Mathematical Methods V 1 Linear Algebra Normed Spaces Distributions Integration
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Mathematical Methods
Author | : Jacob Korevaar |
Publisher | : Elsevier |
Total Pages | : 518 |
Release | : 2014-05-12 |
Genre | : Mathematics |
ISBN | : 1483270742 |
Mathematical Methods, Volume I: Linear Algebra, Normed Spaces, Distributions, Integration focuses on advanced mathematical tools used in applications and the basic concepts of algebra, normed spaces, integration, and distributions. The publication first offers information on algebraic theory of vector spaces and introduction to functional analysis. Discussions focus on linear transformations and functionals, rectangular matrices, systems of linear equations, eigenvalue problems, use of eigenvectors and generalized eigenvectors in the representation of linear operators, metric and normed vector spaces, and delta sequences and convergence and approximation. The text then examines the Lebesgue integral, including approximation of integrable functions and applications, integration of sequences and series, functions of bounded variation and the Stieltjes integral, and multiple integrals. Curves and integrals, holomorphic functions and integrals in the complex plane, and multiple integrals are also discussed. The book is a valuable reference for students in the physical sciences, mathematics students interested in applications, and mathematically oriented engineering students.
Measure Theory
Author | : Vladimir I. Bogachev |
Publisher | : Springer Science & Business Media |
Total Pages | : 1075 |
Release | : 2007-01-15 |
Genre | : Mathematics |
ISBN | : 3540345140 |
This book giving an exposition of the foundations of modern measure theory offers three levels of presentation: a standard university graduate course, an advanced study containing some complements to the basic course, and, finally, more specialized topics partly covered by more than 850 exercises with detailed hints and references. Bibliographical comments and an extensive bibliography with 2000 works covering more than a century are provided.
Real and Functional Analysis
Author | : Vladimir I. Bogachev |
Publisher | : Springer Nature |
Total Pages | : 586 |
Release | : 2020-02-25 |
Genre | : Mathematics |
ISBN | : 3030382192 |
This book is based on lectures given at "Mekhmat", the Department of Mechanics and Mathematics at Moscow State University, one of the top mathematical departments worldwide, with a rich tradition of teaching functional analysis. Featuring an advanced course on real and functional analysis, the book presents not only core material traditionally included in university courses of different levels, but also a survey of the most important results of a more subtle nature, which cannot be considered basic but which are useful for applications. Further, it includes several hundred exercises of varying difficulty with tips and references. The book is intended for graduate and PhD students studying real and functional analysis as well as mathematicians and physicists whose research is related to functional analysis.
Optimization by Vector Space Methods
Author | : David G. Luenberger |
Publisher | : John Wiley & Sons |
Total Pages | : 348 |
Release | : 1997-01-23 |
Genre | : Technology & Engineering |
ISBN | : 9780471181170 |
Engineers must make decisions regarding the distribution of expensive resources in a manner that will be economically beneficial. This problem can be realistically formulated and logically analyzed with optimization theory. This book shows engineers how to use optimization theory to solve complex problems. Unifies the large field of optimization with a few geometric principles. Covers functional analysis with a minimum of mathematics. Contains problems that relate to the applications in the book.