An Interactive Introduction to Mathematical Analysis

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This book provides a rigorous course in the calculus of functions of a real variable. Its gentle approach, particularly in its early chapters, makes it especially suitable for students who are not headed for graduate school. For those who are, this book gives an opportunity to engage in a penetrating study of real analysis. The companion onscreen version of this text contains hundreds of links to alternative approaches, more complete explanations and solutions to exercises; links that make it more friendly than any printed book could be. In addition, there are links to a wealth of optional material that an instructor can select for a more advanced course, and that students can use as a reference long after their first course has ended. The CD provides exercises that can be worked interactively with the help of the computer algebra systems that are bundled with Scientific Notebook.

Principles of Mathematical Analysis 3/e 2023 Edition (3版)

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Principles of Mathematical Analysis 3/e 2023 Edition 作者：Walter Rudin ISBN：9786269708116 版次：3 年份：2023 出版商：McGraw-Hill 頁數/規格：342頁/平裝單色 Description This book is intended to serve as a text for the course in analysis that is usually taken by advanced undergraduates or by first-year students who study mathematics. NEW to This Edition The material on functions of several variables in Chapter 9 is significantly rewritten, with many details filled in, and with more examples and more motivation. The proof of the inverse function theorem is simplified by means of the fixed point theorem about contraction mappings. Differential forms are discussed in much greater detail. Several applications of Stokes' theorem are included. The Riemann-Stieltjes integral in Chapter 6 has been trimmed a bit. A short do-it-yourself section on the gamma function has been added to Chapter 8. There is a large number of new exercises throughout the book, most of them with fairly detailed hints. Several references to articles appearing in the American Mathematical Monthly and in Mathematics Magazine are included for students to develop the habit of looking into the journal literature. 目錄 Table of Contents Chapter 1: The Real and Complex Number Systems  Chapter 2: Basic Topology  Chapter 3: Numerical Sequences and Series  Chapter 4: Continuity  Chapter 5: Differentiation  Chapter 6: The Riemann-Stieltjes Integral  Chapter 7: Sequences and Series of Functions  Chapter 8: Some Special Functions  Chapter 9: Functions of Several Variables  Chapter 10: Integration of Differential Forms  Chapter 11: The Lebesgue Theory

MATHEMATICAL ANALYSIS: A CONCISE INTRODUCTION

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Mathematical analysis serves as a common foundation for many research areas of pure and applied mathematics. It is also an important and powerful tool used in many other fields of science, including physics, chemistry, biology, engineering, finance, and economics. In this book, some basic theories of analysis are presented, including metric spaces and their properties, limit of sequences, continuous function, differentiation, Riemann integral, uniform convergence, and series. After going through a sequence of courses on basic calculus and linear algebra, it is desirable for one to spend a reasonable length of time (ideally, say, one semester) to build an advanced base of analysis sufficient for getting into various research fields other than analysis itself, and/or stepping into more advanced levels of analysis courses (such as real analysis, complex analysis, differential equations, functional analysis, stochastic analysis, amongst others). This book is written to meet such a demand. Readers will find the treatment of the material is as concise as possible, but still maintaining all the necessary details.