
Course Outline

Topics 
Background: Vector spaces, dot products, norms, CauchySchwartz inequality 
Contrast the geometry of
and other spaces 
Complete orthonormal sequences, Fourier series, Bessel's and Parseval's inequality 
Projections: closest point projections, linear projections, nonexpansive projections, orthogonal projections, and selfadjoint projections 
Bounded linear functions, Riesz representation theorem, and the LaxMilgram theorem 
Characterizations of finite dimensional and of selfadjoint, normal, compact, or closed linear operators 
A structure for unbounded linear operators, SturmLiouville operators

Contraction Mapping Theorem and applications 
Some illustrative topics according to students' interest 
Normed and Sobolev spaces 


Textbook

Official textbook
Arch W. Naylor, George R. Sell,"Linear Operator Theory in Engineering and Science", Second edition. Applied Mathematical Sciences, 40. SpringerVerlag, New YorkBerlin, 1982
"Linear Operator Theory in Engineering and Science",
Second edition. Applied Mathematical Sciences, 40. SpringerVerlag, New YorkBerlin, 1982
In particular Sections 5.125.24, 7.17.5
Other possible helpful books
N.I. Akhiezer & I.M. Glazman, Theory of Linear Operators in Hilbert Spaces,
Dover, NewYork (1993),
Frigyes Riesz & Béla Sz.Nagy, Functional Analysis, Dover, NewYork (1990),
(return to top)


Homework

One compulsory homework will be offered once every 2 or 3 weeks
Each homework will be graded. The homework grade will count for 35% of the final grade


Final Exam

Thursday December 12th, 2:505:40pm
Skiles 269
(
to calendar)



An absence to the final be graded 0 (zero). However if the absence is justified (disease, injury, ...), the student must (i) warn the instructor as soon as possible, in any case before the end of the exam week, (ii) bring the documents justifying the absence to the Instructor.
Then the student will receive an I (incomplete) and will be responsible to take action during the following semester to complete his/her curriculum.


Grades




90% for an A 
Homeworks 
35% 
Grade distribution 
80% for a B 
Final 
65% 

70% for a C 



60% for a D 
