Fall 2013 Course Syllabus:
Math 473
Course Title: |
Intermediate Differential Equations |
Textbook: |
S. Strogatz, Nonlinear Dynamics and
Chaos with Applications
to Physics, Biology, Chemistry and
Engineering,
Westview Press, 2001, ISBN
9780738204536 |
Prerequisites: |
Math 222 and Math 337 with grade of C
or better |
Required Software: |
MATLAB (with routines
dfield
and
pplane),
XPPAUT |
Instructor: |
Professor Casey Diekman
(diekman@njit.edu) |
Office Hours: |
MoTh 4-5:30pm (or by appointment) in
508 Cullimore Hall |
Course Description
Math 473
is an introduction to the qualitative theory of ordinary differential
equations with an emphasis on geometric techniques.
Examples of applications
to science and engineering will be a significant part of the
course.
|
Course Outline |
|||
Date |
Class |
Sections |
Topic |
Assign. |
9/5 |
1 |
Chap. 1 |
Introduction, Overview, Review |
Sel. Probs. |
9/9 |
2 |
2.0-2.2, 2.4 |
Review, Stability |
Sel. Probs. |
9/12 |
3 |
2.3, 2.5, 2.6 – 2.8
|
Population Dynamics, Potentials and Numerics
|
Sel. Probs. |
9/16 |
4 |
3.0 – 3.3 |
Saddle-Node and Transcritical Bifurcations |
Sel. Probs. |
9/19 |
5 |
3.4 – 3.7 |
Pitchfork and Imperfect Bifurcations |
Sel. Probs. |
9/23 |
6 |
Chap. 4 |
Vector Fields on the Circle |
Sel. Probs. |
9/26 |
7 |
Chap. 5 |
2D Linear Systems |
Sel. Probs. |
9/30 |
8 |
6.0 – 6.2 |
Phase Portraits |
Sel. Probs. |
10/3 |
9 |
6.3 – 6.4 |
Fixed Points and Linearization |
Sel. Probs. |
10/7 |
10 |
6.5 – 6.7 |
Conservative Systems |
Sel. Probs. |
10/10 |
11 |
Chap. 7 |
Limit Cycles
|
Sel. Probs. |
10/14 |
12 |
Notes |
Applications |
Sel. Probs. |
10/17 |
13 |
------------ |
Review for
Midterm Exam |
------------ |
10/21 |
14 |
------------ |
Midterm EXAM |
------------ |
10/24 |
15 |
8.0 – 8.1 |
2D Bifurcations <PROJECT
ASSIGNED (due 12/5)> |
Sel. Probs. |
10/28 |
16 |
8.2 – 8.3 |
Hopf Bifurcation |
Sel. Probs. |
10/31 |
17 |
8.4 – 8.5 |
Global Bifurcations |
Sel. Probs. |
11/4 |
18 |
Notes |
Applications |
Sel. Probs. |
11/7 |
19 |
8.6 – 8.7 |
Coupled Oscillators and Poincaré Maps |
Sel. Probs. |
11/11 |
20 |
9.0 – 9.1 |
Introduction to Chaos |
Sel. Probs. |
11/14 |
21 |
9.3 – 9.6 |
Lorenz Equations |
Sel. Probs. |
11/18 |
22 |
10.5 – 10.6 |
Logistic Map |
Sel. Probs. |
11/21 |
23 |
Chap. 11 |
Fractals and Fractal Dimensions |
Sel. Probs. |
11/25 |
24 |
12.0 – 12.3 |
Strange Attractors |
Sel. Probs. |
11/28 |
|
------------- |
THANKSGIVING
BREAK |
------------ |
12/2 |
25 |
12.4 - 12.5 |
Examples of Chaos |
Sel. Probs. |
12/5 |
26 |
------------- |
Project Presentations
<PROJECT REPORTS DUE> |
------------- |
12/9 |
27 |
------------- |
Review for
Final Exam |
|
IMPORTANT DATES |
|
FIRST DAY OF CLASSES |
September 3, 2013 |
Midterm Exam |
October 21, 2013 |
LAST DAY TO WITHDRAW |
November 4, 2013 |
LAST DAY OF CLASSES |
December 11, 2013 |
FINAL EXAM PERIOD |
December 13 - 19, 2013 |
Grading Policy
Assignment
Weighting |
|
Tentative Grading
Scale |
||
Homework + Projects |
35 % |
|
A |
90 -- 100 |
|
|
|
B+ |
85 -- 89 |
|
|
|
B |
75 -- 84 |
Midterm Exam |
30 % |
|
C+ |
70 – 74 |
|
|
|
C |
60 – 69 |
|
|
|
D |
50 -- 59 |
Final Exam |
35 % |
|
F |
0 -- 60 |
When assigning your
final letter grade for the course, class attendance and
participation may be considered.
Course Policies
Homework assignments
will be announced in class and posted on the course website. The
due date will typically be one week from
the day it is assigned.
Homework not turned in at
the beginning of class on the due date will be considered
late and penalized 10%.
An additional 10%
penalty will be applied each subsequent day that a homework
assignment is late. Students are encouraged to work
together in groups and
discuss the problems with each other, but each student must
write up and submit an individual set of solutions.
Please write out your
solutions neatly (or type them) and staple the sheets together.
Academic integrity and
honesty are of paramount importance. The NJIT Honor Code will be
upheld, and any violations will be brought
to the immediate
attention of the Dean of Students.
Important Departmental and
University Policies
Prepared by Prof. Casey Diekman, August 8, 2013