MTH 480:Systems of Ordinary Differential Equations
Winter 2018

Professor: Dr. Vrushali Bokil
Office: Kidder 048
Phone: 737-2609
Email: bokilv at math dot oregonstate dot edu
Office Hours: M: 3:00pm-3:50pm, W: 10am-10:50am, or by Appt.

  • Time/Classroom: 11:00 am - 11:50am MWF BEXL 328

  • Grader: Will Mayfield
    Email Contact: mayfielw at math dot oregonstate dot edu
  • Required Textbook [HSD]:

    Differential Equations, Dynamical Systems, and an Introduction to Chaos :
    Authors: Morris W. Hirsch, Stephen Smale, Robert L. Devaney

  • Course Description: This course covers the qualitative theory of systems of first order ordinary differential equations (ODEs). We will mainly focus on systems of two first-order autonomous ODEs, though examples of higher dimensional and non-autonomous systems will be provided. We will consider methods for the qualitative analysis of such systems including the study of phase portraits, linearization, equilibria and their stability, bifurcations, periodic solutions and limit cycles. We will consider specific types of systems such as conservative systems, reversible systems and Hamiltonian systems. A major result that we will study in this course is the Poincare-Bendixson theorem. Additional material on Hopf bifurcations will also be cosidered. The course is based on Chapters 2-4, 7-10 of the class textbook. Applications from the physical and life sciences will be used to demonstrate how theoretical concepts can guide physical or biological understanding. Some of the applications from Chapters 11-14 will be considered. Finally, ODE software written in MATLAB will be used to demonstrate specific examples.
  • Course Learning Outcomes: A successful student who has completed MTH 480 will be able to perform qualitative analyses of linear and nonlinear systems of first order autonomous ordinary differential equations. In particular the student will understand how to "linearize" nonlinear ODEs. For the case of planar ODEs, the student will be able to draw phase plane diagrams that include nullclines and equilibria and identify the presence or absence of bifurcations, and oscillatory solutions (periodic solutions and limit cycles). The student will also be able to apply the theory and techniques learned in this class to solve applications in the physical and life sciences.

  • Prerequisites: MTH 256[C-] (or MTH 256H[C-]) and MTH 341[C-].

  • Reading Assignments: Look at the Calendar for sections from [HSD] covered during each lecture, postings, due dates for assignments, exam and review dates, and other information.
    NOTE: While it may not be stated explicitly each day, students are expected to read each section to be covered before class. Students are responsible for any material missed due to absence.

  • Course Grading and Related Policies The course grade is based on written homework assignments, a midterm and a final exam.

    • Percentage Distribution: Total: (100%)
      • Weekly Homework Assignments (40%):
        Homework will be assigned in class. Due dates will be posted on the Calendar. Late assignments may not receive any credit.

      • Midterm (25%):
        A midterm exam will be given Monday Feb 12, 2018, in BEXL 328 from 11:00-11:50 am. There will be no makeup exams. Books, notes, or graphing/programmable calculators will NOT be allowed on exams. You will be allowed (both sides) of a 3x5 index card. Exam problems will (mostly) be similar to problems from the homework assignments and based on lecture notes.

      • Final (35%):
        A comprehensive final exam will be given on Monday March 19th at 6:00 pm in BEXL 328 . There will be no makeup exams. Books, notes, or graphing/programmable calculators will NOT be allowed on exams. You will be allowed (both sides) of two 3x5 index card. Exam problems will (mostly) be similar to homework problems and based on lecture notes Scheduling conflicts with the final exam must be resolved in advance. Please see the university guidelines for Student Petitions to Change the Time of a Final Examination.

    • Grade Scale (by percentage):Final grades for this class will be given based on the scale below. Each letter grade below corresponds to grades scored between the lower limit (including) and less than the upper limit (excluding).
      A 90 - 100%
      A- 87 - 90%
      B+ 84 - 87%
      B 80 - 84%
      B- 77 - 80%
      C+ 74 - 77%
      C 70 - 74%
      C- 67 - 70%
      D+ 64 - 67%
      D 60 - 64%
      D- 57 - 60%
      F below 57%

  • Getting Help: Short questions can be asked during class. Longer questions should be asked during regular office hours. Appointments can also be made at other times, and you can reach me by email. Help is also available at the Mathematics Learning Center (MLC) which provides drop-in help for all lower division mathematics courses. The MLC is located on the ground floor of Kidder Hall (Kidder 108), and is normally open M-F from 9 AM to 4 PM, from the second week of term through Dead Week (Week 10).

  • Contacting Dr. Bokil: The best way to contact me is via email. Best place/time to see me for questions is in my office during office hours. If you are unable to make it to office hours you may email your questions to me or setup an appointment by email. You can expect a response within 24 hours. Do not expect an immediate response .

  • Student Conduct Policies and Cheating Policy: I have a zero tolerance policy for cheating. All suspected cheating will be reported to the appropriate office, usually the Dean of your College. Provable cases of cheating will also result in a score of 0 on the assignment in question, and may lead to a grade of F in the class. This is highly detrimental to any long term career goals. It also will make it difficult for the student to obtain letters of recommendation. Please consult the OSU Student Conduct and Community Standards page.

  • Special arrangements: Accommodations for students with disabilities are determined and approved by Disability Access Services (DAS). If you, as a student, believe you are eligible for accommodations but have not obtained approval please contact DAS immediately at 541-737-4098 or at Disability Access Services. DAS notifies students and faculty members of approved academic accommodations and coordinates implementation of those accommodations. While not required, students and faculty members are encouraged to discuss details of the implementation of individual accommodations.

  • Course Drop/Add Information: See Office of the Registrar and Academic Calendars

My Links:

Calendar for Math 480
ODE software: Dfield and Pplane

Other Links: