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MAT 331 A: Introduction to Ordinary Differential Equations  

Fall Semester: September 2011

CourseMAT 331 A “Introduction to Ordinary Differential Equations“.

Prereq. MAT 120 and MAT 214 both with minimum grade of C.
Course Description: See CUCA Calendar, or


Course Instructor:

Name: Dr. A. N. (Tom) Tavouktsoglou, PhD
Professor of Mathematics & Chemistry
Coordinator of the Department of Mathematical and Computing Sciences

Office: Faculty House F.H.-204 (main level).

Tel: 780-479-9360.

e-mail: tomtavou@math.concordia.ab.ca

web: http://www.math.concordia.ab.ca/tomtavou/

Note: Students must phone (780-479-9360) and leave a message (or send an e-mail) ahead of
time, if they are unable to present themselves for a test/exam..

Office Hours: M./W/F.: 12:55 – 13:45 T./R.: 09:50 – 10:40

Books & Supplies (Available at Concordia University College of Alberta Bookstore):

  1. Elementary Differential Equations“; by W. E. Boyce & R. C. DiPrima; 9th Edition, John Wiley & Sons, Inc.

  2. A copy of “Mathematica® – Student Version” appropriate for the student’s own computer is recommended, but not required.

  3. A copy of the Students’ Solutions Manual is on Reserve at the Library.

Course Schedule:

M./W./F.: 11:10 – 12:00 in T-103 (Math Lab).

Additional Bibliography(optional – do NOT purchase).

  1. Elementary Differential Equations“; by E. D. Rainville & P. E. Bedient; MacMillan Publishing Company.

  2. Differential Equation with Computer Lab Experiments“; by D. G. Zill; Brooks/Cole Publishing Company.

  3. Differential Equations: An Introduction with Mathematica“; by C. C. Ross; Springer-Verlag.

  4. Differential Equations with Mathematica“; by M. L. Abell & J. P. Braselton; Academic Press Inc.

  5. Differential Equations with Mathematica“; by K. R. Coombes, B. R. Hunt, R. L. Lipsman, J. E. Osborn & G. J. Stuck; John Wiley & Sons, Inc.

  6. Other books on the subject available at the Library.


  • This schedule is tentative & subject to modifications. Chapter numbers refer to the textbook.

  • Approximately one week’s notice will be given before each test.

  • It is possible that one of the tests may be replaced by a homework project.

  1. Ch. 1 Introduction to the O.D.E.s
    1.1 Some Basic Mathematical Models; Direction Fields
    1.2 Solutions of Some Differential Equations
    1.3 Classification of Differential Equations
    1.4 Historical Remarks (Self-Study)
    Ch. 2
     First – Order O.D.E.s
    2.1 Linear Equations; Method of Integrating Factors
    2.2 Separable Equations
    2.3 Modeling with First Order Equations
    2.4 Differences Between Linear and Nonlinear Equations
    2.5 Autonomous Equations and Population Dynamics
    2.6 Exact Equations and Integrating Factors
    2.7 Numerical Approximations: Euler’s Method
    2.8 The Existence and Uniqueness Theorem
    2.9 First Order Difference Equations

    Test #1. Weight: 20%. Length: 50 min. Date: T.B.A.

  2. Ch. 3 Second – Order Linear O.D.E.s
    3.1 Homogeneous Equations with Constant Coefficients
    3.2 Solutions of Linear Homogeneous Equations; the Wronskian
    3.3 Complex Roots of the Characteristic Equation
    3.4 Repeated Roots; Reduction of Order
    3.5 Nonhomogeneous Equations; Method of Undetermined Coefficients
    3.6 Variation of Parameters
    3.7 Mechanical and Electrical Vibrations
    3.8 Forced Vibrations

    Test #2. Weight: 20%. Length: 50 min. Date: T.B.A.

  3. Ch. 5 Series Solutions of Second – Order O.D.E.s
    5.1 Review of Power Series
    5.2 Series Solutions near an Ordinary Point, Part I
    5.3 Series Solutions near an Ordinary Point, Part II
    5.4 Euler Equations ; Regular Singular Points
    5.5 Series Solutions near a Regular Singular Point, Part I
    5.6 Series Solutions near a Regular Singular Point, Part II
    5.7 Bessel’s Equation

    Test #3. Weight: 20%. Length: 50 min. Date: T.B.A.

  4. Ch. 6 The Laplace Transform
    6.1 Definition of the Laplace Transform
    6.2 Solution of the Initial Value Problem
    6.3 Step Functions
    6.4 Differential Equations with Discontinuous Forcing Functions
    6.5 Impulse Functions
    6.6 The Convolution Integral

Final Examination (cumulative). Weight: 40%. Length: 2 hours.
Date: as per Exam Schedule, issued by the Registrar’s Office.

Test/Exam Regulations:

  1. Tests/Exams may not be missed. There are NO MAKE-UP TESTS.

  2. Students must inform the instructor ahead of time by telephone (leave a message at 780-479-9360) or by e-mail (tomtavou@math.concordia.ab.ca), if unable to present themselves for a test due to illness or other serious extenuating circumstances.

  3. Students must contact the instructor in person as soon as possible after a missed test. At that time, they should present a physician’s note or other appropriate proof (of the reason the test was missed). In this case, the weight of the missed test will be added to the final exam.

