Review Sheet for Math 20580, Spring ‘09, Final Exam
Disclaimer. The following review sheet represents a sincere attempt to help you prepare
for the exam. It is not in any sense a practice exam. Nor is it necessarily complete. There
might be things on the exam that are not mentioned directly here, problems that look
diﬀerent than the review problems suggested here, etc. Nonetheless, we think it’s better
Practical details. The exam runs from 1:45-3:45 on Wednesday, May 6. There will be
a review session Tuesday, May 5 from 7-8 PM in Debartolo 141 (same as for last two review
The exam will be comprehensive, including all material (with one exception noted below)
covered on the midterms together with sections 2.3, 2.5 and 3.1-3.5 from Boyce and DiPrima
covered in lecture after the third midterm. The format will be similar to that of the midterms,
except that there will be no partial credit this time. No calculators, books, or notes will be
A dozen or so students have a conﬂict between our ﬁnal and that of probability and
statistics which takes place at the same time. If you are one of those students (and you
haven’t already done so), you MUST email Jeﬀ Diller (email@example.com) before 4/30/09. So
that we can set a time for the makeup, we ask that you also list the times of other ﬁnals you
have scheduled after ours. We will announce the time of the makeup on 4/30/09, though it
might take a bit longer to get a location for it.
Things to know
Material covered on the ﬁrst three midterms. You are responsible for all material
listed on the review sheets of the ﬁrst three midterms. The only exception here is that all
vector spaces in linear algebra problems on the exam will be subspaces of Rn (i.e. no vector
spaces of polynomials, matrices, etc).
Material covered in lecture since the third midterm.
Terminology: autonomous ODE, homogeneous linear ODE, constant coeﬃcient ODE,
superposition principle, reduction of order.
Computational skills: Setting up and solving word problems involving ODEs. Find-
ing and classifying equilibrium points of autonomous ODEs. Determining asymptotic
behavior of solutions to autonomous ODEs, solving 2nd order constant coeﬃcient
ODEs and initial value problems—in particular, dealing with complex and repeated
roots of the characteristic equation. Dealing with ez where z is a complex number.
Using reduction of order to ﬁnd an additional solution to a 2nd order ODE. Solving
inhomogenous 2nd order linear ODEs using the method of undetermined coeﬃcients.