NJIT HONOR CODE

All Students should be aware that the Department of Mathematical Sciences takes the NJIT Honor code very seriously and enforces it strictly.  This means there must not be any forms of plagiarism, i.e., copying of homework, class projects, or lab assignments, or any form of cheating in quizzes and exams.  Under the Honor Code, students are obligated to report any such activities to the Instructor.

 

Mathematics 672-001:

Math Models of Bio Wave

Fall 2006

 

Course Schedule Link

¥   Instructors:     Prof. Bose  and  Prof. Nadim

¥   Textbook:  None. Chapter 10 of “Dynamical Systems in Neuroscience: The Geometry of Excitability and Bursting” (available online http://www.nsi.edu/users/izhikevich/publications/dsn.pdf) and research papers provided in class.

¥   Grading Policy:  The final grade in this course will be determined as follows:

ª     Homework:

 

35%

ª     Midterm:

 

25%

ª     Final Exam:

 

40%

 

 

CLASS POLICIES

Attendance and Participation:  Students must attend all classes. Absences from class will inhibit your ability to fully participate in class discussions and problem solving sessions and, therefore, affect your grade. Tardiness to class is very disruptive to the instructor and students and will not be tolerated.

 

Makeup Exam Policy: There will be no makeup exams, except in rare situations where the student has a legitimate reason for missing an exam, including illness, death in the family, accident, requirement to appear in court, etc. The student must notify the Math office and the Instructor that he/she will miss an exam. In all cases, the student must present proof for missing the exam, e.g., a doctor's note, police report, court notice, etc., clearly stating the date AND times.

 

Cellular Phones:  All cellular phones and beepers must be switched off during all class times.

 

 

Course Outline:

 

 

1.

Review of Basic Concepts: Flows, Equilibria, Limit Cycles, Invariant Manifolds, Poincare Return Maps

2.

Systems of Coupled Oscillators and Averaging: Pairs of Coupled Oscillators, Chains and Limits, Averaging Theory, Stability

3.

Reduction to Invariant Manifolds: Fenichel’s Theorem, Application to Coupled Oscillators

4.

Neural Oscillators, Bursting and Network Oscillators: Single Cell and Network Oscillators, Effects of Coupling by Inhibitory, Excitatory and Electrical Synapses, Multiple-Time-Scale Oscillators and Bursting

5.

Geometry of Singularly Perturbed Systems: Singular Solutions, Exchange Lemma (Jones & Kopell)

FINAL EXAM WEEK:  DECEMBER 15-21, 2006

 

Prepared By:  Prof. Bose and Prof. Nadim

Last revised:  August 7, 2006

 

 

CALANDER OF WEEKS FOR FALL 2006 SEMESTER:

 

Week 1 
(9/4 - 9/8)

Week 2 
(9/11 - 9/15)

Week 3 
(9/18 - 9/22)

Week 4 
(9/25 - 9/29)

Week 5 
(10/2 - 10/6)

Week 6 
(10/9 - 10/13)

Week 7 
(10/16 - 10/20)

Week 8 
(10/23 - 10/27)

Week 9 
(10/30 - 11/3)

Week 10 
(11/6 - 11/10)

Week 11 
(11/13 - 11/17)

Week 12 
(11/20 - 11/24)

Week 13 
(11/27 - 12/1)

Week 14 
(12/4 - 12/8)

Week 15 
(12/11 - 12/13)

Finals
(12/15 - 12/21)

September 4

M

Labor Day – No Classes Scheduled

November 6

M

Last Day to Withdraw from Classes

November 21

T

Classes Follow a Thursday Schedule

November 22

W

Classes Follow a Friday Schedule

November 23-24

R-F

Thanksgiving – No Classes Scheduled