 |
Course Outline
|
|
Topics |
| Background: Vector spaces, dot products, norms, Cauchy-Schwartz 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, non-expansive projections, orthogonal projections, and self-adjoint projections |
| Bounded linear functions, Riesz representation theorem, and the Lax-Milgram theorem |
| Characterizations of finite dimensional and of self-adjoint, normal, compact, or closed linear operators |
| A structure for unbounded linear operators, Sturm-Liouville operators
|
| Contraction Mapping Theorem and applications |
| Some illustrative topics according to students' interest |
| Normed and Sobolev spaces |
|
|
Textbook
|
 Arch W. Naylor, George R. Sell, "Linear Operator Theory in Engineering and Science", Second edition. Applied Mathematical Sciences, 40. Springer-Verlag, New York-Berlin, 1982
In particular Sections 5.12-5.24, 7.1-7.5
|
|
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
|
Wednesday December 12th, 2:50-5:40pm
Skiles 269
|
|
|
|
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 |
|
)