1. Contact Information
  2. Prerequisites
  3. Course Description and Credit Hours
  4. Required Texts
  5. Course Objectives
  6. Student Learning Outcomes
  7. Other Course Materials
  8. Outline Of Topics
  9. Exams and Assignments
  10. Grading Policy
  11. Policy on Missed Exams and Coursework
  12. Attendance Policy
  13. Notification of Changes
  14. Custom Sections
  15. Statements on Academic Misconduct
  16. Statement On Disability Accommodations
  17. Severe Weather Protocol
  18. Pregnant Student Accommodations
  19. Religious Observances
  20. UAct Statement

Theory Diff Equations I

MATH 588-001Spring 2020 | 3 Credit Hours


Shibin Dai

Contact Information

UA Campus Directory:

Office : GP 328C

Email: sdai4@ua.edu

Office Hours: Tuesday and Thursday 8:30-11:00 am


UA Course Catalog Prerequisites:

MATH 238 and MATH 586

Course Description

Course Description and Credit Hours

Topics covered include existence and uniqueness of solutions, Picard theorem, homogenous linear equations, Floquet theory, properties of autonomous systems, Poincare-Bendixson theory, stability, and bifurcations.

Required Texts

Required Texts from UA Supply Store:
  • Perko, Lawrence M. / Differential Equations and Dynamical Systems (Choose One)

Student Learning Outcomes

  1. Students will analyze the existence and uniqueness of solutions of ordinary differential equations.

  2. Students will study properties of homogeneous linear ordinary differential equations.

  3. Students will apply analytical techniques to study properties of autonomous systems.

  4. Students will analyze the stability and bifurcation of dynamical systems.

Other Course Materials

Outline of Topics

  1. Basic Theory: Existence and uniqueness of solutions (Peano and Pichard theorems)

  2. Linear Systems: Homogeneous and inhomogeneous systems of linear differential equations; Linear independence and the fundamental matrix solution of systems with constant coefficients, Floquet theory

  3. Autonomous Systems: Phase space, orbits and properties of autonomous systems; Poincare-Bendixson theory

  4. Stability: Lyapumov and orbital stability, orbits near an equilibrium point, Lyapunov functions, structural stability and bifurcation

Exams and Assignments

There will be one midterm test and one comprehensive final exam. Homework will be assigned and collected weekly.

Grading Policy

Grades will be determined by homework (30%), one midterm test (30%), and the comprehensive final exam (40%).

Policy on Missed Exams and Coursework

No late homework will be accepted, unless there is a documented legitimate reason. 

There will be no makeup for the midterm exams or the final, unless there is a documented legitimate reason. The only allowed excuses for a makeup are 

  • documented illnesses

  • university sponsored events

  • a religious holiday

  • a family emergency

Unless there is a true emergency, makeup exams should be arranged at least two weeks before the exam date. 

Attendance Policy

Attendance is required. It is the students' responsibility to attend every class and actively participate in class activities.

Notification of Changes

The instructor will make every effort to follow the guidelines of this syllabus as listed; however, the instructor reserves the right to amend this document as the need arises. In such instances, the instructor will notify students in class and/or via email and will endeavor to provide reasonable time for students to adjust to any changes.

