Elementary Analysis

The Theory of Calculus

Author: Kenneth A. Ross

Publisher: Springer Science & Business Media

ISBN: 1461462711

Category: Mathematics

Page: 412

View: 6396

For over three decades, this best-selling classic has been used by thousands of students in the United States and abroad as a must-have textbook for a transitional course from calculus to analysis. It has proven to be very useful for mathematics majors who have no previous experience with rigorous proofs. Its friendly style unlocks the mystery of writing proofs, while carefully examining the theoretical basis for calculus. Proofs are given in full, and the large number of well-chosen examples and exercises range from routine to challenging. The second edition preserves the book’s clear and concise style, illuminating discussions, and simple, well-motivated proofs. New topics include material on the irrationality of pi, the Baire category theorem, Newton's method and the secant method, and continuous nowhere-differentiable functions.

Elementary Analysis

The Theory of Calculus

Author: Kenneth A. Ross

Publisher: Springer Science & Business Media

ISBN: 1475739710

Category: Mathematics

Page: 264

View: 4093

Designed for students having no previous experience with rigorous proofs, this text can be used immediately after standard calculus courses. It is highly recommended for anyone planning to study advanced analysis, as well as for future secondary school teachers. A limited number of concepts involving the real line and functions on the real line are studied, while many abstract ideas, such as metric spaces and ordered systems, are avoided completely. A thorough treatment of sequences of numbers is used as a basis for studying standard calculus topics, and optional sections invite students to study such topics as metric spaces and Riemann-Stieltjes integrals.

Elementary Analysis

The Theory of Calculus

Author: Kenneth A. Ross

Publisher: Springer Science & Business Media

ISBN: 9780387904597

Category: Mathematics

Page: 264

View: 2851

Designed for students having no previous experience with rigorous proofs, this text on analysis is intended to follow a standard calculus course. It will be useful for students planning to continue in mathematics (with, for example, complex variables, differential equations, numerical analysis, multivariable calculus, or statistics), as well as for future secondary school teachers.

Elementary Classical Analysis

Author: Jerrold E. Marsden,Michael J. Hoffman,University Michael J Hoffman

Publisher: Macmillan

ISBN: 9780716721055

Category: Mathematics

Page: 738

View: 3371

Designed for courses in advanced calculus and introductory real analysis, the second edition of Elementary Classical Analysis strikes a careful and thoughtful balance between pure and applied mathematics, with the emphasis on techniques important to classical analysis, without vector calculus or complex analysis. As such, it’s a perfect teaching and learning resource for mathematics undergraduate courses in classical analysis. The book includes detailed coverage of the foundations of the real number system and focuses primarily on analysis in Euclidean space with a view towards application. As well as being suitable for students taking pure mathematics, it can also be used by students taking engineering and physical science courses. There’s now even more material on variable calculus, expanding the textbook’s already considerable coverage of the subject.

CounterExamples

From Elementary Calculus to the Beginnings of Analysis

Author: Andrei Bourchtein,Ludmila Bourchtein

Publisher: CRC Press

ISBN: 1482246678

Category: Mathematics

Page: 362

View: 6724

This book provides a one-semester undergraduate introduction to counterexamples in calculus and analysis. It helps engineering, natural sciences, and mathematics students tackle commonly made erroneous conjectures. The book encourages students to think critically and analytically, and helps to reveal common errors in many examples. In this book, the authors present an overview of important concepts and results in calculus and real analysis by considering false statements, which may appear to be true at first glance. The book covers topics concerning the functions of real variables, starting with elementary properties, moving to limits and continuity, and then to differentiation and integration. The first part of the book describes single-variable functions, while the second part covers the functions of two variables. The many examples presented throughout the book typically start at a very basic level and become more complex during the development of exposition. At the end of each chapter, supplementary exercises of different levels of complexity are provided, the most difficult of them with a hint to the solution. This book is intended for students who are interested in developing a deeper understanding of the topics of calculus. The gathered counterexamples may also be used by calculus instructors in their classes.

