The Second Edition offers a major re-organization of the book, with the goal of making it much more competitive as a text for students. The revised edition will be appropriate for a one- or two-semester introductory real analysis course. Like the first edition, the primary audience is the large collection of students who will never take a graduate level analysis course. The choice of topics and level of coverage is suitable for future high school teachers, and for students who will become engineers or other professionals needing a sound working knowledge of undergraduate mathematics.
The Second Edition offers a major re-organization of the book, with the goal of making it much more competitive as a text for students. The revised edition will be appropriate for a one- or two-semester introductory real analysis course.
An accessible introduction to real analysis and its connection to elementary calculus Bridging the gap between the development and history of real analysis, Introduction to Real Analysis: An Educational Approach presents a comprehensive introduction to real analysis while also offering a survey of the field. With its balance of historical background, key calculus methods, and hands-on applications, this book provides readers with a solid foundation and fundamental understanding of real analysis. The book begins with an outline of basic calculus, including a close examination of problems illustrating links and potential difficulties. Next, a fluid introduction to real analysis is presented, guiding readers through the basic topology of real numbers, limits, integration, and a series of functions in natural progression. The book moves on to analysis with more rigorous investigations, and the topology of the line is presented along with a discussion of limits and continuity that includes unusual examples in order to direct readers' thinking beyond intuitive reasoning and on to more complex understanding. The dichotomy of pointwise and uniform convergence is then addressed and is followed by differentiation and integration. Riemann-Stieltjes integrals and the Lebesgue measure are also introduced to broaden the presented perspective. The book concludes with a collection of advanced topics that are connected to elementary calculus, such as modeling with logistic functions, numerical quadrature, Fourier series, and special functions. Detailed appendices outline key definitions and theorems in elementary calculus and also present additional proofs, projects, and sets in real analysis. Each chapter references historical sources on real analysis while also providing proof-oriented exercises and examples that facilitate the development of computational skills. In addition, an extensive bibliography provides additional resources on the topic. Introduction to Real Analysis: An Educational Approach is an ideal book for upper- undergraduate and graduate-level real analysis courses in the areas of mathematics and education. It is also a valuable reference for educators in the field of applied mathematics.
With its balance of historical background, key calculus methods, and hands-on applications, this book provides readers with a solid foundation and fundamental understanding of real analysis.
This text forms a bridge between courses in calculus and real analysis. Suitable for advanced undergraduates and graduate students, it focuses on the construction of mathematical proofs. 1996 edition.
This text forms a bridge between courses in calculus and real analysis. Suitable for advanced undergraduates and graduate students, it focuses on the construction of mathematical proofs. 1996 edition.
This text is a single variable real analysis text, designed for the one-year course at the junior, senior, or beginning graduate level. It provides a rigorous and comprehensive treatment of the theoretical concepts of analysis. The book contains most of the topics covered in a text of this nature, but it also includes many topics not normally encountered in comparable texts. These include the Riemann-Stieltjes integral, the Lebesgue integral, Fourier series, the Weiestrass approximation theorem, and an introduction to normal linear spaces. The Real Number System; Sequence Of Real Numbers; Structure Of Point Sets; Limits And Continuity; Differentiation; The Riemann And Riemann-Stieltjes Integral; Series of Real Numbers; Sequences And Series Of Functions; Orthogonal Functions And Fourier Series; Lebesgue Measure And Integration; Logic and Proofs; Propositions and Connectives For all readers interested in real analysis.
This text is a single variable real analysis text, designed for the one-year course at the junior, senior, or beginning graduate level.
Assuming minimal background on the part of students, this text gradually develops the principles of basic real analysis and presents the background necessary to understand applications used in such disciplines as statistics, operations research, and engineering. The text presents the first elementary exposition of the gauge integral and offers a clear and thorough introduction to real numbers, developing topics in n-dimensions, and functions of several variables. Detailed treatments of Lagrange multipliers and the Kuhn-Tucker Theorem are also presented. The text concludes with coverage of important topics in abstract analysis, including the Stone-Weierstrass Theorem and the Banach Contraction Principle.
Assuming minimal background on the part of students, this text gradually develops the principles of basic real analysis and presents the background necessary to understand applications used in such disciplines as statistics, operations ...
Market_Desc: · Mathematicians Special Features: · The book present results that are general enough to cover cases that actually arise, but do not strive for maximum generality· It also present proofs that can readily be adapted to a more general situation· It contains a rather extensive lists of exercises, some difficult for the more challenged. Moderately difficult exercises are broken down into a sequence of steps About The Book: In recent years, mathematics has become valuable in many areas, including economics and management science as well as the physical sciences, engineering and computer science. Therefore, this text provides the fundamental concepts and techniques of real analysis for readers in all of these areas. It helps one develop the ability to think deductively, analyze mathematical situations and extend ideas to a new context. Like the first two editions, this edition maintains the same spirit and user-friendly approach with some streamlined arguments, a few new examples, rearranged topics, and a new chapter on the Generalized Riemann Integral.
Therefore, this text provides the fundamental concepts and techniques of real analysis for readers in all of these areas.
