Download or read book Multidimensional Real Analysis I written by J. J. Duistermaat and published by Cambridge University Press. This book was released on 2004-05-06 with total page 444 pages. Available in PDF, EPUB and Kindle. Book excerpt: Part one of the authors' comprehensive and innovative work on multidimensional real analysis. This book is based on extensive teaching experience at Utrecht University and gives a thorough account of differential analysis in multidimensional Euclidean space. It is an ideal preparation for students who wish to go on to more advanced study. The notation is carefully organized and all proofs are clean, complete and rigorous. The authors have taken care to pay proper attention to all aspects of the theory. In many respects this book presents an original treatment of the subject and it contains many results and exercises that cannot be found elsewhere. The numerous exercises illustrate a variety of applications in mathematics and physics. This combined with the exhaustive and transparent treatment of subject matter make the book ideal as either the text for a course, a source of problems for a seminar or for self study.
Download or read book Multidimensional Real Analysis I written by J. J. Duistermaat and published by . This book was released on 2004-05-06 with total page 798 pages. Available in PDF, EPUB and Kindle. Book excerpt: Part one of a comprehensive text on multidimensional real analysis, including numerous exercises with partial solutions.
Download or read book Multidimensional Real Analysis II written by J. J. Duistermaat and published by Cambridge University Press. This book was released on 2004-05-06 with total page 398 pages. Available in PDF, EPUB and Kindle. Book excerpt: Part two of the authors' comprehensive and innovative work on multidimensional real analysis. This book is based on extensive teaching experience at Utrecht University and gives a thorough account of integral analysis in multidimensional Euclidean space. It is an ideal preparation for students who wish to go on to more advanced study. The notation is carefully organized and all proofs are clean, complete and rigorous. The authors have taken care to pay proper attention to all aspects of the theory. In many respects this book presents an original treatment of the subject and it contains many results and exercises that cannot be found elsewhere. The numerous exercises illustrate a variety of applications in mathematics and physics. This combined with the exhaustive and transparent treatment of subject matter make the book ideal as either the text for a course, a source of problems for a seminar or for self study.
Download or read book Measure and Integral written by Richard Wheeden and published by CRC Press. This book was released on 1977-11-01 with total page 289 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume develops the classical theory of the Lebesgue integral and some of its applications. The integral is initially presented in the context of n-dimensional Euclidean space, following a thorough study of the concepts of outer measure and measure. A more general treatment of the integral, based on an axiomatic approach, is later given.
Download or read book Multidimensional Analysis written by George W. Hart and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 242 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book deals with the mathematical properties of dimensioned quantities, such as length, mass, voltage, and viscosity. Beginning with a careful examination of how one expresses the numerical results of a measurement and uses these results in subsequent manipulations, the author rigorously constructs the notion of dimensioned numbers and discusses their algebraic structure. The result is a unification of linear algebra and traditional dimensional analysis that can be extended from the scalars to which the traditional analysis is perforce restricted to multidimensional vectors of the sort frequently encountered in engineering, systems theory, economics, and other applications.
Download or read book Multidimensional Real Analysis written by Johannes Jisse Duistermaat and published by . This book was released on 2004 with total page 798 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Real Analysis written by N. L. Carothers and published by Cambridge University Press. This book was released on 2000-08-15 with total page 420 pages. Available in PDF, EPUB and Kindle. Book excerpt: A text for a first graduate course in real analysis for students in pure and applied mathematics, statistics, education, engineering, and economics.
Download or read book Multidimensional Real Analysis written by Johannes Jisse Duistermaat and published by Cambridge Studies in Advanced Mathematics. This book was released on 2004 with total page 798 pages. Available in PDF, EPUB and Kindle. Book excerpt: Two-volume set of the authors' comprehensive and innovative work on multidimensional real analysis.
