MTH 481/581:Applied Ordinary Differential Equations
Fall 2018

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

Grader: Patrik Nabelek
Office: Kidder 008
Email: nabelekp at oregonstate dot edu
Office Hours: R 2pm.


  • Time/Classroom: 9:00 am - 9:50am MWF, BEXL 328

  • Course Information
    1. MTH 481: 3 credits, Section 001, CRN 10312
    2. MTH 581: 3 credits, Section 001, CRN 10318
  • Required Textbook [BD]:

    Elementary Differential Equations, and Boundary Value Problems :
    Authors: William E. Boyce and Richard C. DiPrima,
    11th edition, 2018.

  • Course Description: This course covers different aspects of the theory of ordinary differential equations (ODEs). We will consider linear and nonlinear systems of ordinary differential equations, elementary stability theory, higher order equations, series solution of ordinary differential equations and two point boundary value problems. These topics are covered in Chapters 4, 5, 7, 9 and 10 of the class text [BD]. We will cover select sections from these chapters.
  • Student Learning Outcomes for Math 481: A successful student who has completed MTH 481 will have an understanding of the theoretical and qualitative analysis of systems of linear ODEs theory and their use in understanding the dynamical and qualitative properties of systems of non-linear ODEs. The student will be able to use this understanding to
    1. Find solutions of general linear systems of ODEs, and in particular of first order systems of linear autonomous ODEs. This involves computing eigenvalues and eigenvectors of the matrix associated to such a system, and using matrix transformation techniques (similarity transformations) to diagonalize the matrix.
    2. Solve linear ODEs of higher order using a variety of techniques: converting the higher order ODE to a system of first order ODEs, the undetermined coefficients method.
    3. Analyze autonomous first order linear and nonlinear two dimensional systems in the phase plane; compute equilibrium solutions and perform stability analysis using linearization.
    4. Draw phase portraits for first order systems of two linear or nonlinear autonomous ODEs.
    5. Know examples of models arising in applications, such as the Lotka-Volterra predator-prey and competition models.
    6. Solve linear ODEs using power series methods.

  • Student Learning Outcomes for Math 581: A successful student who has completed MTH 581 will have an understanding of the theoretical and qualitative analysis of systems of linear ODEs theory and their use in understanding the dynamical and qualitative properties of systems of non-linear ODEs. The student will be able to use this understanding to
    1. find solutions of general linear systems of ODEs, and in particular of first order systems of linear autonomous ODEs. This involves computing eigenvalues and eigenvectors of the matrix associated to such a system, and using matrix transformation techniques (similarity transformations) to diagonalize the matrix.
    2. solve linear ODEs of higher order using a variety of techniques: converting the higher order ODE to a system of first order ODEs, the undetermined coefficients method.
    3. analyze autonomous first order linear and nonlinear two dimensional systems in the phase plane; compute equilibrium solutions and perform stability analysis using linearization.
    4. Draw phase portraits for first order systems of two linear or nonlinear autonomous ODEs.
    5. Know examples of models arising in applications, such as the Lotka-Volterra predator-prey and competition models.
    6. Solve linear ODEs using power series methods.

  • Prerequisites: All courses used to satisfy MTH prerequisites must be completed with a C- or better. Prerequisites: (MTH 256 with C- or better or MTH 256H with C- or better) and (( (MTH 253 with C- or better or MTH 253H with C- or better) and MTH 341 [C-]) or (MTH 306 [C-] or MTH 306H [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%)
      • Homework Assignments and Computer Labs (35%):
        Homework will be assigned in class every week and students will be given a week to complete the assignment. Due dates will be posted on the Calendar. Late assignments may not receive any credit.

      • Midterm (30%):
        A midterm exam will be given Wednesday Oct 31, 2018, in BEXL 328 from 9:00-9:50 am, i.e. during the usual class hour. There will be no makeup exams. Books, notes, or graphing/programmable calculators will NOT be allowed on exams. You will be allowed the following
        1. (both sides) of one 3x5 index card.
        2. A simple (non-programmable, non-graphing) scientific calculator.
        3. pen or pencil.
        Exam problems will be based on class lectures, similar to problems covered in lectures, and similar to problems from the homework.

      • Final (35%):
        A comprehensive final exam will be given on Monday December 3rd, 2018 at 2:00 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 the following
        1. (both sides) of two 3x5 index card.
        2. A simple (non-programmable, non-graphing) scientific calculator.
        3. pen or pencil.
        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 (AR 16: Finals Week) 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 \& Statistics Learning Center (MSLC) 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). Additional resources can be found at the Get Help in Your OSU Math Classes site.

  • 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 Ethical Conduct Policies: Students are expected to be familiar with Oregon State University’s Statement of Expectations for Student Conduct. Please review this statement as well as review and consult material at the following sites.

  • 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.

  • Student Evaluation of Courses: The online Student Evaluation of Teaching system opens to students the Monday of dead week and closes the Monday following the end of finals. Students will receive notification, instructions and the link through their ONID. They may also log into the system via Online Services. Course evaluation results are extremely important and used to help improve courses and the learning experience of future students. Responses are anonymous (unless a student chooses to “sign” their comments agreeing to relinquish anonymity) and unavailable to instructors until after grades have been posted. The results of scaled questions and signed comments go to both the instructor and their unit head/supervisor. Anonymous (unsigned) comments go to the instructor only.

  • Course Drop/Add and Other Informational Sites: See


Images created with the ODE software Pplane from Rice University

My Links:

Calendar for Math 481/581
ODE software: Dfield and PPlane
MATLAB


Other Links: