Scheduling Information: 
Time: Tuesday, May 9, from 1:004:00pm.
Location: DH 2210.
Review Session:
Sunday, May 7, from 7:309:00pm, in MM A14.


Reading:

Classification of Equilibrium Points.
Section 10.2.
Section 10.3.
Section 11.1.
Section 11.2.
Section 11.3.
Section 12.1.
Section 12.2.
Section 12.4


Review Questions:


What does it mean to say that T is a "period" of a function f?

What does it mean to say that T is the "fundamental period" of f?

What are the Fourier coefficients of a piecewise continuous function
with period 2L?

What is the Fourier series of a piecewise continuous function with
period 2L?

What is an even function? An odd function?

What useful facts do you know about integrals of even functions? Odd
functions?

If f:[0,L]>R, how can you extend this to an even function on [L,L]? On
odd function on [L,L]?

What is the Fourier sine series of a function f:[0,L]R?

What is the Fourier cosine series of a function f:[0,L]>R?

What is a partial differential equation?

What is the wave equation?

What do the boundary conditions u(0,t)=u(L,t)=0 say about our vibrating
string?

What does the initial condition u(x,0)=f(x) say about our
vibrating string?

What does the initial condition du/dt(x,0)=g(x) say about our
vibrating string?

What is separation of variables? What do we assume about out solutions
u(x,t)?

How does the the separation of variables lead to the boundary value
problem X"+\lambda X=0, X(0)=X(L)=0?

What are the solutions to the boundary value problem X"+\lambda X=0,
X(0)=X(L)=0?

How do we solve our "wave equation problem" when g(x)=0? When f(x)=0?
When both f(x) and g(x) are nonzero?


Exercises:

Section 10.3 #11, 13, 15, 29 (You should be able to sketch a phase portrait for these systems)
Section 11.2 #1, 5, 7, 21
Section 11.3 #1, 3, 5, 7, 11, 13, 17, 25, 27, 49.
Section 12.1 #1, 5, 7.
Section 12.4 #1, 3, 5.


Old Exam Problems:

Here is a final exam I gave when I taught
Differential Equations in a previous semester.
Also here is the table of Laplace transforms
you will be given on the exam.
Before the questions come in  no, I don't have solutions available for these
problems. You have a large number of problems from the text with answers,
and it's important for you to get used to working on problems where the answers
are not available. You'll have a chance to ask questions at the Review
Session, and during your TA's office hours, too.

