# Mathematical Analysis: A Concise Introduction

## Bernd S. W. Schröder

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A self-contained introduction to the fundamentals of mathematical analysis

Mathematical Analysis: A Concise Introduction presents the foundations of analysis and illustrates its role in mathematics. By focusing on the essentials, reinforcing learning through exercises, and featuring a unique "learn by doing" approach, the book develops the reader's proof writing skills and establishes fundamental comprehension of analysis that is essential for further exploration of pure and applied mathematics. This book is directly applicable to areas such as differential equations, probability theory, numerical analysis, differential geometry, and functional analysis.

Mathematical Analysis is composed of three parts:

?Part One presents the analysis of functions of one variable, including sequences, continuity, differentiation, Riemann integration, series, and the Lebesgue integral. A detailed explanation of proof writing is provided with specific attention devoted to standard proof techniques. To facilitate an efficient transition to more abstract settings, the results for single variable functions are proved using methods that translate to metric spaces.

?Part Two explores the more abstract counterparts of the concepts outlined earlier in the text. The reader is introduced to the fundamental spaces of analysis, including Lp spaces, and the book successfully details how appropriate definitions of integration, continuity, and differentiation lead to a powerful and widely applicable foundation for further study of applied mathematics. The interrelation between measure theory, topology, and differentiation is then examined in the proof of the Multidimensional Substitution Formula. Further areas of coverage in this section include manifolds, Stokes' Theorem, Hilbert spaces, the convergence of Fourier series, and Riesz' Representation Theorem.

?Part Three provides an overview of the motivations for analysis as well as its applications in various subjects. A special focus on ordinary and partial differential equations presents some theoretical and practical challenges that exist in these areas. Topical coverage includes Navier-Stokes equations and the finite element method.

Mathematical Analysis: A Concise Introduction includes an extensive index and over 900 exercises ranging in level of difficulty, from conceptual questions and adaptations of proofs to proofs with and without hints. These opportunities for reinforcement, along with the overall concise and well-organized treatment of analysis, make this book essential for readers in upper-undergraduate or beginning graduate mathematics courses who would like to build a solid foundation in analysis for further work in all analysis-based branches of mathematics.

"Sinopsis" puede pertenecer a otra edición de este libro.

Bernd S.W. Schroder, PhD, is Edmondson/Crump Professor in the Program of Mathematics and Statistics at Louisiana Tech University. Dr. Schröder is the author of over thirty refereed journal articles on subjects such as ordered sets, probability theory, graph theory, harmonic analysis, computer science, and education. He earned his PhD in mathematics from Kansas State University in 1992.

Review:

"This highly original, interesting and very useful book includes over 900 exercises which are ranging in levels of difficulty, from conceptual questions and adaptations of proofs to proofs with and without hints." (Mathematical Reviews, 2008h)

"Sobre este título" puede pertenecer a otra edición de este libro.

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## 1.Mathematical Analysis: A Concise Introduction

Editorial: John Wiley & Sons (2007)
ISBN 10: 0470107960 ISBN 13: 9780470107966
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CollegebookDirect Australia
(Melbourne, VIC, Australia)
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Descripción John Wiley & Sons, 2007. Estado de conservación: Brand New. Brand New Textbook Wrapped MINT in the plastic. Ship from Multiple Locations, including Malaysia, Singapore, and Thailand. Shipping should take from 3-4 business days within US, Canada, UK, and other EU countries, 2-3 business days within Australia, Japan, and Singapore; for faster processing time, please choose to ship with Expedite. Thank you for looking! [7966JWMathAnalySchrJWD2]. Nº de ref. de la librería 978047010796688

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## 2.Mathematical Analysis: A Concise Introduction

ISBN 10: 0470107960 ISBN 13: 9780470107966
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Descripción Paperback. Estado de conservación: New. Softcover Book, New Condition, Fast Shipping. Ready in Stock. 1st Edition. [Please Read Carefully Before Buying], This Is An International Edition. Printed In Black and White. 584 Pages, Book Cover And ISBN No May Be Different From US Edition. Restricted Sales Disclaimer Wordings Not For Sales In USA And Canada May Be Printed On The Cover Of The Book. Standard Shipping 7-14 Business Days. Expedited Shiping 4-8 Business Days. ***WE DO NOT ENTERTAIN BULK ORDERS.*** The Books May Be Ship From Overseas For Inventory Purpose. Nº de ref. de la librería 370036

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## 3.Mathematical Analysis: A Concise Introduction

ISBN 10: 0470107960 ISBN 13: 9780470107966
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Descripción Paperback. Estado de conservación: New. New, Softcover International Edition, Printed in Black and White, Only USPS Media mail Shipping ONLY, Different ISBN, Same Content As US edition, Book Cover may be Different, in English Language. Nº de ref. de la librería 23751

