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MATH 473 Course Syllabus
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 that 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.
Math 473-101: Intermediate Differential Equations
FALL 2009
Textbook: Nonlinear Dynamics and Chaos with Applications to Physics, Biology, Chemistry, and Engineering by Steven Strogatz; ISBN: 0-738-20453-6.
Suggested Further Reading:
▪ Chaos: An Introduction to Dynamical Systems by Alligood, Sauer, and Yorke;
▪ Differential Equations, Dynamical Systems & and Introduction to Chaos, 2nd Ed. by Hirsch, Smale, Devaney;
▪ Nonlinear Oscillations, Dynamical Systems, and Bifurcations of Vector Fields by Guckenheimer and Holmes.
Required Software & MATLAB Routines: Dynamics Solver (DS) (Windows) by J. M. Aguirregabiria (or the more advanced DSTool and XPP), and MATLAB routines dfield and pplane (pick the appropriate codes for your particular version of MATLAB, and download these programs).
Prerequisites: Math 222 or Math 337 with a grade of C or better.
Grading Policy: The final grade in this course will be determined as follows:
|
▪ Homework & Projects: |
30% |
|
▪ Midterm Exam: |
30% |
|
▪ Final Exam: |
40% |
Your final letter grade will be based on
the following tentative curve. This curve may be adjusted slightly
at the end of the semester.
|
A |
90-100 |
C |
60-69 |
|
B+ |
85-89 |
D |
50-59 |
|
B |
80-84 |
F |
0-49 |
|
C+ |
70-79 |
|
|
Drop Date: Please note that the University Drop Date November 2, 2009 deadline will be strictly enforced.
Homework Policy: You must hand in all indicated homework and projects on time, as they account for a significant portion of your overall grade. There will be several homework assignments to submit, and two or three MATLAB type projects – including a Final Project.
Attendance: Attendance at all classes will be recorded and is mandatory. Please make sure you read and fully understand the Department’s Attendance Policy. This policy will be strictly enforced.
Exams: There will be one midterm exam held in class and one comprehensive final exam during the semester. Exams are on the following days:
|
Midterm Exam: |
October 14, 2009 |
|
Final Exam Week: |
December 11-17, 2009 |
The final exam will test your
knowledge of all the course material taught in the entire course.
Make sure you read and fully understand the department's to
Examination Policy. This policy will be strictly enforced. Please note that calculators, cellular phones, beepers, and all other electronic devices may
not be used during any exam.
Makeup Exam Policy: There will be No make-up EXAMS during the semester. In the event the Final Exam is not taken, under rare circumstances where the student has a legitimate reason for missing the final exam, a makeup exam will be administered by the math department. In any case the student must notify the Math Department Office and the Instructor that the exam will be missed and present written verifiable proof of the reason for missing the exam, e.g., a doctors note, police report, court notice, etc., clearly stating the date AND time of the mitigating problem.
Further Assistance: For further questions, students should contact their Instructor. All Instructors have regular office hours during the week. These office hours are listed at the link above by clicking on the Instructor’s name. Teaching Assistants are also available in the math learning center.
Cellular Phones: All cellular phones and beepers must be switched off during all class times.
MATH DEPARTMENT CLASS POLICIES LINK
All DMS students must familiarize themselves with and adhere to the Department of Mathematical Sciences Course Policies, in addition to official university-wide policies. DMS takes these policies very seriously and enforces them strictly. For DMS Course Policies, please click here.
