Basic Methods of Linear Functional Analysis

" An introduction to the themes of mathematical analysis, this text is geared toward advanced undergraduate and graduate students. Topics include operators, function spaces, Hilbert spaces, and elemen

This introduction to the ideas and methods of linear functional analysis shows how familiar and useful concepts from finite-dimensional linear algebra can be extended or generalized to infinite-dimens

Functional analysis provides a concise conceptual framework for linear control theory. This self-contained text, geared toward engineering students, demonstrates the subject's unity. A wide range of p

This text is designed both for students of probability and stochastic processes, and for students of functional analysis. For the reader not familiar with functional analysis a detailed introduction to necessary notions and facts is provided. However, this is not a straight textbook in functional analysis; rather, it presents some chosen parts of functional analysis that can help understand ideas from probability and stochastic processes. The subjects range from basic Hilbert and Banach spaces, through weak topologies and Banach algebras, to the theory of semigroups of bounded linear operators. Numerous standard and non-standard examples and exercises make the book suitable as a course textbook or for self-study.

This text is a basic course in functional analysis for senior undergraduate and beginning postgraduate students. It aims at providing some insight into basic abstract analysis which is now the contextual language of much modern mathematics. Although it is assumed that the student will have familiarity with elementary real and complex analysis and linear algebra and have studied a course in the analysis of metric spaces, a knowledge of integration theory or general topology is not required. The theme of this text concerns structural properties of normed linear spaces in general, especially associated with dual spaces and continuous linear operators on normed linear spaces. But the implications of the general theory are illustrated with a great variety of example spaces.

This book provides a concise and meticulous introduction to functional analysis. Since the topic draws heavily on the interplay between the algebraic structure of a linear space and the distance struc

This self-contained introduction to numerical linear algebra provides a comprehensive, yet concise, overview of the subject. It includes standard material such as direct methods for solving linear systems and least-squares problems, error, stability and conditioning, basic iterative methods and the calculation of eigenvalues. Later chapters cover more advanced material, such as Krylov subspace methods, multigrid methods, domain decomposition methods, multipole expansions, hierarchical matrices and compressed sensing. The book provides rigorous mathematical proofs throughout, and gives algorithms in general-purpose language-independent form. Requiring only a solid knowledge in linear algebra and basic analysis, this book will be useful for applied mathematicians, engineers, computer scientists, and all those interested in efficiently solving linear problems.

This book provides a broad overview of the basic theory and methods of applied multivariate analysis. The presentation integrates both theory and practice including both the analysis of formal linear

The main goal of this book is to introduce readers to functional analysis methods, in particular, time dependent analysis, for reliability models. Understanding the concept of reliability is of key im

A unique introduction to the theory of linear operators on Hilbert space. The author presents the basic facts of functional analysis in a form suitable for engineers, scientists, and applied mathemati

In this volume, expert practitioners present a compilation of methods of functional data analysis (often referred to as “systems biology”) and its applications in drug discovery, medicine, and basic d

This book gives an introduction to Linear Functional Analysis, a synthesis of algebra, topology, and analysis. In addition to the basic theory it explains operator theory, distributions, Sobolev space

A comprehensive graduate textbook that introduces functional analysis with an emphasis on the theory of linear operators and its application to differential equations, integ

This concise text provides a gentle introduction to functional analysis. Chapters cover essential topics such as special spaces, normed spaces, linear functionals, and Hilbert spaces. Numerous example

Updated in its 3rd edition, Basic Methods of Policy Analysis and Planning presents quickly applied methods for analyzing and resolving planning and policy issues at state, regional, and urban levels.

A Polynomial Approach to Linear Algebra is a text which is heavily biased towards functional methods. In using the shift operator as a central object, it makes linear algebra a perfect introduction to

This book introduces the basic principles of functional analysis and areas of Banach space theory that are close to nonlinear analysis and topology. The text can be used in graduate courses or for ind

State-space methods form the basis of modern control theory. This graduate text is devoted to a description of these methods in the analysis of linear multi-input, multi-output dynamic systems. Following a chapter which sets out the basic concepts and definitions, state equations of finite dimensional systems, and their solution, are discussed in detail. The principles of time-domain and frequency-domain analysis are then presented, as are the properties and applications of the Z-transformation. Separate chapters deal with the controllability, observability, and stability of linear systems. A useful tutorial review of the key results from matrix theory and linear algebra is given in the appendix. The book includes several worked examples, and there are problems at the end of each chapter. It will be of great use to advanced undergraduate and graduate students of electrical or mechanical engineering taking courses in linear systems or control systems.

The second edition of this successful textbook, first published in 1970, retains the aims of the first, namely to provide a truly introductory course in functional analysis, but the opportunity has been taken to add more detail and worked examples. The main changes are complete revisons of the work on convex sets, metric and topological linear spaces, reflexivity and weak convergence. Additional material on the Weiner algebra of absolutely convergent Fourier series and on weak topologies is included. A final chapter includes elementary applications of functional analysis to differential and integral equations.

This book presents methods for the computational solution of some important problems of linear algebra: linear systems, linear least squares problems, eigenvalue problems, and linear programming probl

The techniques that can be used to solve non-linear problems are far different than those that are used to solve linear problems. Many courses in analysis and applied mathematics attack linear cases simply because they are easier to solve and do not require a large theoretical background in order to approach them. Professor Schechter's 2005 book is devoted to non-linear methods using the least background material possible and the simplest linear techniques. An understanding of the tools for solving non-linear problems is developed whilst demonstrating their application to problems in one dimension and then leading to higher dimensions. The reader is guided using simple exposition and proof, assuming a minimal set of pre-requisites. For completion, a set of appendices covering essential basics in functional analysis and metric spaces is included, making this ideal as an accompanying text on an upper-undergraduate or graduate course, or even for self-study.

