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General Theory Of Functions And Integration
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Book Synopsis General Theory of Functions and Integration by : Angus Ellis Taylor
Download or read book General Theory of Functions and Integration written by Angus Ellis Taylor and published by Courier Corporation. This book was released on 1985-01-01 with total page 451 pages. Available in PDF, EPUB and Kindle. Book excerpt: Uniting a variety of approaches to the study of integration, a well-known professor presents a single-volume "blend of the particular and the general, of the concrete and the abstract." 1966 edition.
Book Synopsis General Theory of Functions and Integration by : Angus E. Taylor
Download or read book General Theory of Functions and Integration written by Angus E. Taylor and published by Courier Corporation. This book was released on 2012-05-24 with total page 456 pages. Available in PDF, EPUB and Kindle. Book excerpt: Presenting the various approaches to the study of integration, a well-known mathematics professor brings together in one volume "a blend of the particular and the general, of the concrete and the abstract." This volume is suitable for advanced undergraduates and graduate courses as well as for independent study. 1966 edition.
Book Synopsis Geometric Integration Theory by : Hassler Whitney
Download or read book Geometric Integration Theory written by Hassler Whitney and published by Princeton University Press. This book was released on 2015-12-08 with total page 404 pages. Available in PDF, EPUB and Kindle. Book excerpt: A complete theory of integration as it appears in geometric and physical problems must include integration over oriented r-dimensional domains in n-space; both the integrand and the domain may be variable. This is the primary subject matter of the present book, designed to bring out the underlying geometric and analytic ideas and to give clear and complete proofs of the basic theorems. Originally published in 1957. The Princeton Legacy Library uses the latest print-on-demand technology to again make available previously out-of-print books from the distinguished backlist of Princeton University Press. These editions preserve the original texts of these important books while presenting them in durable paperback and hardcover editions. The goal of the Princeton Legacy Library is to vastly increase access to the rich scholarly heritage found in the thousands of books published by Princeton University Press since its founding in 1905.
Book Synopsis General Theory of Functions and Integration by : Angus Ellis Taylor
Download or read book General Theory of Functions and Integration written by Angus Ellis Taylor and published by . This book was released on 1965 with total page 472 pages. Available in PDF, EPUB and Kindle. Book excerpt: The real numbers. Point sets and sequences -- Euclidean space. Topology and continuous functions -- Abstract spaces -- The theory of measure -- The Lebesgue integral -- Integration by the Daniell method -- Iterated integrals and Fubini's theorem -- The theory of signed measures -- Functions of one real variable.
Book Synopsis General Theory of Functions and Integration by : Angus E. Taylor
Download or read book General Theory of Functions and Integration written by Angus E. Taylor and published by . This book was released on 1965 with total page 472 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis General Theory of Algebraic Equations by : Etienne Bézout
Download or read book General Theory of Algebraic Equations written by Etienne Bézout and published by Princeton University Press. This book was released on 2009-01-10 with total page 363 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book provides the first English translation of Bezout's masterpiece, the General Theory of Algebraic Equations. It follows, by almost two hundred years, the English translation of his famous mathematics textbooks. Here, Bézout presents his approach to solving systems of polynomial equations in several variables and in great detail. He introduces the revolutionary notion of the "polynomial multiplier," which greatly simplifies the problem of variable elimination by reducing it to a system of linear equations. The major result presented in this work, now known as "Bézout's theorem," is stated as follows: "The degree of the final equation resulting from an arbitrary number of complete equations containing the same number of unknowns and with arbitrary degrees is equal to the product of the exponents of the degrees of these equations." The book offers large numbers of results and insights about conditions for polynomials to share a common factor, or to share a common root. It also provides a state-of-the-art analysis of the theories of integration and differentiation of functions in the late eighteenth century, as well as one of the first uses of determinants to solve systems of linear equations. Polynomial multiplier methods have become, today, one of the most promising approaches to solving complex systems of polynomial equations or inequalities, and this translation offers a valuable historic perspective on this active research field.
Book Synopsis Theories of Integration by : Douglas S. Kurtz
Download or read book Theories of Integration written by Douglas S. Kurtz and published by World Scientific. This book was released on 2004 with total page 286 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents a historical development of the integration theories of Riemann, Lebesgue, Henstock-Kurzweil, and McShane, showing how new theories of integration were developed to solve problems that earlier theories could not handle. It develops the basic properties of each integral in detail and provides comparisons of the different integrals. The chapters covering each integral are essentially independent and can be used separately in teaching a portion of an introductory course on real analysis. There is a sufficient supply of exercises to make the book useful as a textbook.
Book Synopsis A Concise Introduction to the Theory of Integration by : Daniel W Stroock
Download or read book A Concise Introduction to the Theory of Integration written by Daniel W Stroock and published by World Scientific Publishing Company. This book was released on 1990-03-01 with total page 160 pages. Available in PDF, EPUB and Kindle. Book excerpt: Readership: Mathematicians, physicists and engineers.
