Applied Functional Analysis (Textbooks in Mathematics)

Applied Functional Analysis, Third Edition provides a solid mathematical foundation for the subject. It motivates students to study functional analysis by providing many contemporary applications and examples drawn from mechanics and science. This well-received textbook starts with a thorough introduction to modern mathematics before continuing with detailed coverage of linear algebra, Lebesque measure and integration theory, plus topology with metric spaces. The final two chapters provides readers with an in-depth look at the theory of Banach and Hilbert spaces before concluding with a brief introduction to Spectral Theory. The Third Edition is more accessible and promotes interest and motivation among students to prepare them for studying the mathematical aspects of numerical analysis and the mathematical theory of finite elements.

Science & Math

Oden, J. Tinsley

Demkowicz, Leszek

Mathematics

Chapman and Hall/CRC

Through numerous illustrative examples and comments, Applied Functional Analysis, Second Edition demonstrates the rigor of logic and systematic, mathematical thinking. It presents the mathematical foundations that lead to classical results in functional analysis. More specifically, the text prepares students to learn the variational theory of partial differential equations, distributions and Sobolev spaces, and numerical analysis with an emphasis on finite element methods. While retaining the structure of its best-selling predecessor, this second edition includes revisions of many original examples, along with new examples that often reflect the authors’ own vast research experiences and perspectives. This edition also provides many more exercises as well as a solutions manual for qualifying instructors. Each chapter begins with an extensive introduction and concludes with a summary and historical comments that frequently refer to other sources. New to the Second Edition <ul>
<li>Completely revised section on lim sup and lim inf </li> <li>New discussions of connected sets, probability, Bayesian statistical inference, and the generalized (integral) Minkowski inequality</li> <li>New sections on elements of multilinear algebra and determinants, the singular value decomposition theorem, the Cauchy principal value, and Hadamard finite part integrals</li> <li>New example of a Lebesgue non-measurable set</li> </ul> Ideal for a two-semester course, this proven textbook teaches students how to prove theorems and prepares them for further study of more advanced mathematical topics. It helps them succeed in formulating research questions in a mathematically rigorous way.

Applied Functional Analysis, Second Edition (Textbooks in Mathematics)

Applied Functional Analysis, Third Edition provides a solid mathematical foundation for the subject. It motivates students to study functional analysis by providing many contemporary applications and examples drawn from mechanics and science. This well-received textbook starts with a thorough introduction to modern mathematics before continuing with detailed coverage of linear algebra, Lebesque measure and integration theory, plus topology with metric spaces. The final two chapters provides readers with an in-depth look at the theory of Banach and Hilbert spaces before concluding with a brief introduction to Spectral Theory. The Third Edition is more accessible and promotes interest and motivation among students to prepare them for studying the mathematical aspects of numerical analysis and the mathematical theory of finite elements.

Offering the only existing finite element (FE) codes for Maxwell equations that support hp refinements on irregular meshes, Computing with hp-ADAPTIVE FINITE ELEMENTS: Volume 1. One- and Two-Dimensional Elliptic and Maxwell Problems presents 1D and 2D codes and automatic hp adaptivity. This self-contained source discusses the theory and implementation of hp-adaptive FE methods, focusing on projection-based interpolation and the corresponding hp-adaptive strategy. The book is split into three parts, progressing from simple to more advanced problems. Part I examines the hp elements for the standard 1D model elliptic problem. The author develops the variational formulation and explains the construction of FE basis functions. The book then introduces the 1D code (1Dhp) and automatic hp adaptivity. This first part ends with a study of a 1D wave propagation problem. In Part II, the book proceeds to 2D elliptic problems, discussing two model problems that are slightly beyond standard-level examples: 3D axisymmetric antenna problem for Maxwell equations (example of a complex-valued, indefinite problem) and 2D elasticity (example of an elliptic system). The author concludes with a presentation on infinite elements - one of the possible tools to solve exterior boundary-value problems. Part III focuses on 2D time-harmonic Maxwell equations. The book explains the construction of the hp edge elements and the fundamental de Rham diagram for the whole family of hp discretizations. Next, it explores the differences between the elliptic and Maxwell versions of the 2D code, including automatic hp adaptivity. Finally, the book presents 2D exterior (radiation and scattering) problems and sample solutions using coupled hp finite/infinite elements. In Computing with hp-ADAPTIVE FINITE ELEMENTS, the information provided, including many unpublished details, aids in solving elliptic and Maxwell problems.

Computing with Hp-Adaptive Finite Elements, Vol. 1: One and Two Dimensional Elliptic and Maxwell Problems

Computers & Technology

Computer Science

See the best price to sell, buy, or rent books by Demkowicz, Leszek. BookScouter helps to compare book prices from 25+ online bookstores and 30+ buyback vendors with a single search.

Books by Demkowicz, Leszek

See the best price to sell, buy, or rent books by Demkowicz, Leszek. BookScouter helps to compare book prices from 25+ online bookstores and 30+ buyback vendors with a single search.

Applied Functional Analysis (Textbooks in Mathematics)

Applied Functional Analysis, Second Edition (Textbooks in Mathematics)

Applied Functional Analysis (Textbooks in Mathematics)

Computing with Hp-Adaptive Finite Elements, Vol. 1: One and Two Dimensional Elliptic and Maxwell Problems