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.

Les informations fournies dans la section « Synopsis » peuvent faire référence à une autre édition de ce titre.

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)

Les informations fournies dans la section « A propos du livre » peuvent faire référence à une autre édition de ce titre.

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1.Mathematical Analysis: A Concise Introduction

Edité par John Wiley & Sons (2007)
ISBN 10 : 0470107960 ISBN 13 : 9780470107966
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Description du livre John Wiley & Sons, 2007. État : 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![7966JW MathemaAnaly]. N° de réf. du libraire 978047010796688

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

Edité par Hoboken, New Jersey, U.S.A.: Wiley-Interscience (2007)
ISBN 10 : 0470107960 ISBN 13 : 9780470107966
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6.Mathematical Analysis: A Concise Introduction

Edité par John Wiley & Sons (2007)
ISBN 10 : 0470107960 ISBN 13 : 9780470107966
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Description du livre John Wiley & Sons, 2007. État : 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![7966JW MathemaAnaly]. N° de réf. du libraire 978047010796688

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7.Mathematical Analysis: A Concise Introduction

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8.Mathematical Analysis

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9.Mathematical Analysis: A Concise Introduction (Hardback)

Edité par John Wiley and Sons Ltd, United States (2007)
ISBN 10 : 0470107960 ISBN 13 : 9780470107966
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Description du livre John Wiley and Sons Ltd, United States, 2007. Hardback. État : New. 1. Auflage. Language: English . 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. N° de réf. du libraire AAH9780470107966

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10.Mathematical Analysis: A Concise Introduction (Hardback)

Edité par John Wiley and Sons Ltd, United States (2007)
ISBN 10 : 0470107960 ISBN 13 : 9780470107966
Neuf(s) Couverture rigide Edition originale Quantité : 1
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Description du livre John Wiley and Sons Ltd, United States, 2007. Hardback. État : New. 1. Auflage. Language: English . 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. N° de réf. du libraire AAH9780470107966

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