Welcome to the wonderful world of ordinary differential equations.
Differential equations (partial and ordinary) are the language of the universe. To understand the
motion of the planets, the spread of disease (or rumors ...), or the stability of buildings during
earthquakes, one must first understand differential equations. When an engineer computes the
voltage in a circuit, a coroner places the
time of death of the victim of a crime or NASA computes the trajectory of a shuttle mission,
differential equations are there! Differential equations show up most anytime you look at the
world and try to understand it in some quantitative (or qualitative) way. In addition to the
vast applicability of ODE's the study of their properties (do there exists solutions? what
are the solutions like? how do you find the solutions?) involves a amazing and intricate interplay
of linear algebra, calculus and many other areas of mathematics.
This is the focus of Math 2413! By the end
of this course we should all be familiar with the language of ODE's, methods to study linear ODE's
and techniques to push beyond the linear world into the, still developing world, of non-linear ODE's
and chaos.
Announcements:
- The first test will be in discussion session on September 27. It will cover all the material up to, but
not including, undetermined coefficients and variation of parameters. If you have any questions, I will be in
my office on Monday, September 26, from 10 till around 3.
- Due to several requests I have decided to add an optional project to the course requirements. You can ignore
the project and your grade will be computed as discussed in the course outline below. Details on what I expect out
of a project and how it affects your grade can be found by following the link below.
- The second test will be in discussion session on November 3. Here is an outline
for the test and here are some practice problems.
If you have any questions I will be in my office Monday, October 31, from 10 to about 3 and Tuesday, November 1,
from about 10 to 1. You can also catch me after class on Wednesday (probably till about 12).
- The final exam will be Wednesday, Dec 14th, 8:00-10:50 in Skiles 108B. The exam will be comprehensive, but
focus mainly on everything since the last test, that is Series Solutions to ODEs and the Laplace transform. The best
way to study for the exam is to go over your previous tests and Homeworks 11, 12, and 13. If you have more time it might
also be useful to go over your class notes and all the other homeworks. I will be available for questions from 11:30 to
3:30 on
Friday, December 9 and from 9:00 to 1:00 and 3:00 to 4:30 on Tuesday, December 13. You can also get me anytime
via e-mail.
- The optional projects should be turned into me anytime before the Final Exam on the 14th.
- Here is an outline and set of sample problems for the new material on the final exam.
Course Information:
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