PMath 450/650, Winter 2012
Instructor:
Nico Spronk
Office Hours: M 11am-noon, W 3:30-5pm (or by appointment; email
nspronk at uwaterloo dot ca.)
Time: MWF 2:30-3:20pm. Location:PHY 313.
See
here too.
Course outline
Recommended text: Real Analysis by Bruckner,
Bruckner and Thompson.
There are TWO OPTIONS for this book.
ONE: Visit
classicalrealanalysis.com and obtain the PDF via the link under [BBT].
TWO: A paper version of this book can be purchased for a modest cost at
createspace.
I will aim to make the course self-contained, so the book is not
required.
Supplementary texts:
The book An Introduction to Harmonic Analysis by Y. Katznelson,
Third edition, Cambridge University Press, Cambridge (2004) [there is a
reprinting of the first edition: Dover, New York (1976) -- which might
be a lot cheaper if you can find it] is a brisk but excellent little book
on Fourier analysis. It has no measure theory content and is quite advanced.
The book Real Analysis by H.L. Royden, Third Edition
Prentice Hall, Upper Saddle River NJ (1988), is a standard reference
for measure theory and analysis in metric spaces. It is often used in
successor courses such as PM451. However, it has no Fourier analysis content.
The photo is by my wife, Stephenie,
who wanted photographs of toys for a lighting class. She wished
to stage the toys in various workplace settings,
including mine: math professor.
The caption is a play on Mattel's misadventure of the early `90s
where they made a talking teen Barbie who exclaimed "Math class is tough!"
(See NYT, or
Wikipedia.)
Homework Assignments:
Assignment #1
Assignment #2
Assignment #3
Assignment #4
Assignment #5
Assignment #6 You may hand-in, Monday, April 2.
Sample Solutions: Log into UWACE/Learn and visit PMATH 450/PMATH 650.
Illustrations of the
Dirichlet and Fejer kernels of order 10, along with
suggested Maple code for producing them.
A proof I screwed-up in class:
not all c_0(Z) sequences are sequences
arising form Fourier series.
Illustrations of
Gibbs Phenomenon.
A pictorial examination of
best approximation of certain Lipschitz functions .
Piecewise differentiable functions with integrable derivative
satisfy the assumptions of Hardy's Tauberian Theorem.
Final Exam: Wednesday, April 11, 4:00-6:30PM, in RCH 301.
See the Winter 2012
exam schedule (PDF).
Review sheet
Special Office Hours: Monday April 9 3-5PM,
Tuesday April 10 3-5PM, or by appointment.