Mathematical Analysis Linear and Metric Structures and Continuity /

• Main Authors: Giaquinta, Mariano (Author), Modica, Giuseppe (Author)
• Corporate Author: SpringerLink (Online service)
• Format: Electronic eBook
• Language: English
• Published: Boston, MA : Birkhäuser Boston, 2007.
• Subjects: Mathematics.; Mathematical analysis.; Analysis (Mathematics).; Functional analysis.; Differential equations.; Functions of real variables.; Applied mathematics.; Engineering mathematics.; Topology.; Analysis.; Ordinary Differential Equations.; Functional Analysis.; Real Functions.; Applications of Mathematics.

This self-contained work on linear and metric structures focuses on studying continuity and its applications to finite- and infinite-dimensional spaces. The book is divided into three parts. The first part introduces the basic ideas of linear and metric spaces, including the Jordan canonical form of...

Table of Contents:

• Linear Algebra
• Vectors, Matrices and Linear Systems
• Vector Spaces and Linear Maps
• Euclidean and Hermitian Spaces
• Self-Adjoint Operators
• Metrics and Topology
• Metric Spaces and Continuous Functions
• Compactness and Connectedness
• Curves
• Some Topics from the Topology of ?n
• 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.