Math 357

Dynamical Systems

 

How to get in touch with me

Professor Tom LoFaro


Office: Olin 314
Office Hours: see schedule
Phone: 933-7463
Email: tlofaro@gustavus.edu

 

Text

Dynamical Systems and Bifurcations, J. Hale and H. Kocak, Springer-Verlag.

 

Objective

This course introduces the fundamental ideas and applications of both continuous and discrete dynamical systems.

 

Chapters Covered

We will be covering parts or all of chapters 1 through 12.  These chapters will be supplemented with additional material as necessary.   Here is the tentative schedule for the semester.

 

Grading

Homework Assignments

50 points

3 Exams

300 points

4 Projects

100 points

1 Final Exam

150 points

 

Homework

Homework assignments will be given in class period and will be posted on the Math 357 homework page.  Explain your work clearly and concisely in complete sentences when appropriate.  Each set is worth 10 points.  Homework will be collected on the date indicated in class. No late homework is accepted for any reason.  The lowest homework score will be dropped.  Staple each homework set separately.

 

Exams

The three midterm exams will be individual exams. 

 

 

Exam Schedule

Midterm I

10/3

Midterm II

11/4

Midterm III

12/5

Final Exam

TBD

   





Projects

You will be doing four projects in this class.  The projects will be done in groups of 2 or 3.  Projects may cover applications, theory, and/or computer simulations of dynamical systems.  The final report will be graded on both mathematical content and accuracy as well as on style and grammar.  I will provide you with guidelines on the project later in the semester.  Here is the schedule for the projects.

Project 1

8/7

Project 2

8/28

Project 3

TBD

Project 4

TBD

 

Helpful Links

·       A graphical analysis applet. (from my pal Bob D.)

·       A bifurcation diagram applet. (again from big Bob)

·       If you don’t like Bob’s then try these by C.J. Kentler who wrote them for me at WSU.

·       There is a ton of this stuff out on the web.  If you find any you like better than these (in particular ones that will print) then let me know and I’ll add the links).

 

Maple Worksheets

You may or not need these.  I’m just leaving the links here in case we use them.

In Firefox: To download these worksheets right click on the link and choose Save link as …from the drop-down menu.  Save the file as whatever.mw (the browser may add the extension xml._ If so delete this.)  After you save the file you can then open it in Maple 13.

In Internet Explorer: To download these worksheets right click on the link and choose Save Target as …from the drop-down menu.  Save the file as whatever.mw (the browser may add the extension xml._ If so delete this.)  After you save the file you can then open it in Maple 13.

·      An Introduction to Maple for Discrete Dynamical Systems (Project 1)

·      Plotting and Graphical Analysis using Maple (Chap. 4 homework)

·      Fixed and Periodic Points (Chap. 5 homework)

 

Academic Honesty:

As a community of scholars, the faculty and students of Gustavus Adolphus College have formulated an academic honesty policy and honor code system, which is printed in the Academic Bulletin and in the Gustavus Guide. As a student at Gustavus Adolphus College I agree to uphold the honor code. This means that I will abide by the academic honesty policy, and abide by decisions of the joint student/faculty Honor Board.

 

Disability Services

Gustavus Adolphus College is committed to ensuring the full participation of all students in its programs. If you have a documented disability (or you think you may have a disability of any nature) and, as a result, need reasonable academic accommodation to participate in class, take tests or benefit from the College’s services, then you should speak with the Disability Services Coordinator, for a confidential discussion of your needs and appropriate plans. Course requirements cannot be waived, but reasonable accommodations may be provided based on disability documentation and course outcomes.  Accommodations cannot be made retroactively; therefore, to maximize your academic success at Gustavus, please contact Disability Services as early as possible. Disability Services (https://gustavus.edu/advising/disability/) is located in the Advising and Counseling Center.

 

 

English as a Second Language

Support for English Language Learners (ELL) and Multilingual students is available via the College's ELL Support staff person, Andrew Grace (agrace@gustavus.edu or x7395).  He can meet individually with students to consult about academic tasks and to help students seek other means of support. The ELL Support person can also consult with faculty members who have ELL and multilingual students enrolled in their classes. The College’s ELL staff person can provide students with a letter to a professor that explains and supports academic accommodations (i.e. additional time on tests, additional revisions for papers). Professors make decisions based on those recommendations at their own discretion. In addition, ELL and multilingual students can seek help from peer tutors in the Writing Center.


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