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Author: Terence Tao
Publisher: Springer
ISBN: 9811017891
Category : Mathematics
Languages : en
Pages : 366
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Book Description
This is part one of a two-volume book on real analysis and is intended for senior undergraduate students of mathematics who have already been exposed to calculus. The emphasis is on rigour and foundations of analysis. Beginning with the construction of the number systems and set theory, the book discusses the basics of analysis (limits, series, continuity, differentiation, Riemann integration), through to power series, several variable calculus and Fourier analysis, and then finally the Lebesgue integral. These are almost entirely set in the concrete setting of the real line and Euclidean spaces, although there is some material on abstract metric and topological spaces. The book also has appendices on mathematical logic and the decimal system. The entire text (omitting some less central topics) can be taught in two quarters of 25–30 lectures each. The course material is deeply intertwined with the exercises, as it is intended that the student actively learn the material (and practice thinking and writing rigorously) by proving several of the key results in the theory.
Author: Terence Tao
Publisher: Springer
ISBN: 9811017891
Category : Mathematics
Languages : en
Pages : 366
Get Book Here
Book Description
This is part one of a two-volume book on real analysis and is intended for senior undergraduate students of mathematics who have already been exposed to calculus. The emphasis is on rigour and foundations of analysis. Beginning with the construction of the number systems and set theory, the book discusses the basics of analysis (limits, series, continuity, differentiation, Riemann integration), through to power series, several variable calculus and Fourier analysis, and then finally the Lebesgue integral. These are almost entirely set in the concrete setting of the real line and Euclidean spaces, although there is some material on abstract metric and topological spaces. The book also has appendices on mathematical logic and the decimal system. The entire text (omitting some less central topics) can be taught in two quarters of 25–30 lectures each. The course material is deeply intertwined with the exercises, as it is intended that the student actively learn the material (and practice thinking and writing rigorously) by proving several of the key results in the theory.
Author: Barry Simon
Publisher:
ISBN: 9781470411039
Category : Mathematical analysis
Languages : en
Pages : 749
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Book Description
A Comprehensive Course in Analysis by Poincar Prize winner Barry Simon is a five-volume set that can serve as a graduate-level analysis textbook with a lot of additional bonus information, including hundreds of problems and numerous notes that extend the text and provide important historical background. Depth and breadth of exposition make this set a valuable reference source for almost all areas of classical analysis
Author: Yoav Benyamini
Publisher: American Mathematical Soc.
ISBN: 0821808354
Category : Mathematics
Languages : en
Pages : 503
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Book Description
A systematic study of geometric nonlinear functional analysis. The main theme is the study of uniformly continuous and Lipschitz functions between Banach spaces. This study leads to the classification of Banach spaces and of their important subsets in the uniform and Lipschitz categories.
Author: Andy Mitchell
Publisher: ESRI, Inc.
ISBN: 9781879102064
Category : Computers
Languages : en
Pages : 190
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Book Description
Backed by the collective knowledge and expertise of the worlds leading Geographic Information Systems company, this volume presents the concepts and methods unleashing the full analytic power of GIS.
Author: Edmund Landau
Publisher:
ISBN: 9781950217083
Category :
Languages : en
Pages : 142
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Book Description
Natural numbers, zero, negative integers, rational numbers, irrational numbers, real numbers, complex numbers, . . ., and, what are numbers? The most accurate mathematical answer to the question is given in this book.
Author: Alex Karagrigoriou
Publisher: John Wiley & Sons
ISBN: 1119821576
Category : Business & Economics
Languages : en
Pages : 304
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Book Description
BIG DATA, ARTIFICIAL INTELLIGENCE AND DATA ANALYSIS SET Coordinated by Jacques Janssen Data analysis is a scientific field that continues to grow enormously, most notably over the last few decades, following rapid growth within the tech industry, as well as the wide applicability of computational techniques alongside new advances in analytic tools. Modeling enables data analysts to identify relationships, make predictions, and to understand, interpret and visualize the extracted information more strategically. This book includes the most recent advances on this topic, meeting increasing demand from wide circles of the scientific community. Applied Modeling Techniques and Data Analysis 1 is a collective work by a number of leading scientists, analysts, engineers, mathematicians and statisticians, working on the front end of data analysis and modeling applications. The chapters cover a cross section of current concerns and research interests in the above scientific areas. The collected material is divided into appropriate sections to provide the reader with both theoretical and applied information on data analysis methods, models and techniques, along with appropriate applications.
Author: Richard Courant
Publisher: Springer Science & Business Media
ISBN: 3642571492
Category : Mathematics
Languages : en
Pages : 585
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Book Description
From the reviews: "...one of the best textbooks introducing several generations of mathematicians to higher mathematics. ... This excellent book is highly recommended both to instructors and students." --Acta Scientiarum Mathematicarum, 1991
Author: Kenneth A. Ross
Publisher: CUP Archive
ISBN:
Category : Mathematics
Languages : en
Pages : 192
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Book Description
Author: Jean-Claude Trigeassou
Publisher: John Wiley & Sons
ISBN: 1786302691
Category : Technology & Engineering
Languages : en
Pages : 316
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Book Description
This book introduces an original fractional calculus methodology (‘the infinite state approach’) which is applied to the modeling of fractional order differential equations (FDEs) and systems (FDSs). Its modeling is based on the frequency distributed fractional integrator, while the resulting model corresponds to an integer order and infinite dimension state space representation. This original modeling allows the theoretical concepts of integer order systems to be generalized to fractional systems, with a particular emphasis on a convolution formulation.
Author: Olivier Piva
Publisher: John Wiley & Sons
ISBN: 1786303493
Category : Science
Languages : en
Pages : 314
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Book Description
For chemists, attempting to mimic nature by synthesizing complex natural products from raw material is a challenge that is fraught with pitfalls. To tackle this unique but potentially rewarding task, researchers can rely on well-established reactions and methods of practice, or apply their own synthesis methods to verify their potential. Whatever the goal and its complexity, there are multiple ways of achieving it. We must now establish a strategic and effective plan that requires the minimum number of steps, but lends itself to widespread use. This book is structured around the study of a dozen target products (butyrolactone, macrolide, indole compound, cyclobutanic terpene, spiro- and polycyclic derivatives, etc.). For each product, the different disconnections are presented and the associated syntheses are analyzed step by step. The key reactions are described explicitly, followed by diagrams showing the range of impact of certain transformations. This set of data alone is conducive to understanding syntheses and indulging in this difficult, but worthwhile activity.