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## 4.Mathematical Analysis: A Concise Introduction

ISBN 10: 0470107960 ISBN 13: 9780470107966
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## 5.Mathematical Analysis: A Concise Introduction

Editorial: Hoboken, New Jersey, U.S.A.: Wiley-Interscience (2007)
ISBN 10: 0470107960 ISBN 13: 9780470107966
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Descripción Hoboken, New Jersey, U.S.A.: Wiley-Interscience, 2007. Hardcover. Estado de conservación: New. Ship out 1-2 business day,Brand new,US edition, Free tracking number usually 2-4 biz days delivery to worldwide Same shipping fee with US, Canada,Europe country, Australia, item will ship out from either LA or Asia. Nº de ref. de la librería ABE-7344703519

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## 6.Mathematical Analysis: A Concise Introduction

Editorial: Wiley-Interscience, Hoboken, New Jersey, U.S.A. (2007)
ISBN 10: 0470107960 ISBN 13: 9780470107966
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Descripción Wiley-Interscience, Hoboken, New Jersey, U.S.A., 2007. Hardcover. Estado de conservación: Brand New. US edition Brand New HARD COVER FEDEX delivery. Nº de ref. de la librería 001317

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## 7.Mathematical Analysis: A Concise Introduction Format: Hardcover

Editorial: John Wiley and Sons
ISBN 10: 0470107960 ISBN 13: 9780470107966
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Descripción John Wiley and Sons. Estado de conservación: New. Brand New. Nº de ref. de la librería 0470107960

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## 8.Mathematical Analysis: A Concise Introduction

Editorial: Wiley-Interscience (2007)
ISBN 10: 0470107960 ISBN 13: 9780470107966
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Descripción Wiley-Interscience, 2007. Hardcover. Estado de conservación: New. Never used!. Nº de ref. de la librería P110470107960

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## 9.Mathematical Analysis: A Concise Introduction

Editorial: Wiley-Interscience (2007)
ISBN 10: 0470107960 ISBN 13: 9780470107966
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Descripción Wiley-Interscience, 2007. Hardcover. Estado de conservación: New. book. Nº de ref. de la librería M0470107960

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## 10.Mathematical Analysis: A Concise Introduction (Hardback)

Editorial: John Wiley and Sons Ltd, United States (2007)
ISBN 10: 0470107960 ISBN 13: 9780470107966
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Descripción John Wiley and Sons Ltd, United States, 2007. Hardback. Estado de conservación: New. 1. Auflage. Language: English . This book usually ship within 10-15 business days and we will endeavor to dispatch orders quicker than this where possible. Brand New Book. A self-contained introduction to the fundamentals of mathematical analysis Mathematical Analysis: A Concise Introduction presents the foundations of analysis and illustrates its role in mathematics. By focusing on the essentials, reinforcing learning through exercises, and featuring a unique learn by doing approach, the book develops the reader s proof writing skills and establishes fundamental comprehension of analysis that is essential for further exploration of pure and applied mathematics. This book is directly applicable to areas such as differential equations, probability theory, numerical analysis, differential geometry, and functional analysis. Mathematical Analysis is composed of three parts: ?Part One presents the analysis of functions of one variable, including sequences, continuity, differentiation, Riemann integration, series, and the Lebesgue integral. A detailed explanation of proof writing is provided with specific attention devoted to standard proof techniques. To facilitate an efficient transition to more abstract settings, the results for single variable functions are proved using methods that translate to metric spaces. ?Part Two explores the more abstract counterparts of the concepts outlined earlier in the text. The reader is introduced to the fundamental spaces of analysis, including Lp spaces, and the book successfully details how appropriate definitions of integration, continuity, and differentiation lead to a powerful and widely applicable foundation for further study of applied mathematics. The interrelation between measure theory, topology, and differentiation is then examined in the proof of the Multidimensional Substitution Formula. Further areas of coverage in this section include manifolds, Stokes Theorem, Hilbert spaces, the convergence of Fourier series, and Riesz Representation Theorem. ?Part Three provides an overview of the motivations for analysis as well as its applications in various subjects. A special focus on ordinary and partial differential equations presents some theoretical and practical challenges that exist in these areas. Topical coverage includes Navier-Stokes equations and the finite element method. Mathematical Analysis: A Concise Introduction includes an extensive index and over 900 exercises ranging in level of difficulty, from conceptual questions and adaptations of proofs to proofs with and without hints. These opportunities for reinforcement, along with the overall concise and well-organized treatment of analysis, make this book essential for readers in upper-undergraduate or beginning graduate mathematics courses who would like to build a solid foundation in analysis for further work in all analysis-based branches of mathematics. Nº de ref. de la librería BZV9780470107966

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