MATH 473 Course Syllabus - FALL 2013

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