Functions of a Real Variable

Functions of a Real Variable
Author: N. Bourbaki
Publisher: Springer Science & Business Media
Total Pages: 343
Release: 2013-12-01
Genre: Mathematics
ISBN: 3642593151
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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.

Functions of Real Variables

Functions of Real Variables
Author: Edgar Jerome Townsend
Publisher:
Total Pages: 430
Release: 1928
Genre: Functions
ISBN:
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Theory of Functions of a Real Variable (Teoria Functsiy Veshchestvennoy Peremennoy, Chapters I to IX)

Theory of Functions of a Real Variable (Teoria Functsiy Veshchestvennoy Peremennoy, Chapters I to IX)
Author: I P (Isidor Pavlovich) Natanson
Publisher: Hassell Street Press
Total Pages: 288
Release: 2021-09-09
Genre:
ISBN: 9781013315244
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This work has been selected by scholars as being culturally important and is part of the knowledge base of civilization as we know it. This work is in the public domain in the United States of America, and possibly other nations. Within the United States, you may freely copy and distribute this work, as no entity (individual or corporate) has a copyright on the body of the work. Scholars believe, and we concur, that this work is important enough to be preserved, reproduced, and made generally available to the public. To ensure a quality reading experience, this work has been proofread and republished using a format that seamlessly blends the original graphical elements with text in an easy-to-read typeface. We appreciate your support of the preservation process, and thank you for being an important part of keeping this knowledge alive and relevant.

Real Analysis

Real Analysis
Author: Miklós Laczkovich
Publisher: Springer
Total Pages: 486
Release: 2015-10-08
Genre: Mathematics
ISBN: 1493927663
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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.

Functions of Several Real Variables

Functions of Several Real Variables
Author: Martin A. Moskowitz
Publisher: World Scientific
Total Pages: 733
Release: 2011
Genre: Mathematics
ISBN: 981429926X
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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 are proved in detail and many of them with novel proofs. The authors develop the theory in a logical sequence building one theorem upon the other, enriching the development with numerous explanatory remarks and historical footnotes. A number of well chosen illustrative examples and counter-examples clarify the theory and teach the reader how to apply it to solve problems in mathematics and 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, Brouwer's fixed point theorem, Picard's theorem and the Weierstrass approximation theorem are discussed in stared sections.

Theory of Functions of a Real Variable

Theory of Functions of a Real Variable
Author: Shlomo Sternberg
Publisher: Orange Grove Texts Plus
Total Pages: 0
Release: 2009-09-24
Genre:
ISBN: 9781616100780
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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.

Theory of Approximation of Functions of a Real Variable

Theory of Approximation of Functions of a Real Variable
Author: A. F. Timan
Publisher: Elsevier
Total Pages: 644
Release: 2014-07-22
Genre: Mathematics
ISBN: 1483184811
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Theory of Approximation of Functions of a Real Variable discusses a number of fundamental parts of the modern theory of approximation of functions of a real variable. The material is grouped around the problem of the connection between the best approximation of functions to their structural properties. This text is composed of eight chapters that highlight the relationship between the various structural properties of real functions and the character of possible approximations to them by polynomials and other functions of simple construction. Each chapter concludes with a section containing various problems and theorems, which supplement the main text. The first chapters tackle the Weierstrass's theorem, the best approximation by polynomials on a finite segment, and some compact classes of functions and their structural properties. The subsequent chapters describe some properties of algebraic polynomials and transcendental integral functions of exponential type, as well as the direct theorems of the constructive theory of functions. These topics are followed by discussions of differential and constructive characteristics of converse theorems. The final chapters explore other theorems connecting the best approximations functions with their structural properties. These chapters also deal with the linear processes of approximation of functions by polynomials. The book is intended for post-graduate students and for mathematical students taking advanced courses, as well as to workers in the field of the theory of functions.