Department of Mathematics Academic Misconduct Policy

  1. During tests you may only use a calculator that has been specifically approved by the instructor.  Using or being in possession of an unauthorized calculator will be considered academic misconduct. 
  2. Taking a test for another student will be treated as academic misconduct by both parties.  In particular, showing an instructor a fake ID or another student’s ACT card will be treated as academic misconduct.
  3. Receiving or providing assistance of any kind during an exam will be treated as academic misconduct by both parties.
  4. Cellphones must be turned completely off and placed with other belongings on the floor.  All watches must be taken off and put away.  DO NOT put your phone or watch in your lap or on your chair or desk.  Physically holding or concealing on your person a phone, watch or other unauthorized technological device (including but not limited to headsets, earphones, earbuds, microphones, cameras, or scanning pens) will be treated as academic misconduct.
  5. If you are seen using an unauthorized device, the instructor may request that you turn it over.  It will be returned at the end of the exam.  However, the instructor does not have to request your device in order to charge you with academic misconduct.
  6. If for any reason you must have access to your phone while taking a test, you must inform an instructor prior to accessing your phone.  The instructor must be present while you use the phone.  Failure to do so will be treated as academic misconduct.
  7. If necessary, scratch paper will be provided.  No other paper is allowed; being in possession of any unauthorized papers will be treated as academic misconduct.
  8. You may review your test before leaving the exam.  You may not photograph your exam or write down or copy any information pertaining to the test, nor may you share any information about the test with anyone by any means.  This includes sharing information by word of mouth, written correspondence, electronic device or any type of social media.  Providing information about the test to other students will be treated as academic misconduct.  Also, having in your possession information about any test prior to the test that was not given to you by the instructor will be treated as academic misconduct. 
  9. You may not leave your place during a test for any reason.  This includes getting water or going to the restroom.  You must take care of these things before the start of the test.  If you leave your test without permission, your test will be collected and you will not be allowed to continue working on it.
  10. Interrupting the exam or creating a disturbance to cause a distraction during the exam will be treated as academic misconduct. 
  11. In order to enforce these rules, an instructor may require you to do any of the following.  Failure to comply will be treated as academic misconduct.
    1. Remove hats, hoods, scarves, or other head coverings.
    2. Remove bulky coats, sweaters or other over-garments.
    3. Roll up sleeves.
    4. Remove anything seen in your ears or on your person.
    5. Empty your pockets and display the contents.
    6. Sit in assigned seats prior to the start of the exam.
    7. Require you to move to a new seat during the exam.

If you wear a hat, head covering or long-sleeved garment for religious reasons, the instructor may still request to examine under them.  If you would prefer to have this done privately, or by an instructor or staff member of the same sex, you will be accommodated.  To ensure accommodation, you must discuss this with your instructor prior to the test.

If you use a hearing aid or other adaptive technology that could be mistaken for an earbud or other unauthorized electronic device, please notify your instructor prior to the test.  You may be asked to provide documentation of your need to use such a device.

MTLC Specific Policies

  1. In the MTLC, you may only use either the Casio fx-SOLAR SCHOOL or the Casio fx-260 SOLAR II.
  2. In the MTLC, swiping another student’s ACT card will be treated as academic misconduct. 
  3. In the MTLC having any other website other than the test open during a test will be treated as academic misconduct.
  4. In the MTLC, if you leave your computer during a test without permission, your exam will be closed and you will forfeit any remaining exam time.

Statement on Academic Misconduct

Students are expected to be familiar with and adhere to the official Academic Misconduct Policy provided in the Online Catalog.

Statement On Disability Accommodations

Contact the Office of Disability Services (ODS) as detailed in the Online Catalog.

Severe Weather Protocol

Please see the latest Severe Weather Guidelines in the Online Catalog.

Pregnant Student Accommodations

Title IX protects against discrimination related to pregnancy or parental status. If you are pregnant and will need accommodations for this class, please review the University’s FAQs on the UAct website.

Religious Observances

Under the Guidelines for Religious Holiday Observances, students should notify the instructor in writing or via email during the first two weeks of the semester of their intention to be absent from class for religious observance. The instructor will work to provide reasonable opportunity to complete academic responsibilities as long as that does not interfere with the academic integrity of the course. See full guidelines at Religious Holiday Observances Guidelines.

UAct Statement

The University of Alabama is committed to an ethical, inclusive community defined by respect and civility.  The UAct website (www.ua.edu/uact)  provides extensive information on how to report or obtain assistance with a variety of issues, including issues related to dating violence, domestic violence, stalking, sexual assault, sexual violence or other Title IX violations, illegal discrimination, harassment, hate or bias incidents, child abuse or neglect, hazing, threat assessment, retaliation, and ethical violations or fraud.