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
Page : 361 pages
File Size : 24,78 MB
Release : 2012-01-27
Category : Mathematics
ISBN : 0486158136
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 :
Page : 430 pages
File Size : 17,1 MB
Release : 1928
Category : Functions
ISBN :
Author : Martin Moskowitz
Publisher : World Scientific Publishing Company
Page : 732 pages
File Size : 13,4 MB
Release : 2011-04-29
Category : Mathematics
ISBN : 9813100915
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.
Author : N. Bourbaki
Publisher : Springer Science & Business Media
Page : 343 pages
File Size : 21,80 MB
Release : 2013-12-01
Category : Mathematics
ISBN : 3642593151
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 : Martin A. Moskowitz
Publisher : World Scientific
Page : 733 pages
File Size : 46,85 MB
Release : 2011
Category : Mathematics
ISBN : 981429926X
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 : Shmuel Kantorovitz
Publisher : Springer
Page : 317 pages
File Size : 27,94 MB
Release : 2016-02-09
Category : Mathematics
ISBN : 3319279564
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 : R. L. Jeffery
Publisher : Dover Publications
Page : 260 pages
File Size : 10,59 MB
Release : 1985
Category : Mathematics
ISBN :
Author : John Meigs Hubbell Olmsted
Publisher :
Page : 646 pages
File Size : 42,21 MB
Release : 1959
Category : Functions of real variables
ISBN :
Author : Ralph Cooper
Publisher :
Page : 248 pages
File Size : 45,62 MB
Release : 1966
Category : Functions of real variables
ISBN :
Author : Lawrence Murray Graves
Publisher :
Page : 432 pages
File Size : 27,8 MB
Release : 1956
Category : Functions of real variables
ISBN :