MATH 133 -SPRING 2007
Introduction to Fourier Analysis
MWF 9:00 MS 6221, and Tues 9:00 MS 6221
Office
hours:
J. Garnett MWF 10:30 in
MS 7941, and by appointment;
Text: E. M. Stein and R.
Shakarchi, FourierAnalysis,AnIntroduction(required).
Material: Wave
equation, heat equation,
convolutions, approximate identities, Ces`aro means, Fej´er’s theorem, Dirichlet problem for
the disc, L2convergence
and Hilbert space, applications: isoperimetric inequality, Weyl’s
theorem on equidistributed points, nowhere
differentiable
functions. Fourier transforms on R and Rd,
Plancherel’s theorem, the Weierstrass approximation theorem, the
Heisenberg
uncertainty principle, applications to partial
differential equations. Further topics, as time allows.
Grade: Homework 40%, &final 40%, midterm 20%. Each student must present at least one homework problem at the blackboard in quiz section.
Prerequisite: 131A and 131B and/or the ability to make and write a correct proof.
Homework: Assigned
biweekly, due at the beginning of quiz section every second week. You
may work on the homework problems together, but you must write up your
solutions alone.You will be askedto present your homeworksolutions at
the blackboard in class.
TypesetbyAMS-TEX