We meet on Tuesdays from 2PM to
3PM, (sometimes also until 3.40 pm), room GC 283 B
My office hours are on Tuesday, 3.45 pm-4.30 pm.
Thursday,1.30pm-3pm but mostly by
appointment.
Office: DM 436B.
Class and office hours cancellation.
2) There is no class on Tuesday, Nov. 10.
Problems solved in class.
So far we have solved the following problems about Riemann integrable functions:
1) State a definition of Riemann integrable function. Can a Riemann integrable function be discontinuous? If yes which kind of discontinuities and how many discontinuities can such function have?
2) Show an example of bounded non integrable function in [0,1]
3) Let m be an integer. Show that the integral of |cos (m x)| in [0, pi] does not depend on m
4) What is the definition of rectifiable function? Prove the well known formula to compute the arc length of continuous and differentiable functions in an interval [a,b]. Show an example (a pictorial example will do) of bounded differentiable function in [0,1] which is not rectifiable.
We have also reviewed
the fundamental identity e^(i x)= cos x
+ i sin x (see Louis’ presentation)
We have also
discussed some linear differential equations with constant coefficients
(example: a y” +b y’+ cy= f(x)) and
separable equations (example y’= x y^m with initial conditions); we have discussed existence and uniqueness of the
solutions and the methods for finding
thems.
Last time we
have worked on Problem 1 of last year’s exit exam
Presentations
As you know, preparing a written and oral presentation for the class is part of your evaluation. Please download the presentations of your classmates below.
E-mail
FIU is using an unpredictable SPAM filter which quarantines all
kind of messages.
Make sure to you check your junk mail folder regularly because you may loose
important e-mail. It is advisable that you send me e-mail from your FIU
address because of the SPAM filter. Keep in mind that I
always reply to e-mail ... when I get it, of course!
Samuel F. presentation (zip format)