| M |
Labor Day Holiday ~ University Closed |
|
| M |
Last Day to Withdraw from this course |
|
| T |
Classes follow a Thursday Schedule |
|
|
November 25, 2009 |
W |
Classes follow a Friday Schedule |
|
November 26-29, 2009 |
R-Su |
Thanksgiving Recess ~ University Closed |
Course Outline and Homework Assignments:
|
Week |
Section & Topic |
Homework Assignments |
|
|
|
|||
|
Week
1 |
Chapter 1 & Chapter 2 |
Introduction, Overview, Review, |
Ex: 2.1.1, 2.1.2, 2.2.1, 2.2.2, 2.3.1a (222 review problem), 2.4.1, 2.7.2, 2.8.1, 2.8.2; HW: 2.2.3, 2.2.9, 2.3.4, 2.4.2, 2.4.7, 2.6.1, 2.7.6 |
|
Week
2 |
3.0 - 3.5 |
Series Solutions (notes), Saddle-Node, Transcritical, and Pitchfork Bifurcations |
Ex: 3.1.2, 3.2.1, 3.4.4, 3.5.2; HW: 3.1.1, 3.2.3, 3.3.1, 3.4.8, 3.4.13 (dfield), 3.5.7a |
|
Week
3 |
► ► |
Imperfect Bifurcations, Flow on a Circle, |
Various Examples |
|
Week
4 |
5.0 - 5.2 |
2D Linear Systems |
Ex: 5.1.8, 5.2.1, 5.2.2; HW: 5.1.9, 5.1.13, 5.2.6 |
|
Week
5 |
6.0 - 6.3 |
Phase Portraits, Fixed Points, |
Ex: 6.1.1, 6.3.1, 6.3.2; HW: 6.1.3, 6.1.10, 6.2.1, 6.2.2, 6.3.6, 6.3.11, DS problem |
|
Week
6 |
6.4 - 6.5 |
Lotka-Volterra Equations, |
Ex: 6.4.2, 6.5.1, 6.5.4; HW: 6.4.6, 6.5.2, 6.5.15, 6.5.16 |
|
Week
7 |
└► |
REVIEW FOR Midterm EXAM |
|
|
└► |
MIDTERM EXAM I: Wednesday ~ October 14, 2009 |
||
|
Week
8 |
6.7, 7.0 - 7.3 |
Pendulum, Limit Cycles |
Ex: 6.7.1, 7.1.2, 7.1.4, 7.3.6; HW: 6.7.2, 7.1.8, 7.2.5, 7.2.6, 7.3.1, 7.3.2, 7.3.7 |
|
Week 9 |
8.0 - 8.4 |
Bifurcations in 2D, Hopf Bifurcation |
Ex: 8.1.1, 8.1.3, 8.2.2; HW: 8.1.6, 8.1.10, 8.2.3, 8.3.1 |
|
└► |
final Project assigned: Due on December 2, 2009 |
||
|
└► |
(mon. Nov. 2) Last Day to Withdraw from this course |
||
|
Week
10 |
8.6, 8.7, |
Quasiperiodicity, Poincare Maps Introduction to Chaos |
Ex: 8.7.2, 8.7.9; HW: 8.6.1, 8.6.5, 8.7.3, 9.1.4a, 9.2.4 |
|
Week
11 |
9.3, 9.4, |
Lorenz Map 1D Maps |
Ex: 10.1.1, 10.1.3, 10.1.7, 10.2.2; HW: 9.3.1a, 10.1.11, 10.1.12, 10.2.5, 10.2.8 |
|
Week 12 |
10.3 - 10.6 |
Logistic Map Lyapunov Exponent |
Ex: 10.5.3, 10.5.5; HW: 10.3.6, 10.4.6, 10.4.9, 10.5.7, 10.6.1 |
|
Week 13 |
└► |
(Wed. Nov. 25) Classes follow a Friday schedule |
|
|
└► |
(Thurs.-Sun. Nov. 26-29) Thanksgiving Recess ~ University Closed |
||
|
Week 14
Week 15 |
11.0 - 11.4 |
Fractals |
Ex: 11.1.1, 11.1.2, 11.3.7, 11.4.1; HW: 11.1.5, 11.2.4, 11.3.3, 11.3.9, 11.4.3 |
|
12.0 - 12.5 |
Fractals, Strange Attractors, Henon Map |
Ex: 12.1.2, 12.2.2, 12.2.4, 12.2.5; HW: 12.1.3, 12.1.6, 12.1.9, 12.2.8. |
|
|
└► |
REVIEW FOR FINAL EXAM |
STUDY FOR FINAL EXAM |
|
|
|
|||
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Finals |
Final EXAM WEEK: December 11-17, 2009 |
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Prepared By: Prof. Michael Booty
Last revised: July 31, 2009