Elementary Real Analysis, Second Edition

Author: Brian S. Thomson,Judith B. Bruckner,Andrew M. Bruckner

Publisher: ClassicalRealAnalysis.com

ISBN: 143484367X

Category: Mathematics

Page: 638

View: 5184

This is the second edition of the text Elementary Real Analysis originally published by Prentice Hall (Pearson) in 2001.Chapter 1. Real NumbersChapter 2. SequencesChapter 3. Infinite sumsChapter 4. Sets of real numbersChapter 5. Continuous functionsChapter 6. More on continuous functions and setsChapter 7. Differentiation Chapter 8. The IntegralChapter 9. Sequences and series of functionsChapter 10. Power seriesChapter 11. Euclidean Space R^nChapter 12. Differentiation on R^nChapter 13. Metric Spaces

Introductory Real Analysis

Author: A. N. Kolmogorov,S. V. Fomin

Publisher: Courier Corporation

ISBN: 0486134741

Category: Mathematics

Page: 416

View: 699

Comprehensive, elementary introduction to real and functional analysis covers basic concepts and introductory principles in set theory, metric spaces, topological and linear spaces, linear functionals and linear operators, more. 1970 edition.

Trace Elemental Analysis of Metals

Methods and Techniques

Author: ThomasR. Dulski

Publisher: Routledge

ISBN: 135140735X

Category: Technology & Engineering

Page: 592

View: 8787

This work details minor, trace and ultratrace methods; addresses the essential stages that precede measurement; and highlights the measurement systems most likey to be used by the pragmatic analyst. It features key material on inclusion and phase isolation. The book is designed to provide useful maps and signposts for metals analysts who must verify that stringent trace level compositional specifications have been met.

Elementary Functional Analysis

Author: Charles Swartz

Publisher: World Scientific Publishing Company

ISBN: 9813107529

Category: Science

Page: 192

View: 3086

This text is an introduction to functional analysis which requires readers to have a minimal background in linear algebra and real analysis at the first-year graduate level. Prerequisite knowledge of general topology or Lebesgue integration is not required. The book explains the principles and applications of functional analysis and explores the development of the basic properties of normed linear, inner product spaces and continuous linear operators defined in these spaces. Though Lebesgue integral is not discussed, the book offers an in-depth knowledge on the numerous applications of the abstract results of functional analysis in differential and integral equations, Banach limits, harmonic analysis, summability and numerical integration. Also covered in the book are versions of the spectral theorem for compact, symmetric operators and continuous, self adjoint operators.

Elementary Heat Transfer Analysis

Pergamon Unified Engineering Series

Author: Stephen Whitaker

Publisher: Elsevier

ISBN: 1483181723

Category: Science

Page: 388

View: 491

Elementary Heat Transfer Analysis provides information pertinent to the fundamental aspects of the nature of transient heat conduction. This book presents a thorough understanding of the thermal energy equation and its application to boundary layer flows and confined and unconfined turbulent flows. Organized into nine chapters, this book begins with an overview of the use of heat transfer coefficients in formulating the flux condition at phase interface. This text then explains the specification as well as application of flux boundary conditions. Other chapters consider a derivation of the transient heat conduction equation. This book discusses as well the convective energy transport based on the understanding and application of the thermal energy equation. The final chapter deals with the study of the processes of heat transfer during boiling and condensation. This book is a valuable resource for Junior or Senior engineering students who are in an introductory course in heat transfer.

A Problem Book in Real Analysis

Author: Asuman G. Aksoy,Mohamed A. Khamsi

Publisher: Springer Science & Business Media

ISBN: 1441912967

Category: Mathematics

Page: 254

View: 4840

Education is an admirable thing, but it is well to remember from time to time that nothing worth knowing can be taught. Oscar Wilde, “The Critic as Artist,” 1890. Analysis is a profound subject; it is neither easy to understand nor summarize. However, Real Analysis can be discovered by solving problems. This book aims to give independent students the opportunity to discover Real Analysis by themselves through problem solving. ThedepthandcomplexityofthetheoryofAnalysiscanbeappreciatedbytakingaglimpseatits developmental history. Although Analysis was conceived in the 17th century during the Scienti?c Revolution, it has taken nearly two hundred years to establish its theoretical basis. Kepler, Galileo, Descartes, Fermat, Newton and Leibniz were among those who contributed to its genesis. Deep conceptual changes in Analysis were brought about in the 19th century by Cauchy and Weierstrass. Furthermore, modern concepts such as open and closed sets were introduced in the 1900s. Today nearly every undergraduate mathematics program requires at least one semester of Real Analysis. Often, students consider this course to be the most challenging or even intimidating of all their mathematics major requirements. The primary goal of this book is to alleviate those concerns by systematically solving the problems related to the core concepts of most analysis courses. In doing so, we hope that learning analysis becomes less taxing and thereby more satisfying.

