Beschreibung
Examines linear structures, the topology of metric spaces, and continuity in infinite dimensions, with detailed coverage at the graduate level Includes applications to geometry and differential equations, numerous beautiful illustrations, examples, exercises, historical notes, and comprehensive index May be used in graduate seminars and courses or as a reference text by mathematicians, physicists, and engineers
Inhaltsverzeichnis
Preface.- Part I: Linear Algebra.- Vectors, Matrices and Linear Systems.- Vector Spaces and Linear Maps.- Euclidean and Hermitian Spaces.- Self-Adjoint Operators.- Part II: Metrics and Topology.- Metric Spaces and Continuous Functions.- Compactness and Connectedness.- Curves.- Some Topics from the Topology of Rn.- Part III.- Continuity in Infinite-Dimensional Spaces.- Spaces of Continuous functions, Banach Spaces and Abstract Equations.- Hilbert Spaces, Dirichlet¿s Principle and Linear compact Operators.- Some Applications.- A. Mathematicians and Other Scientists.- B. Bibliographical Notes.- C. Index.
