Contents1 Metric Spaces2 Normed Spaces, Banach Spaces3 Inner Product Spaces, Hilbert Spaces4 Fundamental Theorems for Normed and Banach Spaces5 Banach Fixed Point Theorem6 Further Applications: Approximation Theory7 Spectral Theory of Linear Operators in Normed Spaces8 Compact Linear Operators on Normed Spaces and Their Spectrum9 . Springer Science & Business Media Providing an introduction to functional analysis, this text treats in detail its application to boundary-value problems and nite elements, and is distinguished by the fact that abstract concepts are motivated and illustrated wherever possible. Donate . 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