Dynamical Systems, Spring 2008
| Basic Information | |
| Course Title | Dynamical Systems (110.421) |
| Professor | Qiao Zhang (qzhang@math.jhu.edu) at 412 Krieger Hall |
| Office Hours | Tuesdays and Thursdays 3:00 pm--4:00 pm at Krieger 412 |
| Lecture | Tuesdays 1:30--2:45 pm at Maryland 114; Thursdays 1:30--2:45 pm at Maryland 110 |
| Course Information | |
| Description | A basic introduction to the general theory of dynamical systems from a mathematical standpoint, this course studies the properties of continuous and discrete dynamical systems, in the form of ordinary differential and difference equations and iterated maps. Topics include contracting and expanding maps, interval and circle maps, toral flows, billiards, limit sets and recurrence, topological transitivity, bifurcation theory and chaos. Applications include classical mechanics and optics, inverse and implicit functions theorems, the existence and uniqueness of general ODEs, stable and center manifolds, and structural stability. Prerequisites: Calculus III, Linear Algebra, and 110.302. |
| Textbook | Boris Hasselblatt and Anatole Katok, A First Course in Dynamical Systems: with a Panorama of Recent Developments, Cambridge University Press, ISBN-13 9780521587501. |
| Homework and Exams | |
| Homework | Homework assignment will appear in the course homepage after each class, and will be due on the following Tuesday. Sufficient practice in the homework is essential to master the material, so it is highly recommended to try, with the assistance from our Math Help Room at Krieger 213 if necessary, to complete every assignment. The Help Room will be open from 9:00am to 9:00 pm, Monday through Friday, and everyone is encouraged to make the best use of it. |
| Exams Policy | There will be one in-class midterm exams scheduled on March 25, and a three-hour final exam at May 11, 2--5pm. No calculator, lecture notes or other study materials will be allowed in the exam. If you have time conflicts with an exam or need special arrangements, you must notify the instructor in writing at least one week in advance. There will be no makeup exams; if you miss an exam with a valid excuse (with documents from either the Office of Student Life and/or doctors), then your grade for the missing exam will be the weighted average of your other grades. |
| Grading Policy | The grade for this course will be determined as follows.
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| Special Aid | Students with disabilities or other special needs who require classroom accommodations must first contact Dr. Richard Sanders, the Homewood Undergraduate Disability Services Coordinator, in the Office of Academic Advising, Garland Suite 3A, (410) 516-8216, to discuss reasonable and appropriate accommodations. To arrange for testing accommodations, the request must be submitted to the instructor at least 7 days (including the weekend) before each of the midterms or final exam. You may make this request during office hours, after class or by sending me an email. |
| Academic Ethics | The strength of the university depends on academic and personal integrity. In this course, you must be honest and truthful. Ethical violations include cheating on exams, plagiarism, reuse of assignments, improper use of the Internet and electronic devices, unauthorized collaboration, alteration of graded assignments, forgery and falsification, lying, facilitating academic dishonesty, and unfair competition. Report any violations you witness to the instructor. You may consult the associate dean of student affairs and/or the chairman of the Ethics Board beforehand. See the guide on "Academic Ethics for Undergraduates" and the Ethics Board Web Site for more information. |