Department of Applied Mathematics & Theoretical Physics -- (302) 857-7516 (main), -7517 (fax)
Ordinary Differential Equations
Math-551 (17040) : MW, 2:00–2:50 pm, EH
247
[Topics][Schedule][Assignments][Welcome]
Grading recipe (no make-ups are given, except in cases of proven medical emergency):
Component |
Time |
Remark |
% of Grade |
---|---|---|---|
Weekly projects |
See in weekly schedule |
May overlap with individual contributions to the
term-project |
50% |
Term-project |
Incrementally, through semester |
Classification of solved ODEs |
50% |
Ordinary Differential Equations (Math 551) introduces and develops its subject, differential equations, which turn out to provide the fundamental concept used in modeling phenomena in Nature. Applications occur throughout the sciences, both natural and social, but also in practical daily life and business. The emphasis of the course is then divided between the underlying mathematics and the various applications.
“Success
= 1% inspiration + 99% perspiration”--T.A. Edison
But, learning is still 100% learning!
§1: Fist Order Differential Equations
§2: Linear Equations of Higher Order
§3: Power Series Methods
§4: Laplace Transform Methods
§5: Linear Systems of Differential Equations
§6: Nonlinear Systems and Phenomena
08/29: Introductory
Matters
08/31: Course goal and arrangements
09/03: Labor Day Recess
09/05–07: Seven differential veils, or cookbook recipes for
solving ODEs: handout No.1
09/10–14: Seven veils,
cont’d
09/17–21: • Bernuolli’s equations
– exploring the class
09/24–28: • Separable subclass of
Bernuolli’s equations
10/01–05: • Non-separable (?) Bernuolli’s
equations
10/08–12: • Ricatti’s equation
10/15–19: • Special properties of
Ricatti’s equation
10/22–26: • Clairault’s equation,
parametric solutions & applications
10/29–02: • Exact and related ODEs
11/05–09: • From exact ODEs to cohomology
11/12–16: • 2nd and higher order (Euler)
homogeneous equations
11/19–21: • Linear ODE systems
with constant coefficients
11/23: Thanksgivings
Recess
11/26–30: • Linear ODE systems with polynomial
coefficients & power series methods
12/03–05: • Orthogonal function series methods
Starting in week 09/17–21, on the topic indicated in the weekly schedule.
All weekly assignments are due by 5:00 pm of the end of the week indicated and should be submitted via e-mail attachments, or alternatively handed in either to the instructor in hand, left in the instructor's mailbox in ETV#116. Late assignments will not be accepted, except in cases of proven emergency.
Collaboration policy
Collaboration -- but not blind copying -- on the weekly assignments is strongly encouraged; students should use this to learn from each other. All assignments are open text and other sources, as indicated in the textbook listing above.
Presentation and organization
While a neat presentation of the Student’s work is not required for full credit, it certainly makes it easier to assess the quality of the work and give the proper credit due. In all cases, include sketches if they might help conveying the approach or the calculations. Where necessary, include all units and symbols such as the measure of an integral, arrow on a vector, vertical bars for the absolute value of a quantity, for the magnitude of a vector or for the determinant of a matrix, etc.
© Tristan Hübsch, 2007