The Theory of Functions of Real Variables PDF Download
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Author: Lawrence M Graves
Publisher: Courier Corporation
ISBN: 0486158136
Category : Mathematics
Languages : en
Pages : 361
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Book Description
This balanced introduction covers all fundamentals, from the real number system and point sets to set theory and metric spaces. Useful references to the literature conclude each chapter. 1956 edition.
Author: Lawrence M Graves
Publisher: Courier Corporation
ISBN: 0486158136
Category : Mathematics
Languages : en
Pages : 361
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Book Description
This balanced introduction covers all fundamentals, from the real number system and point sets to set theory and metric spaces. Useful references to the literature conclude each chapter. 1956 edition.
Author: Edgar Jerome Townsend
Publisher:
ISBN:
Category : Functions
Languages : en
Pages : 426
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Book Description
Author: Martin A. Moskowitz
Publisher: World Scientific
ISBN: 981429926X
Category : Mathematics
Languages : en
Pages : 733
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Book Description
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.
Author: N. Bourbaki
Publisher: Springer Science & Business Media
ISBN: 3642593151
Category : Mathematics
Languages : en
Pages : 343
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Book Description
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.
Author: Shmuel Kantorovitz
Publisher: Springer
ISBN: 3319279564
Category : Mathematics
Languages : en
Pages : 317
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Book Description
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.
Author: Ralph Cooper
Publisher:
ISBN:
Category : Functions of real variables
Languages : en
Pages : 248
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Book Description
Author: R. L. Jeffery
Publisher: Dover Publications
ISBN:
Category : Mathematics
Languages : en
Pages : 260
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Book Description
Author: Lawrence Murray Graves
Publisher:
ISBN:
Category : Functions
Languages : en
Pages : 222
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Book Description
Author: Ernest William Hobson
Publisher:
ISBN:
Category : Calculus
Languages : en
Pages : 760
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Book Description
Author: A. F. Timan
Publisher: Elsevier
ISBN: 1483184811
Category : Mathematics
Languages : en
Pages : 644
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Book Description
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.
