Course Syllabus
MA5510 – Ordinary Differential Equations
College of Science and Arts
Fall 2014
Instructor Information
Instructor:
Office Location:
Telephone:
E-mail:
Office Hours:
Jiguang Sun, PhD, Associate Professor
313 Fisher Hall
Office – (906)487-3172
jiguangs@mtu.edu
MWF 11:00am – 12:00pm or by appointment
Course Identification
Course Number:
Course Name:
Course Location:
Class Times:
Prerequisites:
MA5510-R01
Ordinary Differential Equations
327B Fisher Hall
MWF 2:05pm – 2:55pm
MA4450 – Real Analysis, MA4330 – Linear Algebra
Course Description/Overview
The course covers necessary topics for a clear understanding of the qualitative theory of
ordinary differential equations and the concept of a dynamical system. The topics includes
first order equations, general theory of linear equations, constant coefficient equations,
matrix methods, singular points, infinite series methods, plane autonomous systems.
Course Learning Objectives
The objective of this course will be to ensure that students:
1. Obtain a clear understanding of the qualitative theory of ordinary differential
equations and the concept of a dynamical system.
2. Be able to solve linear systems and describe their stability.
3. Understand the fundamental existence and uniqueness theorem for nonlinear
systems and solve related problems.
4. Be able to analyze limit sets and attractors.
5. Understand plane autonomous systems and bifurcation and solve the related
problems.
Course Resources
Course Website(s)


Canvas<http://www.courses.mtu.edu>
Personal Website <http://www.mtu.edu/~jiguangs>
Required Course Text

Differential Equations and Dynamical System, 3rd Edition, by Lawrence Perko,
©2001 Springer, ISBN 0-387-95116-4
Grading Scheme
Grading System
Letter
Grade
A
AB
B
BC
C
CD
D
F
I
X
Grade
Percentage
points/credit Rating
90% & above
4.00
Excellent
85% – 89%
3.50
Very good
80% – 84%
3.00
Good
75% – 79%
2.50
Above average
70% – 74%
2.00
Average
65% – 69%
1.50
Below average
60% - 64%
1.00
Inferior
59% and below 0.00
Failure
Incomplete; given only when a student is unable to complete a
segment of the course because of circumstances beyond the
student’s control.
Conditional, with no grade points per credit; given only when
the student is at fault in failing to complete a minor segment of
a course, but in the judgment of the instructor does not need to
repeat the course. It must be made up by the close of the next
semester or the grade becomes a failure (F). A (X) grade is
computed into the grade point average as a (F) grade.
Grading Policy
Grades will be based on the following:
Homework
Midterm Exam
Final Exam
Total
50%
20%
30%
100%
Late Assignments
Late assignments will be returned without grading.
Collaboration/Plagiarism Rules
Collaboration on homework is encouraged. However, the final work needs to be done
independently.
Cell phones, Blackberries, iPods, PDAs, or any other electronic devices are not to be used in
the classroom. Please make sure to bring a calculator with you to class. Calculators on
other devices are strictly prohibited. Information exchanges on these devices during class
are also prohibited and violate the Academic Integrity Code of Michigan Tech.
University Policies
Michigan Tech has standard policies on academic misconduct and complies
with all federal and state laws and regulations regarding discrimination, including the
Americans with Disabilities Act of 1990. For more information about reasonable
accommodation for or equal access to education or services at Michigan Tech, please call
the Dean of Students Office, at (906) 487- 2212 or go to
http://www.mtu.edu/provost/faculty-resources/syllabus-policies/
Further Information:
Academic Integrity:
http://www.mtu.edu/dean/conduct/policy/academic-integrity
Academic regulations and procedures are governed by University policy. Academic misconduct cases will
be handled in accordance the University's policies.
Disability Services:
http://www.mtu.edu/dean/disability/policies/
If you have a disability that could affect your performance in any class or that requires an accommodation
under the Americans with Disabilities Act, please contact your instructor as soon as possible so that
appropriate arrangements can be made.
Affirmative Programs:
http://www.admin.mtu.edu/aao/
The Affirmative Programs Office has asked that you be made aware of the following: Michigan
Technological University complies with all federal and state laws and regulations regarding discrimination,
including the Americans with Disabilities Act of 1990. If you have a disability and need a reasonable
accommodation for equal access to education or services at Michigan Tech, please call the Dean of
Students Office at 487-2212.
Equal Opportunity, Discrimination, or Harassment Statement:
http://www.admin.mtu.edu/admin/boc/policy/ch5/
For other concerns about discrimination, you may contact your advisor, Chair/Dean of your academic unit,
or the Affirmative Programs Office at 487-3310.
Course Schedule (Tentative)
Week 1
W 9/3
Course introduction
1.1 Uncouple Linear System
Week 2
M 9/8
W 9/10
F 9/12
1.2 Diagonalization
1.3 Exponentials of Operators
1.4 The Fundamental Theorem for Linear Systems
Week 3
M 9/15
W 9/17
F 9/19
1.5 Linear Systems in R^2
1.6 Complex Eigenvalues
1.7 Multiple Eigenvalues
Week 4
M 9/22
W 9/24
F 9/26
1.8 Jordan Forms
1.9 Stability Theory
1.9 Stability Theory
Week 5
M 9/29
W 10/1
F 10/3
1.10 Nonhomogeneous Linear Systems
2.1 Some Preliminary Concepts and Definitions
2.2 The Fundamental Existence-Uniqueness Theorem
Week 6
M 10/6
W 10/8
F 10/10
2.2 The Fundamental Existence-Uniqueness Theorem
2.3 Dependence on Initial Conditions and Parameters
2.4 The Maximal Interval of Existence
Week 7
M 10/13
W 10/15
F 10/17
2.5 The Flow Defined by a Differential Equation
2.6 Linearization
2.9 Stability and Liapunov Fuctions
Week 8
M 10/20
W 10/22
F 10/24
2.10 Saddles, Nodes, Foci and Centers
Review
Midterm
Week 9
M 10/27
3.1 Dynamical Systems and Global Existence Theorems
W 10/29
F 10/31
3.2 Limit Sets and Attractors
3.3 Periodic Orbits, Limit Cycles and Separatrix Cycles
Week 10
M 11/3
W 11/5
F 11/7
3.4 The Poincare Map
3.5 The Stable Manifold Theorem for Periodic Orbits
Review
Week 11
M 11/10
W 11/12
F 11/14
4.1 Structural Stability and Peixoto’s Theorem
4.2 Bifurcations at Nonhyperbolic Equilibrium Points
4.3 Higher Codimension Bifurcations at Nonhyperbolic Equilibrium Points
Week 12
M 11/17
W 11/19
F 11/21
4.4 Hopf Bifurcations and Bifurcation of Limit Cycles from a Multiple Focus
4.5 Bifurcations at Nonhyperbolic Equilibrium Points
Review
Week 13
M 12/1
W 12/3
F 12/5
Supplemental Material 1
Supplemental Material 2
Supplemental Material 3
Week 14
M 12/8
W 12/10
F 12/12
Review
Review
Review
Finals Week
TDB