Description
Elementary analysis mostly studies real-valued functions on the real line R or on n-dimensional space Rn. Functional analysis, by contrast, shifts the point of view: we collect all the functions of a given class (for instance, all bounded continuous functions) into a space of functions, and we study that space (and operations on it) as an object in its own right. Since spaces of functions are nearly always infinite-dimensional, we are led to study analysis on infinite-dimensional vector spaces, of which the most important cases are Banach spaces and Hilbert spaces. This course provides an introduction to the basic concepts of functional analysis. These concepts are crucial in the modern study of partial differential equations, Fourier analysis, quantum mechanics, probability and many other fields.
Module deliveries for 2024/25 academic year
Last updated
This module description was last updated on 19th August 2024.
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