Created by the founder of modern functional analysis, this is the first text on the theory of linear operators, written in 1932 and translated into English in 1987. In addition to the basics of the al

The rapid development of the theories of Volterra integral and functional equations has been strongly promoted by their applications in physics, engineering and biology. This text shows that the theory of Volterra equations exhibits a rich variety of features not present in the theory of ordinary differential equations. The book is divided into three parts. The first considers linear theory and the second deals with quasilinear equations and existence problems for nonlinear equations, giving some general asymptotic results. Part III is devoted to frequency domain methods in the study of nonlinear equations. The entire text analyses n-dimensional rather than scalar equations, giving greater generality and wider applicability and facilitating generalizations to infinite-dimensional spaces. The book is generally self-contained and assumes only a basic knowledge of analysis. The many exercises illustrate the development of the theory and its applications, making this book accessible to res

Functional analysis deals with infinite-dimensional spaces. Its results are among the greatest achievements of modern mathematics and it has wide-reaching applications to probability theory, statistics, economics, classical and quantum physics, chemistry, engineering, and pure mathematics. This book deals with measure theory and discrete aspects of functional analysis, including Fourier series, sequence spaces, matrix maps, and summability. Based on the author's extensive teaching experience, the text is accessible to advanced undergraduate and first-year graduate students. It can be used as a basis for a one-term course or for a one-year sequence, and is suitable for self-study for readers with an undergraduate-level understanding of real analysis and linear algebra. More than 750 exercises are included to help the reader test their understanding. Key background material is summarized in the Preliminaries.

Written in an easy-to-understand manner, this comprehensive textbook brings together both basic and advanced concepts of numerical methods in a single volume. Important topics including error analysis, nonlinear equations, systems of linear equations, interpolation and interpolation for Equal intervals and bivariate interpolation are discussed comprehensively. The textbook is written to cater to the needs of undergraduate students of mathematics, computer science, mechanical engineering, civil engineering and information technology for a course on numerical methods/numerical analysis. The text simplifies the understanding of the concepts through exercises and practical examples. Pedagogical features including solved examples and unsolved exercises are interspersed throughout the book for better understanding.

The Classical Stefan Problem: Basic Concepts, Modeling and Analysis with Quasi-Analytical Solutions and Methods, Second Edition provides the fundamental theory, concepts, modeling and analysis of the

Analysis Volume IV introduces the reader to functional analysis (integration, Hilbert spaces, harmonic analysis in group theory) and to the methods of the theory of modular functions (theta and L seri

Bayesian Data Analysis in Ecology Using Linear Models with R, BUGS, and STANintroduces the Bayesian and frequentist methods of conducting data analyses. The book provides the theoretical background in

The Functional Analysis of English is an introduction to the analysis and description of English, based on the principles of systemic functional linguistics. It sets out the tools and analytic techniq

Global Analysis of Nonlinear Dynamics collects chapters on recent developments in global analysis of non-linear dynamical systems with a particular emphasis on cell mapping methods developed by Profes

This text introduces students of mathematics, science, and technology to the methods of applied functional analysis and applied convexity. The three-part treatment consists of roots and extremal probl

The book contains the methods and bases of functional analysis that are directly adjacent to the problems of numerical mathematics and its applications; they are what one needs for the understand- ing

This functional needs analysis assesses the ability of current U.S. Air Force assets to deliver the airlift capabilities identified in the functional area analysis.

This book expounds the theory of non-linear vibrations, a topic of great interest at present because of its many applications to important fields in physics and engineering. After introducing chapters giving the basic techniques for the study of non-linear systems the authors develop in detail the theory of selected topics encountered in their own work, presenting original material, approaches and results of analysis, and providing illustrations of useful applications.

Prenter introduces the numerical solution of boundary value problems by variational methods to serious students of engineering and mathematics who are familiar with basic applied linear algebra and sl

Hageman, with a large electric company, and Young (numerical analysis, U. of Texas-Austin) explain how to use iterative methods to solve large, sparse systems of linear algebraic equations. They focus

This book deals primarily with the numerical solution of linear systems of equations by iterative methods. The first part of the book is intended to serve as a textbook for a numerical linear algebra course. The material assumes the reader has a basic knowledge of linear algebra, such as set theory and matrix algebra, however it is demanding for students who are not afraid of theory. To assist the reader, the more difficult passages have been marked, the definitions for each chapter are collected at the beginning of the chapter, and numerous exercises are included throughout the text. The second part of the book serves as a monograph introducing recent results in the iterative solution of linear systems, mainly using preconditioned conjugate gradient methods. This book should be a valuable resource for students and researchers alike wishing to learn more about iterative methods.

Classic exposition of modern theories of differentiation and integration and the principal problems and methods of handling integral equations and linear functionals and transformations. Topics includ

In the past few decades, methods of linear algebra have become central to economic analysis, replacing older tools such as the calculus. David Gale has provided the first complete and lucid treatment

Linear and Non-Linear Stability Analysis in Boiling Water Reactors: The Design of Real-Time Stability Monitors presents a thorough analysis of the most innovative BWR reactors and stability phenomena