LECTURE: | MWF 1400 - 1450 | STAG 112 | CRN 18182 |
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Instructor: | R.E. Showalter | Kidder 286 | show@math.oregonstate.edu |

Office Hours: | TBA |

This course will begin with the elements of Hilbert space, where most basic principles appear in their simplest form. Then we move on to the fundamentals of functional analysis, including the Hahn-Banach Theorem, Open Mapping Theorem, the Closed Range Theorem, and the Uniform Boundedness Principle in Banach space. Additional topics include variational principles for minima or saddle points, convex analysis, Lp and Sobolev spaces and corresponding trace spaces of boundary values, semigroup theory, and applications to partial differential equations.

**Prerequisite: ** MTH 511 or comparable.

**Textbook:** *Functional Analysis, Sobolev Spaces and Partial
Differential Equations*, Haim Brezis, Springer, 2011.

Additional materials will be provided for examples, variations and
applications.