Tuesday 20 February, in class, worth 15%.
You may not use books, notes, or electronic devices on the test.
Last chance study session in 141 Altgeld: Monday 19 February, 5-6pm
Material
Sections 1.1-1.6, 2.2, 2.4, and 3.1-3.4,
and all homework to date (including
Iode Projects 1 and 2). Use your lecture notes and
homework as a guide to the level at which you are expected to master the
material. Some of the test questions will be very close to homework
or quiz problems that you have already seen.
But you are expected to study and understand the underlying methods
of differential equations and to be able to apply these methods in new
situations.
The text contains many topics and application areas that we did not cover in
class (e.g. "exact equations" in Section 1.6).
You generally do not need to learn these topics for the test.
You can ignore Sec. 3.1 Th. 3 and Sec. 3.2 Th. 3, on Wronskians.
In class we covered linear independence of exponential functions and sine and
cosine, without
using Wronskians. (Recall that instead we supposed the functions were
linearly dependent, meaning one of them can be written as
a linear combination of the others, and we worked directly with that linear
combination to obtain a contradiction; see the
questions in the "Section 3.2 Summary" at
the handouts page.)
How to study
To study, first make summary notes of the important ideas and methods
from each section.
Wherever possible, express the methods as algorithms or
checklists (step 1, step 2, and so on) so that you have a plan of action
for each type of problem.
If you just work problems without first making
summary notes, you will probably be wasting your time, because you won't
have a mental framework into which to fit the examples you are working.
It is the underlying methods and techniques that we care about; we
work examples to show that we understand the techniques.
Re-work all homework problems, and quiz problems. (Some solutions are
available at the class website.)
Work through relevant examples in the text. Attempt other exercises
e.g. Chapter 1 Review problems.
Write paragraphs summarizing the main conceptual points learned in Iode
Projects 1 and 2. Those projects are examinable!
The HW problems on Sec. 2.2 are useful test preparation, as are the
examples covered in class for that section.
Attempt the Practice Test (on website, with solutions).