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Syllabus for ESM 4114

(PDF can be downloaded at the bottom of the page)

ESM 4114 Spring 2011Nonlinear Dynamics and Chaos

Class Location and Times: Norris Hall 342, Tuesdays and Thursdays 12:20 – 1:35 PM

Instructor:

Mohsen Gheiarieha

Office: 309 Norris Hall

Office Hours: Monday, Wednesday, Friday 1:00 – 4:00 PM and by appointment

Tel: 231-1234

E-mail: gheisari@vt.edu

Please feel free to call or email to set an appointment.

Lorenz Attractor

Course and Class Scope:

By the end of the semester the students will have an understanding of nonlinear and chaotic phenomena in mathematics, nature and technology and how they can be studied.

The students will be asked to submit their ideas, suggestions and solutions before each topic and we will start the topic from discussing these ideas in the class. Useful

information, assignments and grades will be posted on VT scholar regularly.

Course Prerequisites:

ESM 3124 – Intermediate Dynamics and Math 2214 – Differential Equations

A conceptual understanding of what a differential equation and its solution mean, is key to learning this course.

Text:

- Nonlinear Dynamics and Chaos by Steven Strogatz

- Methods, information and solutions that we generate while discussing the students’ ideas in class: these will be posted on scholar under “Resources”.

Learning Objectives:

Students will:

- learn how to model different systems using differential equations. They will be familiar with least one example of modeling physical, social, chemical, biological and electrical systems.

- be able to write a system of differential equations in the form of a dynamical system and analyze it linearly.

- know the characterizations of a chaotic system and explain with examples.

- be able to define and quantify chaos in a dynamical system.

- can explain the notion of fractals and strange attractors quantitatively.

Course Topics:

- Dynamical systems and nature, society, technology

- One-dimensional dynamical systems

- Bifurcations in one dimension

- Two-dimensional dynamical systems

- Analysis of linear 2D systems

- Analysis of non-linear 2D systems

- Bifurcations in multi-dimensional systems

- Chaos

- Maps

- Fractals

- Strange attractors

Assignments

A- The students will be asked to read the posted intro on scholar about the next topic and submit their own ideas about the topic in one page. Each topic takes between 1 to 3 sessions of the class.

B- A problem will be posted after each session.

C- Project: the students will be asked to analyze and simulate a chaotic dynamical system chosen by them. Further information will be posted on scholar. Due date for choosing the topic is 04/02/2011 and due date for the simulation and presentation is 05/05/2011.

Grades

There will be no final exam. Grades will be assigned as follows:

- Pre-course assignments and discussions: 30%

- Assigned problems: 30%

- Project: 20%

- In class quizzes: 20%

In case of missing an assignment or class because of emergency or issues, I will be glad to work with you to do a makeup assignment or quiz.

Virginia Tech Honor System

The honor code will be strictly enforced in this course. All aspects of your course work are covered by the honor system. Any suspected violations of the honor code will be

promptly reported. Please refer to VT honor code website www.honorsystem.vt.edu for more information.

Students with Disabilities

I will be glad to help you for any accommodations needed for the course. Please refer to VT Services for Students with Disabilities www.ssd.vt.edu or call 231-3788 (V), 231-

1740 (TTY) for help and more information. “Students with disabilities are responsible for self-identification.”

Virginia Tech Principles of Community

Virginia Tech is a public land-grant university, committed to teaching and learning, research, and outreach to the Commonwealth of Virginia, the nation, and the world

community. Learning from the experiences that shape Virginia Tech as an institution, we acknowledge those aspects of our legacy that reflected bias and exclusion. Therefore,

we adopt and practice the following principles as fundamental to our on-going efforts to increase access and inclusion and to create a community that nurtures learning and

growth for all of its members:

* We affirm the inherent dignity and value of every person and strive to maintain a climate for work and learning based on mutual respect and understanding.

* We affirm the right of each person to express thoughts and opinions freely. We encourage open expression within a climate of civility, sensitivity, and mutual respect.

* We affirm the value of human diversity because it enriches our lives and the University. We acknowledge and respect our differences while affirming our common

humanity.

* We reject all forms of prejudice and discrimination, including those based on age, color, disability, gender, national origin, political affiliation, race, religion, sexual

orientation, and veteran status. We take individual and collective responsibility for helping to eliminate bias and discrimination and for increasing our own understanding of

these issues through education, training, and interaction with others.

* We pledge our collective commitment to these principles in the spirit of the Virginia Tech motto of Ut Prosim (That I May Serve).