Functional Analysis Tools for Practical Use in Sciences and Engineering
Title | Functional Analysis Tools for Practical Use in Sciences and Engineering PDF eBook |
Author | Carlos A. de Moura |
Publisher | |
Pages | 0 |
Release | 2022 |
Genre | |
ISBN | 9783031105999 |
This textbook describes selected topics in functional analysis as powerful tools of immediate use in many fields within applied mathematics, physics and engineering. It follows a very reader-friendly structure, with the presentation and the level of exposition especially tailored to those who need functional analysis but don't have a strong background in this branch of mathematics. For every tool, this work emphasizes the motivation, the justification for the choices made, and the right way to employ the techniques. Proofs appear only when necessary for the safe use of the results. The book gently starts with a road map to guide reading. A subsequent chapter recalls definitions and notation for abstract spaces and some function spaces, while Chapter 3 enters dual spaces. Tools from Chapters 2 and 3 find use in Chapter 4, which introduces distributions. The Linear Functional Analysis basic triplet makes up Chapter 5, followed by Chapter 6, which introduces the concept of compactness. Chapter 7 brings a generalization of the concept of derivative for functions defined in normed spaces, while Chapter 8 discusses basic results about Hilbert spaces that are paramount to numerical approximations. The last chapter brings remarks to recent bibliographical items. Elementary examples included throughout the chapters foster understanding and self-study. By making key, complex topics more accessible, this book serves as a valuable resource for researchers, students, and practitioners alike that need to rely on solid functional analysis but don't need to delve deep into the underlying theory.
Functional Analysis Tools for Practical Use in Sciences and Engineering
Title | Functional Analysis Tools for Practical Use in Sciences and Engineering PDF eBook |
Author | Carlos A. de Moura |
Publisher | Springer Nature |
Pages | 223 |
Release | 2022-10-13 |
Genre | Mathematics |
ISBN | 3031105982 |
This textbook describes selected topics in functional analysis as powerful tools of immediate use in many fields within applied mathematics, physics and engineering. It follows a very reader-friendly structure, with the presentation and the level of exposition especially tailored to those who need functional analysis but don’t have a strong background in this branch of mathematics. For every tool, this work emphasizes the motivation, the justification for the choices made, and the right way to employ the techniques. Proofs appear only when necessary for the safe use of the results. The book gently starts with a road map to guide reading. A subsequent chapter recalls definitions and notation for abstract spaces and some function spaces, while Chapter 3 enters dual spaces. Tools from Chapters 2 and 3 find use in Chapter 4, which introduces distributions. The Linear Functional Analysis basic triplet makes up Chapter 5, followed by Chapter 6, which introduces the concept of compactness. Chapter 7 brings a generalization of the concept of derivative for functions defined in normed spaces, while Chapter 8 discusses basic results about Hilbert spaces that are paramount to numerical approximations. The last chapter brings remarks to recent bibliographical items. Elementary examples included throughout the chapters foster understanding and self-study. By making key, complex topics more accessible, this book serves as a valuable resource for researchers, students, and practitioners alike that need to rely on solid functional analysis but don’t need to delve deep into the underlying theory.
A Functional Analysis Framework for Modeling, Estimation and Control in Science and Engineering
Title | A Functional Analysis Framework for Modeling, Estimation and Control in Science and Engineering PDF eBook |
Author | H.T. Banks |
Publisher | CRC Press |
Pages | 280 |
Release | 2012-06-18 |
Genre | Mathematics |
ISBN | 1439880840 |
A Modern Framework Based on Time-Tested MaterialA Functional Analysis Framework for Modeling, Estimation and Control in Science and Engineering presents functional analysis as a tool for understanding and treating distributed parameter systems. Drawing on his extensive research and teaching from the past 20 years, the author explains how functional
Applications of Functional Analysis in Engineering
Title | Applications of Functional Analysis in Engineering PDF eBook |
Author | J. Nowinski |
Publisher | |
Pages | 324 |
Release | 1981-05-01 |
Genre | |
ISBN | 9781468439274 |
Applications of Functional Analysis in Engineering
Title | Applications of Functional Analysis in Engineering PDF eBook |
Author | J. Nowinski |
Publisher | Springer Science & Business Media |
Pages | 309 |
Release | 2013-03-09 |
Genre | Science |
ISBN | 146843926X |
Functional analysis owes its OrIgms to the discovery of certain striking analogies between apparently distinct disciplines of mathematics such as analysis, algebra, and geometry. At the turn of the nineteenth century, a number of observations, made sporadically over the preceding years, began to inspire systematic investigations into the common features of these three disciplines, which have developed rather independently of each other for so long. It was found that many concepts of this triad-analysis, algebra, geometry-could be incorporated into a single, but considerably more abstract, new discipline which came to be called functional analysis. In this way, many aspects of analysis and algebra acquired unexpected and pro found geometric meaning, while geometric methods inspired new lines of approach in analysis and algebra. A first significant step toward the unification and generalization of algebra, analysis, and geometry was taken by Hilbert in 1906, who studied the collection, later called 1 , composed of infinite sequences x = Xb X 2, ... , 2 X , ... , of numbers satisfying the condition that the sum Ik"= 1 X 2 converges. k k The collection 12 became a prototype of the class of collections known today as Hilbert spaces.
Functional Analysis for Physics and Engineering
Title | Functional Analysis for Physics and Engineering PDF eBook |
Author | Hiroyuki Shima |
Publisher | CRC Press |
Pages | 282 |
Release | 2016-01-05 |
Genre | Mathematics |
ISBN | 1482223031 |
This book provides an introduction to functional analysis for non-experts in mathematics. As such, it is distinct from most other books on the subject that are intended for mathematicians. Concepts are explained concisely with visual materials, making it accessible for those unfamiliar with graduate-level mathematics. Topics include topology, vecto
Functional Analysis with Applications
Title | Functional Analysis with Applications PDF eBook |
Author | Svetlin G. Georgiev |
Publisher | Walter de Gruyter GmbH & Co KG |
Pages | 402 |
Release | 2019-06-17 |
Genre | Mathematics |
ISBN | 3110657724 |
This book on functional analysis covers all the basics of the subject (normed, Banach and Hilbert spaces, Lebesgue integration and spaces, linear operators and functionals, compact and self-adjoint operators, small parameters, fixed point theory) with a strong focus on examples, exercises and practical problems, thus making it ideal as course material but also as a reference for self-study.