  4. A missed test is considered non-excused, if either rule 2 or 3 above has not been adhered to. The missed test in this case is assigned a grade of zero.

  5. All tests/exams are closed book.

  6. Use of calculators is NOT permitted. Use of Mathematica® is permitted and/or required.

  7. All Concordia University College of Alberta rules and regulations apply; in particular the ones regarding Academic Honesty. See CUCA Calendar.


Students should use the math lab outside classroom time as much as possible. The assigned homework includes problems that need to be done on the computer. Tests and exams will also include questions that need to be answered using the computer and Mathematica®.

Cellular Telephones:

All cellular telephones should be de-activated upon enrty into any classroom or lab. A cellular phone may be left on, only with the express permission of the instructor. Permission MUST be obtained before the class commences. During tests, cellular phones must be de-activated, placed in the student’s bag, and the bag left at the front of the class.

Instructor-Student Communication:

  1. Students should know how to access their e-mail ”yourname@student.concordia.ab.ca‘ and to check it regularly. Instructors use it to send course announcements to students.

  2. The instructor regrets that he is unable to answer assignment questions over e-mail.

Lecture Format:

  1. Each lecture commences with a brief, point-form review of material covered in the previous lecture.

  2. Question period: to clarify and explain concepts further, and to solve homework problems.

  3. Theoretical presentation and treatment of new material.

  4. Model examples (usually different than the ones solved as illustrations in the textbook).

  5. Computer applications.

  6. Some guided self-study will be required for parts of this course.

How to Do Well:

  1. Do not skip classes. Attend regularly. If you miss a class due to illness, obtain the notes and do the homework as soon as possible.

  2. Try to read ahead by one lecture.

  3. In class, pay attention; scrutinize every sentence or statement; never be embarrassed to ask.

  4. Look up your notes as soon as possible after a lecture.

  5. Study systematically, using pencil and paper; do not simply read.

  6. Study notes and textbook carefully. Make sure that you have understood a concept well, before proceeding to the next one. Test your understanding of the concept by mentally defining it or pretending to explain it to someone else; be clear, concise and precise.

  7. After studying solved examples, whether from your textbook or notes, make sure that you can solve the same problems independently.

  8. Try the homework problems after you have done steps 6 and 7 above.

  9. If a particular problem gives you trouble, leave it for a while; come back to it at a later time (or next day). If still unsuccessful, ask in class. If questions still persist, discuss them with your colleagues, and seek help from your professor.

  10. Use the math lab on a regular basis for your homework and for computer practice.

  11. Working in small groups often helps, provided the group participants are all willing to actively contribute to the work and discussions, and they are not simply passive recipients of work done by others.

  12. Remember! Question time is all the time! Ask!

  13. Study regularly. Do not “fall behind”. Every topic is built on the previous one.

  14. Do not cram before exams. Exams are designed to test your understanding of the material and your competence in the course according to established criteria and standards; they are also meant to rank students according to their performance in the course. They are not meant to trick or fool them.

  15. Review often. Reviewing enhances the understanding, aids learning and builds up confidence.

  16. Enjoy the course! I wish you well!

Evaluation Scheme:

  1. The weights of tests/exams are indicated under “Syllabus/Tests/Exams” above.

  2. Tests/exams are marked out of 100.

  3. The final weighted average is calculated as a percentage and reported on the alpha-scale as follows:

% Range

Alpha Scale

98 – 100


95 – 97


90 – 94


85 – 89


80 – 84


75 – 79


70 – 74


65 – 69


60 – 64


55 – 59


50 -54


00 – 49


  1. The Bell curve will NOT be applied. Students know their standing in the course at any point in time as a result of their marks in the tests. Marks are not scaled.

  2. Assignments are given on a regular basis. However, they are not collected or graded. It is the responsibility of the individual student to do his/her homework.

  3. All final marks will be reported on the Four-Point Grading Scale as follows (also see Calendar):

Four-Point Grading Scale


Alpha Grade

Grade Point Value









Very Good


















Minimal Pass






When difficulties arise…
If you feel you need help, do not hesitate to seek it. Here is a list of people who can assist you in various circumstances…

  1. About the course… Contact your professor, Dr. A. N. (Tom) Tavouktsoglou, F.H.-204, Tel. 780-479-9360, tomtavou@math.concordia.ab.ca

  2. General academic or personal… Contact the Dean of Undergraduate Studies, Dr. Jonathan Strand, jonathan.strand@concordia.ab.ca

  3. Psychological, Personal… Contact the Campus Counselling Psychologist, Barbara Van Ingen, barbara.vaningen@concordia.ab.ca

  4. Spiritual, Pastoral… Contact the Campus Chaplain, Rev. Dr. Garry Dombrosky garry.dombrosky@concordia.ab.ca

  5. Career Counseling… Contact our campus career practitioner, Ms. Doreen Kooy, 

  6. Assistance in writing… Make an appointment by contacting Student and Enrollment Services.

Academic Hierarchy:

  1. Dr. Vladimir Pitchko, Associate Professor of Chemistry, Chair of the Science Division,
    F.H. – 305, Tel.: 780-379-9376, 

  2. Dr. Jonathan Strand, Dean of Undergraduate Studies, jonathan.strand@concordia.ab.ca