Functions Of A Real Variable

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Functions Of A Real Variable

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Author : N. Bourbaki
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-12-01

Functions Of A Real Variable written by N. Bourbaki and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-12-01 with Mathematics categories.

This book is an English translation of the last French edition of Bourbaki’s Fonctions d'une Variable Réelle. The first chapter is devoted to derivatives, Taylor expansions, the finite increments theorem, convex functions. In the second chapter, primitives and integrals (on arbitrary intervals) are studied, as well as their dependence with respect to parameters. Classical functions (exponential, logarithmic, circular and inverse circular) are investigated in the third chapter. The fourth chapter gives a thorough treatment of differential equations (existence and unicity properties of solutions, approximate solutions, dependence on parameters) and of systems of linear differential equations. The local study of functions (comparison relations, asymptotic expansions) is treated in chapter V, with an appendix on Hardy fields. The theory of generalized Taylor expansions and the Euler-MacLaurin formula are presented in the sixth chapter, and applied in the last one to thestudy of the Gamma function on the real line as well as on the complex plane. Although the topics of the book are mainly of an advanced undergraduate level, they are presented in the generality needed for more advanced purposes: functions allowed to take values in topological vector spaces, asymptotic expansions are treated on a filtered set equipped with a comparison scale, theorems on the dependence on parameters of differential equations are directly applicable to the study of flows of vector fields on differential manifolds, etc.

The Theory Of Functions Of A Real Variable

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Author : Ralph Lent Jeffery
language : en
Publisher:
Release Date : 1953

The Theory Of Functions Of A Real Variable written by Ralph Lent Jeffery and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1953 with Functions of real variables categories.

Elements Of Mathematics Functions Of A Real Variable

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Author : N. Bourbaki
language : en
Publisher: Springer Science & Business Media
Release Date : 2003-09-18

Elements Of Mathematics Functions Of A Real Variable written by N. Bourbaki and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2003-09-18 with Mathematics categories.

This is an English translation of Bourbaki’s Fonctions d'une Variable Réelle. Coverage includes: functions allowed to take values in topological vector spaces, asymptotic expansions are treated on a filtered set equipped with a comparison scale, theorems on the dependence on parameters of differential equations are directly applicable to the study of flows of vector fields on differential manifolds, etc.

Basic Analysis I

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Author : James K. Peterson
language : en
Publisher: CRC Press
Release Date : 2020-05-13

Basic Analysis I written by James K. Peterson and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-05-13 with Mathematics categories.

Basic Analysis I: Functions of a Real Variable is designed for students who have completed the usual calculus and ordinary differential equation sequence and a basic course in linear algebra. This is a critical course in the use of abstraction, but is just first volume in a sequence of courses which prepare students to become practicing scientists. This book is written with the aim of balancing the theory and abstraction with clear explanations and arguments, so that students who are from a variety of different areas can follow this text and use it profitably for self-study. It can also be used as a supplementary text for anyone whose work requires that they begin to assimilate more abstract mathematical concepts as part of their professional growth. Features Can be used as a traditional textbook as well as for self-study Suitable for undergraduate mathematics students, or for those in other disciplines requiring a solid grounding in abstraction Emphasises learning how to understand the consequences of assumptions using a variety of tools to provide the proofs of propositions

The Theory Of Functions Of A Real Variable And The Theory Of Fourier S Series

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Author : Ernest William Hobson
language : en
Publisher: CUP Archive
Release Date : 1927

The Theory Of Functions Of A Real Variable And The Theory Of Fourier S Series written by Ernest William Hobson and has been published by CUP Archive this book supported file pdf, txt, epub, kindle and other format this book has been release on 1927 with Fourier series categories.

Theory Of Functions Of A Real Variable

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Author : Shlomo Sternberg
language : en
Publisher: Orange Grove Texts Plus
Release Date : 2009-09-24

Theory Of Functions Of A Real Variable written by Shlomo Sternberg and has been published by Orange Grove Texts Plus this book supported file pdf, txt, epub, kindle and other format this book has been release on 2009-09-24 with categories.

