The previous lecture in this series is here. The next lecture in this series is here.
We prove the Fredholm Alternative, the Maximum Principle and the Spectral Theorem for self-adjoint compact operators. The final result is analogous to the statement that every Hermitian matrix is diagonalizable.
These videos are of a lecture course by Casey Rodriguez at the Massachusetts Institute of Technology in 2021, and made available as part of its OpenCourseWare initiative.