Tuesday 8 May, 7-10pm, worth 40%.
You may not use books, notes, or electronic devices on the exam.
Study session in 141 Altgeld: Monday 7 May, 5:00-6:30pm
Office hours after classes finish: Thursday 3 May 3-4pm, Tuesday 8 May noon-1pm. Other times by email appointment
Material
The entire course: 1.1-1.6, 2.2, 2.4, 3.1-3.6, 4.1, 5.1-5.6, 3.8,
9.1-9.7, as well as
additional material introduced in class (e.g. Orthogonality Supplement)
and in the homework assignments and projects.
Formulas will be provided like on Tests 1 and 2, along with the basic
formulas for Fourier coefficients of periodic functions.
Chapter 9 will count for about 40% of the final exam
(to compensate for its not having been examined on Tests 1 or 2).
For further detailed advice on Chapters 1-5 see the
Test 1 Information and
Test 2 Information.
Some of the test questions will be very close to homework or quiz problems or practice exam problems that you have already seen. But some test questions will be new - you are expected to study and understand the underlying methods of differential equations and to be able to apply these methods in new situations.
When studying the Iode projects, I recommend just writing a paragraph about each one to summarize the main conceptual points.
Basic topics to be very familiar with include: solution of y'=ky and y'=-ky, or x'=kx and x'=-kx, solution of y''-k2y=0 in terms of exponentials and in terms of hyperbolic sines/cosines, solution of y''+k2y=0 in terms of complex exponentials and in terms of sines/cosines.
How to study
First make summary notes of the important ideas and methods
from each section. In particular, make notes on Chapter 9, because
this is the least familiar material for you.
Wherever possible, express the methods and theorems as algorithms or
checklists (step 1, step 2, and so on), so that you have a plan of action
for each type of problem.
Re-work some homework problems, and all quiz problems and all test
problems, and all "exam preparation" problems given in class.
Attempt the Practice Exam.
Note. The Practice Exam provides no practice on Chapters 4,5.
You should study the Supplement on Orthogonality of
Eigenfunctions, which we covered after Section 3.8. You are not responsible
for the proofs, but you should know how to apply the Orthogonality
of Eigenfunctions Theorem, like in the given examples.