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| Author | : Steven G. Krantz |
| Publisher | : CRC Press |
| Total Pages | : 306 |
| Release | : 2016-12-12 |
| Genre | : Mathematics |
| ISBN | : 1498777708 |
Download Real Analysis and Foundations, Fourth Edition Book in PDF, ePub and Kindle
A Readable yet Rigorous Approach to an Essential Part of Mathematical Thinking Back by popular demand, Real Analysis and Foundations, Third Edition bridges the gap between classic theoretical texts and less rigorous ones, providing a smooth transition from logic and proofs to real analysis. Along with the basic material, the text covers Riemann-Stieltjes integrals, Fourier analysis, metric spaces and applications, and differential equations. New to the Third Edition Offering a more streamlined presentation, this edition moves elementary number systems and set theory and logic to appendices and removes the material on wavelet theory, measure theory, differential forms, and the method of characteristics. It also adds a chapter on normed linear spaces and includes more examples and varying levels of exercises. Extensive Examples and Thorough Explanations Cultivate an In-Depth Understanding This best-selling book continues to give students a solid foundation in mathematical analysis and its applications. It prepares them for further exploration of measure theory, functional analysis, harmonic analysis, and beyond.
| Author | : Sergei Ovchinnikov |
| Publisher | : Springer Nature |
| Total Pages | : 178 |
| Release | : 2021-03-20 |
| Genre | : Mathematics |
| ISBN | : 3030647013 |
Download Real Analysis: Foundations Book in PDF, ePub and Kindle
This textbook explores the foundations of real analysis using the framework of general ordered fields, demonstrating the multifaceted nature of the area. Focusing on the logical structure of real analysis, the definitions and interrelations between core concepts are illustrated with the use of numerous examples and counterexamples. Readers will learn of the equivalence between various theorems and the completeness property of the underlying ordered field. These equivalences emphasize the fundamental role of real numbers in analysis. Comprising six chapters, the book opens with a rigorous presentation of the theories of rational and real numbers in the framework of ordered fields. This is followed by an accessible exploration of standard topics of elementary real analysis, including continuous functions, differentiation, integration, and infinite series. Readers will find this text conveniently self-contained, with three appendices included after the main text, covering an overview of natural numbers and integers, Dedekind's construction of real numbers, historical notes, and selected topics in algebra. Real Analysis: Foundations is ideal for students at the upper-undergraduate or beginning graduate level who are interested in the logical underpinnings of real analysis. With over 130 exercises, it is suitable for a one-semester course on elementary real analysis, as well as independent study.
| Author | : Miklós Laczkovich |
| Publisher | : Springer |
| Total Pages | : 486 |
| Release | : 2015-10-08 |
| Genre | : Mathematics |
| ISBN | : 1493927663 |
Download Real Analysis Book in PDF, ePub and Kindle
Based on courses given at Eötvös Loránd University (Hungary) over the past 30 years, this introductory textbook develops the central concepts of the analysis of functions of one variable — systematically, with many examples and illustrations, and in a manner that builds upon, and sharpens, the student’s mathematical intuition. The book provides a solid grounding in the basics of logic and proofs, sets, and real numbers, in preparation for a study of the main topics: limits, continuity, rational functions and transcendental functions, differentiation, and integration. Numerous applications to other areas of mathematics, and to physics, are given, thereby demonstrating the practical scope and power of the theoretical concepts treated. In the spirit of learning-by-doing, Real Analysis includes more than 500 engaging exercises for the student keen on mastering the basics of analysis. The wealth of material, and modular organization, of the book make it adaptable as a textbook for courses of various levels; the hints and solutions provided for the more challenging exercises make it ideal for independent study.
| Author | : Richard Johnsonbaugh |
| Publisher | : Courier Corporation |
| Total Pages | : 450 |
| Release | : 2012-09-11 |
| Genre | : Mathematics |
| ISBN | : 0486134776 |
Download Foundations of Mathematical Analysis Book in PDF, ePub and Kindle
Definitive look at modern analysis, with views of applications to statistics, numerical analysis, Fourier series, differential equations, mathematical analysis, and functional analysis. More than 750 exercises; some hints and solutions. 1981 edition.