Elementary Analysis

The Commonwealth and International Library: Mathematics Division

Author: K. S. Snell,J. B. Morgan

Publisher: Elsevier

ISBN: 1483158985

Category: Mathematics

Page: 304

View: 1400

Elementary Analysis, Volume 2 introduces several of the ideas of modern mathematics in a casual manner and provides the practical experience in algebraic and analytic operations that lays a sound foundation of basic skills. This book focuses on the nature of number, algebraic and logical structure, groups, rings, fields, vector spaces, matrices, sequences, limits, functions and inverse functions, complex numbers, and probability. The logical structure of analysis given through the treatment of differentiation and integration, with applications to the trigonometric and logarithmic functions, is also briefly discussed. This volume begins with a description of the trigonometric functions of the general angle and an introduction to the binomial theorem and series. The rest of the chapters cover the numerical solution of equations, analytical geometry, Argand Diagram, numerical methods, and methods of approximation that form an important section of modern applied mathematics. This publication is valuable to teachers and students in training colleges.

Organic Elemental Analysis

Ultramicro, Micro, and Trace Methods

Author: Wolfgang Kirmse

Publisher: Elsevier

ISBN: 0323160891

Category: Science

Page: 158

View: 8069

Organic Elemental Analysis: Ultramicro, Micro, and Trace Methods is a 22-chapter text that presents the methods for ultramicro, micro, and trace organic elemental analysis for commercial routine analysis. Each chapter of this book describes the important features of the methods evaluated, such as gas chromatography, wet absorption, spectrophotometry, diffusion, extraction, flame photometry, and dead-stop titration. These methods are classified into dynamic, multielement, and automatic determination methods. The advantages and limitations, as well as the speed, accuracy, reliability and economic aspects of these methods are examined. Considerable chapters are devoted to the analysis of various elements, including carbon, hydrogen, nitrogen, oxygen, sulfur, chlorine, bromine, iodine, fluorine, and phosphorus. Organic and analytical chemists, as well as chemistry teachers and students will find this work invaluable.

Elementary Functional Analysis

Author: Barbara MacCluer

Publisher: Springer Science & Business Media

ISBN: 0387855297

Category: Mathematics

Page: 208

View: 8637

Functional analysis arose in the early twentieth century and gradually, conquering one stronghold after another, became a nearly universal mathematical doctrine, not merely a new area of mathematics, but a new mathematical world view. Its appearance was the inevitable consequence of the evolution of all of nineteenth-century mathematics, in particular classical analysis and mathematical physics. Its original basis was formed by Cantor’s theory of sets and linear algebra. Its existence answered the question of how to state general principles of a broadly interpreted analysis in a way suitable for the most diverse situations. A.M. Vershik ([45], p. 438). This text evolved from the content of a one semester introductory course in fu- tional analysis that I have taught a number of times since 1996 at the University of Virginia. My students have included ?rst and second year graduate students prep- ing for thesis work in analysis, algebra, or topology, graduate students in various departments in the School of Engineering and Applied Science, and several und- graduate mathematics or physics majors. After a ?rst draft of the manuscript was completed, it was also used for an independent reading course for several und- graduates preparing for graduate school.

Elementary Real Analysis

Author: H. G. Eggleston

Publisher: Cambridge University Press

ISBN: 9780521098687

Category: Mathematics

Page: 296

View: 8862

This textbook covers all the theoretical aspects of real variable analysis which undergraduates reading mathematics are likely to require during the first two or three years of their course. It is based on lecture courses which the author has given in the universities of Wales, Cambridge and London. The subject is presented rigorously and without padding. Definitions are stated explicitly and the whole development of the subject is logical and self-contained. Complex numbers are used but the complex variable calculus is not. 'Applied analysis', such as differential equations and Fourier series, is not dealt with. A large number of examples is included, with hints for the solution of many of them. These will be of particular value to students working on their own.