Functional analysis lecture notes

Ward T.B.

In order to reach the more interesting and useful ideas, we shall adopt a fairly brutal approach to some early material. Lengthy proofs will sometimes be left out, though full versions will be made available. By the end of the course, you should have a good understanding of normed vector spaces, Hilbert and Banach spaces, xed point theorems and examples of function spaces. These ideas will be illustrated with applications to di erential equations.