Web page of Dmytro Savchuk |

Instructor: | Dmytro Savchuk | |

Office: |
LN 2212 | |

Phone: | (607) 777-4221 | |

Fax: | (607) 777-2450 | |

e-mail: | dsavchuk at math dot binghamton dot edu | |

Office Hours: | MW 9:10am - 10:40am or by appontment |

Class Location: | SW 321 MWF 10:50am-11:50am |

SW 331 T 10:05am-11:30am |

**Class web-page:** http://savchuk.myweb.usf.edu/teaching/2010C_math372_dyn_systems/

**Text:** "An Introduction to Dynamical Systems: Continuous and Discrete" by R. Clark Robinson, Pearson Residence Hall, 2004, ISBN: 0-13-143140-4.

**Prerequisites:** Calculus II (Math 222) and Linear Algebra (Math 304). You need to know how to calculate with matrices, especially eigenvalues and eigenvectors,
and you need to know how this is related to diagonal forms for matrices.

**Course content:** The course will cover material from Chapters 1-6, 8-11. If time admits certain material from Chapters 7,12-14 may be covered.

**Learning objectives:** Students will learn to:

- Develop dynamical systems to model problems from biology, physics, and other areas.
- Solve simple dynamical systems; apply computer methods to solve and visualize more complex systems.
- Apply tools from Calculus and Linear Algebra to analyze discrete and continuous dynamical systems. Especially important will be connections between eigenvalues and eigenvectors and the long term behaviour of dynamical systems.
- Set up, analyze, and interpret phase portraits of linear and non-linear systems of differential equations, in low dimensions.
- Use graphical and symbolic methods to represent and interpret dynamical systems.

**Grading:** There will be one midterm exam and a final, also you will
have a grade for quizzes and homeworks (may include projects). Your final grade will be calculated according to the following table.

Midterm I | = | 35% |

Final Exam | = | 40% |

Daily Grade Scores (homeworks, quizzes, projects, etc.) | = | 25% |

I will consider any grade appeals only within one week after the assignemnt was returned. It is your responsibility to check your grades in the Blackboard.

**Attendance:** Attendance is required at all classes. This
includes the Tuesday meeting, which is a regular class, *not* a
discussion session. After 3 unexcused absences I will penalize you for
missed classes. Each missed classes will cost you one tenth of a grade. For
example, 20 missed classes will reduce an **A-** to a **C-**.

**Homework:** I will assign the homework regularly and you will be required to submit it. The assignments will
be available at

http://savchuk.myweb.usf.edu/teaching/2010C_math372_dyn_systems/homeworks.html

Solving homework problems is a crucial part in learning process. No matter how hard you study you will not learn the material
unless you solve the problems on your own. Besides, this is the best way to prepare yourself for the exams.
You can discuss homework problems with other students in the class, but you are required to write the solutions on your own.
Homework is due at the beginning of each class. If you are unable to come to class due to illness, you may turn in your
homework to me either via email or by putting the assignment under my office door. In either case, however, the assignment
must be turned in before the class period when it is due. You must then come to my office hours or make an appointment to
meet with me within the next seven days, to explain to me your situation. If your explanation is satisfactory, then I
will grade and give you credit for the homework assignment.
**Not all homework will be graded.** The problems will be graded on the scale similar to the one below

2 pts = | well written correct solution |

1 pt = | mostly correct solution, or correct but sloppily written solution |

0 pts = | everything else (including correct solutions without justification) |

**Quizzes:** Quizzes will be given in class on a regular basis. They may or may not be announced. There will be NO
make-up quizzes, but at least two quizzes with the lowest grade will be dropped. I will post the solutions to the quizzes at
http://savchuk.myweb.usf.edu/teaching/2010C_math372_dyn_systems/quizzes.html

**Getting Help:** If you are having problems, please stop by my office
LN 2212 during office hours or by appointment. Again, do not hesitate to ask questions - by far this is the most effective way of learning. To make our joint work more efficient, please,
come to office hours prepared. Please have particular questions that cause you difficulties ready.

**Copyright Policy:** All printed materials distributed in class or on the web are
protected by Copyright laws. One xerox copy (or download from the web) is allowed
for personal use only. Multiple copies or sale of any of the materials is strictly
prohibited.