advanced calculus an introduction to classical analysis dover books on mathematics

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Advanced Calculus

Author : Louis Brand
ISBN : UCAL:B4407461
Genre : Calculus
File Size : 29. 68 MB
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Advanced Calculus

Author : Louis Brand
ISBN : 9780486157993
Genre : Mathematics
File Size : 59. 88 MB
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A course in analysis that focuses on the functions of a real variable, this text introduces the basic concepts in their simplest setting and illustrates its teachings with numerous examples, theorems, and proofs. 1955 edition.

Advanced Calculus

Author : Avner Friedman
ISBN : 9780486137865
Genre : Mathematics
File Size : 47. 89 MB
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Intended for students who have already completed a one-year course in elementary calculus, this two-part treatment advances from functions of one variable to those of several variables. Solutions. 1971 edition.

Advanced Calculus

Author : S Zaidman
ISBN : 9789814498838
Genre : Mathematics
File Size : 75. 72 MB
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This book is an introduction to mathematical analysis (i.e real analysis) at a fairly elementary level. A great (unusual) emphasis is given to the construction of rational and then of real numbers, using the method of equivalence classes and of Cauchy sequences. The text includes the usual presentation of: sequences of real numbers, infinite numerical series, continuous functions, derivatives and Riemann-Darboux integration. There are also two “special” sections: on convex functions and on metric spaces, as well as an elementary appendix on Logic, Set Theory and Functions. We insist on a rigorous presentation throughout in the framework of the classical, standard, analysis. Contents: NumbersSequences of Real NumbersInfinite Numerical SeriesContinuous FunctionsDerivativesConvex FunctionsMetric SpacesIntegrationIndexIndex of NotationsAppendix (Logic, Set Theory and Functions)Bibliography Readership: Undergraduate students of calculus and real analysis. keywords:Numbers;Sequences;Series;Continuous Functions;Derivatives;Convex Functions;Metric Spaces;Integration

A Course In Advanced Calculus

Author : Robert S. Borden
ISBN : 9780486150383
Genre : Mathematics
File Size : 30. 16 MB
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An excellent undergraduate text examines sets and structures, limit and continuity in En, measure and integration, differentiable mappings, sequences and series, applications of improper integrals, more. Problems with tips and solutions for some.

Introduction To Analysis

Author : Maxwell Rosenlicht
ISBN : 0486650383
Genre : Mathematics
File Size : 45. 8 MB
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Written for junior and senior undergraduates, this remarkably clear and accessible treatment covers set theory, the real number system, metric spaces, continuous functions, Riemann integration, multiple integrals, and more. Rigorous and carefully presented, the text assumes a year of calculus and features problems at the end of each chapter. 1968 edition.

Intermediate Real Analysis

Author : E. Fischer
ISBN : 9781461394815
Genre : Mathematics
File Size : 26. 62 MB
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There are a great deal of books on introductory analysis in print today, many written by mathematicians of the first rank. The publication of another such book therefore warrants a defense. I have taught analysis for many years and have used a variety of texts during this time. These books were of excellent quality mathematically but did not satisfy the needs of the students I was teaching. They were written for mathematicians but not for those who were first aspiring to attain that status. The desire to fill this gap gave rise to the writing of this book. This book is intended to serve as a text for an introductory course in analysis. Its readers will most likely be mathematics, science, or engineering majors undertaking the last quarter of their undergraduate education. The aim of a first course in analysis is to provide the student with a sound foundation for analysis, to familiarize him with the kind of careful thinking used in advanced mathematics, and to provide him with tools for further work in it. The typical student we are dealing with has completed a three-semester calculus course and possibly an introductory course in differential equations. He may even have been exposed to a semester or two of modern algebra. All this time his training has most likely been intuitive with heuristics taking the place of proof. This may have been appropriate for that stage of his development.

Advanced Calculus Of Several Variables

Author : C. H. Edwards
ISBN : 9781483268057
Genre : Mathematics
File Size : 73. 72 MB
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Advanced Calculus of Several Variables provides a conceptual treatment of multivariable calculus. This book emphasizes the interplay of geometry, analysis through linear algebra, and approximation of nonlinear mappings by linear ones. The classical applications and computational methods that are responsible for much of the interest and importance of calculus are also considered. This text is organized into six chapters. Chapter I deals with linear algebra and geometry of Euclidean n-space Rn. The multivariable differential calculus is treated in Chapters II and III, while multivariable integral calculus is covered in Chapters IV and V. The last chapter is devoted to venerable problems of the calculus of variations. This publication is intended for students who have completed a standard introductory calculus sequence.

Advanced Calculus

Author : Leonard F. Richardson
ISBN : UCSC:32106019495701
Genre : Mathematics
File Size : 30. 24 MB
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Features an introduction to advanced calculus and highlights its inherent concepts from linear algebra "Advanced Calculus" reflects the unifying role of linear algebra in an effort to smooth readers' transition to advanced mathematics. The book fosters the development of complete theorem-proving skills through abundant exercises while also promoting a sound approach to the study. The traditional theorems of elementary differential and integral calculus are rigorously established, presenting the foundations of calculus in a way that reorients thinking toward modern analysis. Following an introduction dedicated to writing proofs, the book is divided into three parts: Part One explores foundational one-variable calculus topics from the viewpoint of linear spaces, norms, completeness, and linear functionals. Part Two covers Fourier series and Stieltjes integration, which are advanced one-variable topics. Part Three is dedicated to multivariable advanced calculus, including inverse and implicit function theorems and Jacobian theorems for multiple integrals. Numerous exercises guide readers through the creation of their own proofs, and they also put newly learned methods into practice. In addition, a "Test Yourself" section at the end of each chapter consists of short questions that reinforce the understanding of basic concepts and theorems. The answers to these questions and other selected exercises can be found at the end of the book along with an appendix that outlines key terms and symbols from set theory. Guiding readers from the study of the topology of the real line to the beginning theorems and concepts of graduate analysis, "Advanced Calculus" is an ideal text for courses in advanced calculus and introductory analysis at the upper-undergraduate and beginning-graduate levels. It also serves as a valuable reference for engineers, scientists, and mathematicians.

A Treatise On Advanced Calculus

Author : Philip Franklin
ISBN : 9780486807072
Genre : Mathematics
File Size : 43. 74 MB
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This classic offers a comprehensive logical treatment that concentrates on theory rather than on techniques and applications, providing students with a substantial base for graduate work in physics. 1940 edition.

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