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Math 6255 (CRN #85562)

Functional Analysis

TR: 9:30 am - 10:45 am, McB 204

Instructor: Martin Klaus (klaus@math.vt.edu)

Office: McBryde 472, phone 231-6533

Office Hours: TR: 2:00 pm - 3:00 pm, or by appointment

Text: ``Introductory Functional Analysis with Applications'' by E. Kreyszig

Course Content: Functional Analysis is an important tool for the study of various branches of physics like quantum mechanics and related areas in mathematics like ordinary and partial differential equations and the calculus of variations. The mathematical problems that arise in these areas require us to work in spaces of infinite dimensions and to combine methods of analysis (real and complex) and linear algebra. For example, we may think of a differential operator as a linear map on a large set of functions (an infinite dimensional function space). This leads to the study of linear functionals and, since the space is infinite dimensional, to questions about the convergence of sequences and series in the space; these questions are then treated with the tools of analysis. This is a two-semester course with the first semester being devoted to the study of spaces and bounded linear operators. In the second semester we will study unbounded operators and their application in various areas.

Homework: Homework will be assigned regularly and it will be graded. You are encouraged to discuss homework problems with me or other students. However, the work you turn in should be written up independently and reflect your understanding of the material.

Evaluation: Your grade will be based on the homework and additional projects including presentations. An important criterion will be the effort you put into your assignments.

Honor system: I will assume that you have read the Va Tech Honor policy and I expect you to abide by it.