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Mathematical Analysis : Linear and Metric Structures and Continuity /

By: Giaquinta, Mariano [author.].
Contributor(s): Modica, Giuseppe [author.] | SpringerLink (Online service).
Material type: materialTypeLabelBookPublisher: Boston, MA : Birkhäuser Boston, 2007.Description: XX, 466 p. online resource.Content type: text Media type: computer Carrier type: online resourceISBN: 9780817645144.Subject(s): Mathematics | Mathematical analysis | Analysis (Mathematics) | Functional analysis | Differential equations | Functions of real variables | Applied mathematics | Engineering mathematics | Topology | Mathematics | Analysis | Ordinary Differential Equations | Topology | Functional Analysis | Real Functions | Applications of MathematicsDDC classification: 515 Online resources: Click here to access online
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.
In: Springer eBooksSummary: 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 matrices and the spectral theorem for self-adjoint and normal operators. The second part examines the role of general topology in the context of metric spaces and includes the notions of homotopy and degree. The third and final part is a discussion on Banach spaces of continuous functions, Hilbert spaces and the spectral theory of compact operators. Mathematical Analysis: Linear and Metric Structures and Continuity motivates the study of linear and metric structures with examples, observations, exercises, and illustrations. It may be used in the classroom setting or for self-study by advanced undergraduate and graduate students and as a valuable reference for researchers in mathematics, physics, and engineering. Other books recently published by the authors include: Mathematical Analysis: Functions of One Variable, and Mathematical Analysis: Approximation and Discrete Processes. This book builds upon the discussion in these books to provide the reader with a strong foundation in modern-day analysis.
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Item type Current location Call number Status Date due Barcode Item holds
E books E books PK Kelkar Library, IIT Kanpur
Available EBK9227
Total holds: 0

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.

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 matrices and the spectral theorem for self-adjoint and normal operators. The second part examines the role of general topology in the context of metric spaces and includes the notions of homotopy and degree. The third and final part is a discussion on Banach spaces of continuous functions, Hilbert spaces and the spectral theory of compact operators. Mathematical Analysis: Linear and Metric Structures and Continuity motivates the study of linear and metric structures with examples, observations, exercises, and illustrations. It may be used in the classroom setting or for self-study by advanced undergraduate and graduate students and as a valuable reference for researchers in mathematics, physics, and engineering. Other books recently published by the authors include: Mathematical Analysis: Functions of One Variable, and Mathematical Analysis: Approximation and Discrete Processes. This book builds upon the discussion in these books to provide the reader with a strong foundation in modern-day analysis.

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