| Author | : Steven G. Krantz |
| Publisher | : CRC Press |
| Total Pages | : 426 |
| Release | : 2016-04-19 |
| Genre | : Mathematics |
| ISBN | : 1466587326 |
Download Real Analysis and Foundations Book in PDF, ePub and Kindle
A Readable yet Rigorous Approach to an Essential Part of Mathematical Thinking Back by popular demand, Real Analysis and Foundations, Third Edition bridges the gap between classic theoretical texts and less rigorous ones, providing a smooth transition from logic and proofs to real analysis. Along with the basic material, the text covers Riemann-Stieltjes integrals, Fourier analysis, metric spaces and applications, and differential equations. New to the Third Edition Offering a more streamlined presentation, this edition moves elementary number systems and set theory and logic to appendices and removes the material on wavelet theory, measure theory, differential forms, and the method of characteristics. It also adds a chapter on normed linear spaces and includes more examples and varying levels of exercises. Extensive Examples and Thorough Explanations Cultivate an In-Depth Understanding This best-selling book continues to give students a solid foundation in mathematical analysis and its applications. It prepares them for further exploration of measure theory, functional analysis, harmonic analysis, and beyond.
| Author | : Douglas S. Bridges |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 328 |
| Release | : 1998 |
| Genre | : Business & Economics |
| ISBN | : 0387982396 |
Download Foundations of Real and Abstract Analysis Book in PDF, ePub and Kindle
A complete course on metric, normed, and Hilbert spaces, including many results and exercises seldom found in texts on analysis at this level. The author covers an unusually wide range of material in a clear and concise format, including elementary real analysis, Lebesgue integration on R, and an introduction to functional analysis. The book begins with a fast-paced course on real analysis, followed by an introduction to the Lebesgue integral. This provides a reference for later chapters as well as a preparation for students with only the typical sequence of undergraduate calculus courses as prerequisites. Other features include a chapter introducing functional analysis, the Hahn-Banach theorem and duality, separation theorems, the Baire Category Theorem, the Open Mapping Theorem and their consequences, and unusual applications. Of special interest are the 750 exercises, many with guidelines for their solutions, applications and extensions of the main propositions and theorems, pointers to new branches of the subject, and difficult challenges for the very best students.
| Author | : Steven G. Krantz |
| Publisher | : CRC Press |
| Total Pages | : 312 |
| Release | : 2014-10-20 |
| Genre | : Mathematics |
| ISBN | : 148222075X |
Download Foundations of Analysis Book in PDF, ePub and Kindle
Foundations of Analysis covers the basics of real analysis for a one- or two-semester course. In a straightforward and concise way, it helps students understand the key ideas and apply the theorems. The book's accessible approach will appeal to a wide range of students and instructors.Each section begins with a boxed introduction that familiarizes
| Author | : Saminathan Ponnusamy |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 575 |
| Release | : 2011-12-16 |
| Genre | : Mathematics |
| ISBN | : 0817682910 |
Download Foundations of Mathematical Analysis Book in PDF, ePub and Kindle
Mathematical analysis is fundamental to the undergraduate curriculum not only because it is the stepping stone for the study of advanced analysis, but also because of its applications to other branches of mathematics, physics, and engineering at both the undergraduate and graduate levels. This self-contained textbook consists of eleven chapters, which are further divided into sections and subsections. Each section includes a careful selection of special topics covered that will serve to illustrate the scope and power of various methods in real analysis. The exposition is developed with thorough explanations, motivating examples, exercises, and illustrations conveying geometric intuition in a pleasant and informal style to help readers grasp difficult concepts. Foundations of Mathematical Analysis is intended for undergraduate students and beginning graduate students interested in a fundamental introduction to the subject. It may be used in the classroom or as a self-study guide without any required prerequisites.
| Author | : Avner Friedman |
| Publisher | : Courier Corporation |
| Total Pages | : 276 |
| Release | : 1982-01-01 |
| Genre | : Mathematics |
| ISBN | : 9780486640624 |
Download Foundations of Modern Analysis Book in PDF, ePub and Kindle
Measure and integration, metric spaces, the elements of functional analysis in Banach spaces, and spectral theory in Hilbert spaces — all in a single study. Only book of its kind. Unusual topics, detailed analyses. Problems. Excellent for first-year graduate students, almost any course on modern analysis. Preface. Bibliography. Index.
| Author | : Malcolm W. Pownall |
| Publisher | : WCB/McGraw-Hill |
| Total Pages | : 467 |
| Release | : 1994 |
| Genre | : Mathematics |
| ISBN | : 9780697129086 |
Download Real Analysis Book in PDF, ePub and Kindle
This introductory textbook covers important mathematical concepts, including the language of mathematics sequences and series, limits and continuity, and a brief introduction to metric spaces.
