance given by me. Further details will be given later. Final Exam, 30%: Another combination in-class/take-home exam. Provisionally, in-class component given on final class day, Monday December 11 with take-home part given during preceding weekend. |
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A preliminary syllabus |
| Last updated 18 September 2000 Mark Haskins |