Ordinary Differential Equations (ODE's)

Mathematics 3008, Winter, 2004
This website's Internet address (URL): http://www.carleton.ca/~angelo/calculus/cal3008.html

Detailed Class Outline

These pages are best viewed with Netscape 2.0 or higher, and not from a Chat prompt.

Using CHAT Who's the Prof? Do I know enough? What must I know?
Classes Begin Where are the lectures? Textbook(s) Can I use a Calculator?
Will I pass? When's the Supplemental Exam? I wanna drop this! Prof's Office Hours
Tutorials FAQ on Tutorials Where's a tutor? When's the next Holiday?

Dr. Angelo B. Mingarelli,
Herzberg Physics Office #4250
Tel/Fax: (613) 520 3534
Electronic mail : angelo@math.carleton.ca
Photograph : Just in case you don't want to come to class...

Office Hours: Wednesdays, after class for at least one hour.

TEXTBOOK(S): Compulsory: Differential Equations- Schaum's Outline Series, McGraw-Hill, (2nd Edition) + additional material in the form of notes along with the following ...
Textbook References (in no specific order):
1. E. L. Ince- Ordinary Differential Equations, Dover, New York, 1956.
2. M. Braun, Differential Equations and Their Applications, 2nd Edition, Springer Verlag, New York, 1978
3. G. M. Murphy, Ordinary Differential Equations and Their Solutions, Van Nostrand, New York, 1960
4. D. L. Kreider, R.G. Kuller and D. R. Ostberg, Elementary Differential Equations, Addison-Wesley, Reading-Mass., 1968.
5. W. Leighton, A First Course in Ordinary Differential Equations, 5th Edition, Wadsworth Publishing, 1981.
6. Burkhill, Ordinary Differential Equations, 1930's (tiny book)
7. Edwards and Penny, Differential Equations and Boundary Value Problems, Prentice Hall, NY, 1996
8. Boyce and DiPrima, Elementary Differential Equations (Any edition), John Wiley & Sons.

Optional: In case you forgot your Methods of Integration, or Inverse functions, see my Calculus book currently used in 69.104 (also available in the Bookstore $59.95 + GST).

The prerequisites for this course are:
Math 2000, 2454 or 2600
Students who have not passed the prerequisite courses may be automatically de-registered during the term Do get advice from the instructor or from the Mathematics Undergraduate Advisor Ken Small, in 4380 Herzberg Building.

Your grade will be calculated either as:
(i) Term Mark 40%;
(ii) Final Examination 60%
(iii) Final Examination 100%, whichever is better.
In any event, your final course grade is the larger of the two numbers: A and B where A=(i)+(ii) and B=(iii).

The term mark (40%) will be derived from:

Note:  The "best x of y" rule allows you to miss some of the term events for any reason (medical or otherwise).
Only under highly exceptional circumstances will a test be postponed to a later date.

You may use any non-programmable calculator for the examinations and tests in this course, although it is not necessary.
The Sharp 531-L is available at the Bookstore for around $19.95 + Tax.

If you decide to leave the course before the end of term, it is much better, in terms of your academic career, to formally withdraw from the course than to simply ignore it and get an F.

Monday, January 5, 2004


Mondays, 516 Southam Hall, 2:30 p.m.
Wednesdays, 515 Southam Hall, 2:30 p.m.


All tutorials are held on Fridays and will begin January 16 . Your TA is Mr. Bevan Ferreira. He can be reached at bcferrei@math.carleton.ca; bcferrei@yahoo.ca; or bcferrei@hotmail.com (I think). His office is Room 230 in Azrieli Pavillion and his office telephone number is: 520-2600 Ext 1889.

WINTER BREAK: February 16-20 --- classes suspended.



Please note that the mathematics TUTORIAL CENTRE , in Herzberg Physics Building, Room 4385, will be opening around Jan. 15th, 2002

Hours for the Centre:
Monday to Thursday: 10 am to 4pm
Evening hours to be announced.
Tutors advertise frequently on the Notice Boards around the Centre.

Detailed Class Outline

Winter, 2004

Jan. 5-7 None    Existence and uniqueness of solutions of second order ode's (1.5 hours)
Jan.12-14 None    Analytic ode's: Series solutions of differential equations about an ordinary point (4.5 hours)
Jan. 19-21 None  Series solutions of differential equations about a regular singular point (Frobenius method)
Jan. 26-28 TEST 1, Jan. 
Tutorial room 
 Orindary Points
Chapter 23
Homework #
28, 32, 34, 39, 
42, 45, 49
Series solutions of differential equations about a regular singular point (cont'd)
Feb 2-4  None  Homework:
Chapter 24 #
26, 28, 29, 30
Series solutions of differential equations about a regular singular point : Bessel functions and the Gamma function
Feb.9-11  TEST 2
Feb. 13
Tutorial Room
Singular Points
Chapter 24
Sturm-Liouville Theory and Asymptotics of solutions (3 hours)
Feb. 16-20     TERM BREAK 
Feb 23-25  None   Sturm-Liouville Theory and Eigenfunction expansions
Mar.1-3  TEST 3
Mar. 5
Tutorial Room 
  Fourier Series
10  Mar. 8-10 None   Fourier Series (and Transforms)
11  Mar.15-17  TEST 4
Mar. 19
Tutorial Room
Fourier Series-Motivation

Fourier Series Formulae

Fourier Series Notes
(No Diagrams) 

Exercises on Fourier Series

Remarks on 
Fourier Coefficients

Page 2 on 
Fourier Coefficients

12  Mar.23-24.  None    Applications and more on special functions...
More on Fourier Series and Transforms - The Heisenberg Uncertainty Principle (if time permits)
13  Mar. 29-31 None    Review

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