Download or read book Mathematical Analysis written by Bernd S. W. Schröder and published by John Wiley & Sons. This book was released on 2008-01-28 with total page 584 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Modern Multidimensional Calculus written by Marshall Evans Munroe and published by Courier Dover Publications. This book was released on 2019-05-15 with total page 401 pages. Available in PDF, EPUB and Kindle. Book excerpt: A second-year calculus text, this volume is devoted primarily to topics in multidimensional analysis. Concepts and methods are emphasized, and rigorous proofs are sometimes replaced by relevant discussion and explanation. Because of the author's conviction that the differential provides a most elegant and useful tool, especially in a multidimensional setting, the notion of the differential is used extensively and matrix methods are stressed in the study of linear transformations. The first three chapters offer introductory material on functions and variables, differentials, and vectors in the plane. Succeeding chapters examine topics in linear algebra, partial derivatives, and applications as well as topics in vector differential calculus. The final chapters explore multiple integrals in addition to line and surface integrals. Exercises appear throughout the text, and answers are provided, making the book ideal for self-study.
Download or read book Real Mathematical Analysis written by Charles Chapman Pugh and published by Springer Science & Business Media. This book was released on 2013-03-19 with total page 445 pages. Available in PDF, EPUB and Kindle. Book excerpt: Was plane geometry your favourite math course in high school? Did you like proving theorems? Are you sick of memorising integrals? If so, real analysis could be your cup of tea. In contrast to calculus and elementary algebra, it involves neither formula manipulation nor applications to other fields of science. None. It is Pure Mathematics, and it is sure to appeal to the budding pure mathematician. In this new introduction to undergraduate real analysis the author takes a different approach from past studies of the subject, by stressing the importance of pictures in mathematics and hard problems. The exposition is informal and relaxed, with many helpful asides, examples and occasional comments from mathematicians like Dieudonne, Littlewood and Osserman. The author has taught the subject many times over the last 35 years at Berkeley and this book is based on the honours version of this course. The book contains an excellent selection of more than 500 exercises.
Download or read book Multidimensional Stationary Time Series written by Marianna Bolla and published by CRC Press. This book was released on 2021-04-29 with total page 318 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book gives a brief survey of the theory of multidimensional (multivariate), weakly stationary time series, with emphasis on dimension reduction and prediction. Understanding the covered material requires a certain mathematical maturity, a degree of knowledge in probability theory, linear algebra, and also in real, complex and functional analysis. For this, the cited literature and the Appendix contain all necessary material. The main tools of the book include harmonic analysis, some abstract algebra, and state space methods: linear time-invariant filters, factorization of rational spectral densities, and methods that reduce the rank of the spectral density matrix. Serves to find analogies between classical results (Cramer, Wold, Kolmogorov, Wiener, Kálmán, Rozanov) and up-to-date methods for dimension reduction in multidimensional time series Provides a unified treatment for time and frequency domain inferences by using machinery of complex and harmonic analysis, spectral and Smith--McMillan decompositions. Establishes analogies between the time and frequency domain notions and calculations Discusses the Wold's decomposition and the Kolmogorov's classification together, by distinguishing between different types of singularities. Understanding the remote past helps us to characterize the ideal situation where there is a regular part at present. Examples and constructions are also given Establishes a common outline structure for the state space models, prediction, and innovation algorithms with unified notions and principles, which is applicable to real-life high frequency time series It is an ideal companion for graduate students studying the theory of multivariate time series and researchers working in this field.
Download or read book Distributions written by J.J. Duistermaat and published by Springer Science & Business Media. This book was released on 2010-08-09 with total page 455 pages. Available in PDF, EPUB and Kindle. Book excerpt: This textbook is an application-oriented introduction to the theory of distributions, a powerful tool used in mathematical analysis. The treatment emphasizes applications that relate distributions to linear partial differential equations and Fourier analysis problems found in mechanics, optics, quantum mechanics, quantum field theory, and signal analysis. The book is motivated by many exercises, hints, and solutions that guide the reader along a path requiring only a minimal mathematical background.
