Functional analysis

Description:

This book introduces functional analysis at an elementary level without assuming any background in real analysis, for example on metric spaces or Lebesgue integration. It focuses on concepts and methods relevant in applied contexts such as variational methods on Hilbert spaces, Neumann series, eigenvalue expansions for compact self-adjoint operators, weak differentiation and Sobolev spaces on intervals, and model applications to differential and integral equations. Beyond that, the final chapters on the uniform boundedness theorem, the open mapping theorem and the Hahn-Banach theorem provide a stepping-stone to more advanced texts. The exposition is clear and rigorous, featuring full and detailed proofs. Many examples illustrate the new notions and results. Each chapter concludes with a large collection of exercises, some of which are referred to in the margin of the text, tailor-made in order to guide the student digesting the new material. Optional sections and chapters supplement the mandatory parts and allow for modular teaching spanning from basic to honors track level. --Provided by publisher.

subjects: Functional analysis,  Textbooks,  Partial Differential equations,  Functional analysis -- Instructional exposition (textbooks, tutorial papers, etc.).,  Functional analysis -- Inner product spaces and their generalizations, Hilbert spaces -- Inner product spaces and their generalizations, Hilbert spaces,  Functional analysis -- Miscellaneous applications of functional analysis -- Applications to differential and integral equations,  Partial differential equations -- Elliptic equations and systems -- Elliptic equations and systems,  Partial differential equations -- Spectral theory and eigenvalue problems -- Spectral theory and eigenvalue problems,  Differential equations, partial,  Functional analysis -- Instructional exposition (textbooks, tutorial papers, etc.)