This text is for a beginning graduate course in real variables and functional analysis. It assumes that the student has seen the basics of real variable theory and point set topology. Contents: 1) The topology of metric spaces. 2) Hilbert Spaces and Compact operators. 3) The Fourier Transform. 4) Measure theory. 5) The Lebesgue integral. 6) The Daniell integral. 7) Wiener measure, Brownian motion and white noise. 8) Haar measure. 9) Banach algebras and the spectral theorem. 10) The spectral theorem. 11) Stone's theorem. 12) More about the spectral theorem. 13) Scattering theory.

Several Real Variables

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Author : Shmuel Kantorovitz
language : en
Publisher: Springer
Release Date : 2016-02-09

Several Real Variables written by Shmuel Kantorovitz and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016-02-09 with Mathematics categories.

This undergraduate textbook is based on lectures given by the author on the differential and integral calculus of functions of several real variables. The book has a modern approach and includes topics such as: •The p-norms on vector space and their equivalence •The Weierstrass and Stone-Weierstrass approximation theorems •The differential as a linear functional; Jacobians, Hessians, and Taylor's theorem in several variables •The Implicit Function Theorem for a system of equations, proved via Banach’s Fixed Point Theorem •Applications to Ordinary Differential Equations •Line integrals and an introduction to surface integrals This book features numerous examples, detailed proofs, as well as exercises at the end of sections. Many of the exercises have detailed solutions, making the book suitable for self-study. Several Real Variables will be useful for undergraduate students in mathematics who have completed first courses in linear algebra and analysis of one real variable.

Functions Of Several Real Variables

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Author : Martin Moskowitz
language : en
Publisher: World Scientific Publishing Company
Release Date : 2011-04-29

Functions Of Several Real Variables written by Martin Moskowitz and has been published by World Scientific Publishing Company this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011-04-29 with Mathematics categories.

This book begins with the basics of the geometry and topology of Euclidean space and continues with the main topics in the theory of functions of several real variables including limits, continuity, differentiation and integration. All topics and in particular, differentiation and integration, are treated in depth and with mathematical rigor. The classical theorems of differentiation and integration such as the Inverse and Implicit Function theorems, Lagrange's multiplier rule, Fubini's theorem, the change of variables formula, Green's, Stokes' and Gauss' theorems are proved in detail and many of them with novel proofs. The authors develop the theory in a logical sequence building one result upon the other, enriching the development with numerous explanatory remarks and historical footnotes. A number of well chosen illustrative examples and counter-examples clarify matters and teach the reader how to apply these results and solve problems in mathematics, the other sciences and economics.Each of the chapters concludes with groups of exercises and problems, many of them with detailed solutions while others with hints or final answers. More advanced topics, such as Morse's lemma, Sard's theorem , the Weierstrass approximation theorem, the Fourier transform, Vector fields on spheres, Brouwer's fixed point theorem, Whitney's embedding theorem, Picard's theorem, and Hermite polynomials are discussed in stared sections.

Real Analysis

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Author : Miklós Laczkovich
language : en
Publisher: Springer
Release Date : 2015-10-08

Real Analysis written by Miklós Laczkovich and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015-10-08 with Mathematics categories.

Based on courses given at Eötvös Loránd University (Hungary) over the past 30 years, this introductory textbook develops the central concepts of the analysis of functions of one variable — systematically, with many examples and illustrations, and in a manner that builds upon, and sharpens, the student’s mathematical intuition. The book provides a solid grounding in the basics of logic and proofs, sets, and real numbers, in preparation for a study of the main topics: limits, continuity, rational functions and transcendental functions, differentiation, and integration. Numerous applications to other areas of mathematics, and to physics, are given, thereby demonstrating the practical scope and power of the theoretical concepts treated. In the spirit of learning-by-doing, Real Analysis includes more than 500 engaging exercises for the student keen on mastering the basics of analysis. The wealth of material, and modular organization, of the book make it adaptable as a textbook for courses of various levels; the hints and solutions provided for the more challenging exercises make it ideal for independent study.

A Brief Course In The Theory Of Functions Of A Real Variable

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Author : Boris Zakharovich Vulikh
language : en
Publisher:
Release Date : 1976

A Brief Course In The Theory Of Functions Of A Real Variable written by Boris Zakharovich Vulikh and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1976 with Mathematics categories.