Download or read book Basic Real Analysis written by Anthony W. Knapp and published by Springer Science & Business Media. This book was released on 2007-10-04 with total page 671 pages. Available in PDF, EPUB and Kindle. Book excerpt: Systematically develop the concepts and tools that are vital to every mathematician, whether pure or applied, aspiring or established A comprehensive treatment with a global view of the subject, emphasizing the connections between real analysis and other branches of mathematics Included throughout are many examples and hundreds of problems, and a separate 55-page section gives hints or complete solutions for most.
Download or read book Introduction to Analysis in Several Variables Advanced Calculus written by Michael E. Taylor and published by American Mathematical Soc.. This book was released on 2020-07-27 with total page 445 pages. Available in PDF, EPUB and Kindle. Book excerpt: This text was produced for the second part of a two-part sequence on advanced calculus, whose aim is to provide a firm logical foundation for analysis. The first part treats analysis in one variable, and the text at hand treats analysis in several variables. After a review of topics from one-variable analysis and linear algebra, the text treats in succession multivariable differential calculus, including systems of differential equations, and multivariable integral calculus. It builds on this to develop calculus on surfaces in Euclidean space and also on manifolds. It introduces differential forms and establishes a general Stokes formula. It describes various applications of Stokes formula, from harmonic functions to degree theory. The text then studies the differential geometry of surfaces, including geodesics and curvature, and makes contact with degree theory, via the Gauss–Bonnet theorem. The text also takes up Fourier analysis, and bridges this with results on surfaces, via Fourier analysis on spheres and on compact matrix groups.
Download or read book Advanced Calculus Revised Edition written by Lynn Harold Loomis and published by World Scientific Publishing Company. This book was released on 2014-02-26 with total page 595 pages. Available in PDF, EPUB and Kindle. Book excerpt: An authorised reissue of the long out of print classic textbook, Advanced Calculus by the late Dr Lynn Loomis and Dr Shlomo Sternberg both of Harvard University has been a revered but hard to find textbook for the advanced calculus course for decades.This book is based on an honors course in advanced calculus that the authors gave in the 1960's. The foundational material, presented in the unstarred sections of Chapters 1 through 11, was normally covered, but different applications of this basic material were stressed from year to year, and the book therefore contains more material than was covered in any one year. It can accordingly be used (with omissions) as a text for a year's course in advanced calculus, or as a text for a three-semester introduction to analysis.The prerequisites are a good grounding in the calculus of one variable from a mathematically rigorous point of view, together with some acquaintance with linear algebra. The reader should be familiar with limit and continuity type arguments and have a certain amount of mathematical sophistication. As possible introductory texts, we mention Differential and Integral Calculus by R Courant, Calculus by T Apostol, Calculus by M Spivak, and Pure Mathematics by G Hardy. The reader should also have some experience with partial derivatives.In overall plan the book divides roughly into a first half which develops the calculus (principally the differential calculus) in the setting of normed vector spaces, and a second half which deals with the calculus of differentiable manifolds.
Download or read book Data Theory and Dimensional Analysis written by William G. Jacoby and published by SAGE. This book was released on 1991 with total page 100 pages. Available in PDF, EPUB and Kindle. Book excerpt: For many readers, data theory is probably unfamiliar. Data isn't usually the subject matter of theory in and of itself. However, in this volume, William Jacoby introduces a theory of data idea. It examines how real world observations are transformed into something to be analyzed that is, data. Jacoby explores some of the basic ideas of data theory, and considers their implications for research strategies in the social sciences. "Like others in the series, it is reassuringly slim. It is intended for a general social science readership and is a worthwhile read even for experienced data analysts. since it draws attention not only to often overlooked assumptions, but also to often ignored analysis possibilities." --Telephone Surveys "On the whole, this book contains a lot of useful information." --Journal of Classification
