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MAT 492 A: Partial Differential Equations

Winter Semester 2011

CourseMAT 492 \”Partial Differential Equations\”.

Prereq. MAT 200, 215 and 331 with a minimum grade of C-.
Course Description: See CUCA Calendar, or


Course Instructor:

Name: 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

www: 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.: 09:50 – 10:40, T./R.: 09:00 – 09:50

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

  1. \”An Introduction to Partial Differential Equations\”; by G. Stephenson, Imperial College Press, London.

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

Course Schedule:

Tues./Thurs.: 08:00 – 09:15, in T-103 (Math Lab). Please be punctual!

Additional Bibliography(optional)

  1. \”Basic Partial Differential Equations\”; by D. Bleecker & G. Csordas, International Press Publications, 1996.

  2. \”Partial Differential Equations and Boundary Value Problems\”; by N. Asmar, Prentice-Hall Inc., 2000.

  3. \”Elementray Applied Partial Differential Equations\”; by R. Haberman, Prentice-Hall Inc., 1998.

  4. \”Partial Differential Equations – Sources and Solutions\”; by A. D. Snider, Prentice-Hall Inc., 1999.

  5. \”Partial Differential Equations with Mathematica\”; by D. Vvedensky, Addison-Wesley Publishing Company, 1993.

  6. \”Partial Differential Equations with Mathematica\”; by P. K. Kythe, P. Puri & M. R. Schaferkotter, CRC Press Inc.,1997.

  7. Other books on the subject available at the library.


  1. Review of O.D.E.s

  2. Basic Concepts in P.D.E.s
    1.1 Introduction
    1.2 The Wave Equation
    1.3 Some Important Equations

  3. Classification of Equations and Boundary Conditions
    2.1 Types of Equations
    2.2 Euler\’s Equation
    2.3 Boundary Conditions
    2.4 Laplace\’s Equation and the Dirichlet Problem
    2.5 D\’ Alembert\’s Solution of the Wave Equation

  4. Orthonormal Functions, The Sturm-Liouville Equation
    3.1 Superposition of Solutions
    3.2 Orthonormal Functions
    3.3 Expansion of a Function in a Series of Orthonormal Functions
    3.4 The Sturm-Liouville Equation

  5. Applications of Fourier\’s Methods
    4.1 Coordinate Systems and Separability
    4.2 Homogeneous Equations
    4.3 Non-Homogeneous Boundary Conditions
    4.4 Inhomogeneous Equations

  6. Problems involving Cylindrical and Spherical Symmetry
    5.1 Simple Solutions of Laplace\’s Equation
    5.2 The Dirichlet Problem for a Circle
    5.3 Special Functions
    5.4 Boundary Value Problems involving Special Functions

  7. Continuous Eigenvalues and Fourier Integrals
    6.1 Introduction
    6.2 The Fourier Integral
    6.3 Application of Fourier Integrals to Boundary Value Problems

  8. The Laplace Transfrom
    7.1 Integral Transforms
    7.2 The Laplace Transform
    7.3 Inverse Laplace Transfroms
    7.4 The Error Function
    7.5 The Heaviside Unit Step Function
    7.6 Laplace Transforms of Derivatives

7.7 Solution of O.D.E.s

  • The syllabus and schedule are tentative and subject to modifications; it may not be possible to cover all units.

  • There will be three 50-minute tests, each contributing 20% to the final grade.

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

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

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@csa.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.

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 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®.

Lecture Format:

Much of this course will be directed/supervised study. Students are expected to do a considerable amount of self-study. Classroom time will be used for discussion and clarification of concepts, and for examples. Working in groups is strongly encouraged.

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 grading 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






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!

Getting help:
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 Student Affairs (Acting), Rev. Dr. Garry Dombrosky, garry.dombrosky@concordia.ab.ca
    c/o Ms. Marilyn Grabinsky, HA-123, Tel. 780-479-9242, marilyn.grabinsky@concordia.ab

  3. Psychological, Personal… Contact the Campus Counselling Psychologist, Barbara Van Ingen,
    c/o Ms. Marilyn Grabinsky, HA-123, Tel. 780-479-9242, 

  4. Spiritual, Pastoral… Contact the Campus Chaplain, Rev. Dr. Garry Dombrosky garry.dombrosky@concordia.ab.ca
    c/o Ms. Marilyn Grabinsky, HA-123, Tel. 780-479-9242, marilyn.grabinsky@concordia.ab

  5. Career Counseling… Contact our campus career practitioner,
    c/o Ms. Marilyn Grabinsky, HA-123, Tel. 780-479-9242, marilyn.grabinsky@concordia.ab

  6. Assistance in writing… Make an appointment by contacting 
    c/o Ms. Marilyn Grabinsky, HA-123, Tel. 780-479-9242, marilyn.grabinsky@concordia.ab

Academic Hierarchy:

  1. Dr. Rossitza Marinova, Associate Professor of Mathematics & Computing Science,
    Chair of the Science Division, F.H. – 203, Tel.: 780-378-8430,

  2. Dr. Catherine Eddy, Professor of English, Dean of Arts and Science, G- 206,
    Tel: 780-479-9217, e-mail: