MTL882: Applied Analysis

3 Credits (3-0-0)

Review of Normed Linear spaces, Banach spaces and Hilbert spaces. Weak and weak* convergence, Spectrum of Bounded Linear operators. Browder and Schauder fixed point theorems and applications to Differential and integral equations, LP spaces.

Distributions and Fourier transforms: Schwartz space, tempered distributions, Fourier transform of tempered distributions, Fourier transform of LP functions and applications.

Sobolev spaces: Density, embedding and extension theorems. Differential Calculus: Derivatives of maps on Banach spaces, inverse and implicit function theorems, Direct methods of Calculus of variations and applications.