Book Synopsis A Course on Integration Theory by : Nicolas Lerner
Download or read book A Course on Integration Theory written by Nicolas Lerner and published by Springer. This book was released on 2014-07-09 with total page 504 pages. Available in PDF, EPUB and Kindle. Book excerpt: This textbook provides a detailed treatment of abstract integration theory, construction of the Lebesgue measure via the Riesz-Markov Theorem and also via the Carathéodory Theorem. It also includes some elementary properties of Hausdorff measures as well as the basic properties of spaces of integrable functions and standard theorems on integrals depending on a parameter. Integration on a product space, change of variables formulas as well as the construction and study of classical Cantor sets are treated in detail. Classical convolution inequalities, such as Young's inequality and Hardy-Littlewood-Sobolev inequality are proven. The Radon-Nikodym theorem, notions of harmonic analysis, classical inequalities and interpolation theorems, including Marcinkiewicz's theorem, the definition of Lebesgue points and Lebesgue differentiation theorem are further topics included. A detailed appendix provides the reader with various elements of elementary mathematics, such as a discussion around the calculation of antiderivatives or the Gamma function. The appendix also provides more advanced material such as some basic properties of cardinals and ordinals which are useful in the study of measurability.
Book Synopsis Integration, Measure and Probability by : H. R. Pitt
Download or read book Integration, Measure and Probability written by H. R. Pitt and published by Courier Corporation. This book was released on 2012-01-01 with total page 130 pages. Available in PDF, EPUB and Kindle. Book excerpt: Introductory treatment develops the theory of integration in a general context, making it applicable to other branches of analysis. More specialized topics include convergence theorems and random sequences and functions. 1963 edition.
Book Synopsis Geometric Integration Theory by : Steven G. Krantz
Download or read book Geometric Integration Theory written by Steven G. Krantz and published by Springer Science & Business Media. This book was released on 2008-12-15 with total page 344 pages. Available in PDF, EPUB and Kindle. Book excerpt: This textbook introduces geometric measure theory through the notion of currents. Currents, continuous linear functionals on spaces of differential forms, are a natural language in which to formulate types of extremal problems arising in geometry, and can be used to study generalized versions of the Plateau problem and related questions in geometric analysis. Motivating key ideas with examples and figures, this book is a comprehensive introduction ideal for both self-study and for use in the classroom. The exposition demands minimal background, is self-contained and accessible, and thus is ideal for both graduate students and researchers.
Book Synopsis A Modern Theory of Integration by : Robert G. Bartle
Download or read book A Modern Theory of Integration written by Robert G. Bartle and published by American Mathematical Society. This book was released on 2024-10-25 with total page 474 pages. Available in PDF, EPUB and Kindle. Book excerpt: The theory of integration is one of the twin pillars on which analysis is built. The first version of integration that students see is the Riemann integral. Later, graduate students learn that the Lebesgue integral is ?better? because it removes some restrictions on the integrands and the domains over which we integrate. However, there are still drawbacks to Lebesgue integration, for instance, dealing with the Fundamental Theorem of Calculus, or with ?improper? integrals. This book is an introduction to a relatively new theory of the integral (called the ?generalized Riemann integral? or the ?Henstock-Kurzweil integral?) that corrects the defects in the classical Riemann theory and both simplifies and extends the Lebesgue theory of integration. Although this integral includes that of Lebesgue, its definition is very close to the Riemann integral that is familiar to students from calculus. One virtue of the new approach is that no measure theory and virtually no topology is required. Indeed, the book includes a study of measure theory as an application of the integral. Part 1 fully develops the theory of the integral of functions defined on a compact interval. This restriction on the domain is not necessary, but it is the case of most interest and does not exhibit some of the technical problems that can impede the reader's understanding. Part 2 shows how this theory extends to functions defined on the whole real line. The theory of Lebesgue measure from the integral is then developed, and the author makes a connection with some of the traditional approaches to the Lebesgue integral. Thus, readers are given full exposure to the main classical results. The text is suitable for a first-year graduate course, although much of it can be readily mastered by advanced undergraduate students. Included are many examples and a very rich collection of exercises. There are partial solutions to approximately one-third of the exercises. A complete solutions manual is available separately.
Book Synopsis Integral, Measure and Derivative by : G. E. Shilov
Download or read book Integral, Measure and Derivative written by G. E. Shilov and published by Courier Corporation. This book was released on 2013-05-13 with total page 258 pages. Available in PDF, EPUB and Kindle. Book excerpt: This treatment examines the general theory of the integral, Lebesque integral in n-space, the Riemann-Stieltjes integral, and more. "The exposition is fresh and sophisticated, and will engage the interest of accomplished mathematicians." — Sci-Tech Book News. 1966 edition.
Book Synopsis General Theory Of Employment , Interest And Money by : John Maynard Keynes
Download or read book General Theory Of Employment , Interest And Money written by John Maynard Keynes and published by Atlantic Publishers & Dist. This book was released on 2016-04 with total page 410 pages. Available in PDF, EPUB and Kindle. Book excerpt: John Maynard Keynes is the great British economist of the twentieth century whose hugely influential work The General Theory of Employment, Interest and * is undoubtedly the century's most important book on economics--strongly influencing economic theory and practice, particularly with regard to the role of government in stimulating and regulating a nation's economic life. Keynes's work has undergone significant revaluation in recent years, and "Keynesian" views which have been widely defended for so long are now perceived as at odds with Keynes's own thinking. Recent scholarship and research has demonstrated considerable rivalry and controversy concerning the proper interpretation of Keynes's works, such that recourse to the original text is all the more important. Although considered by a few critics that the sentence structures of the book are quite incomprehensible and almost unbearable to read, the book is an essential reading for all those who desire a basic education in economics. The key to understanding Keynes is the notion that at particular times in the business cycle, an economy can become over-productive (or under-consumptive) and thus, a vicious spiral is begun that results in massive layoffs and cuts in production as businesses attempt to equilibrate aggregate supply and demand. Thus, full employment is only one of many or multiple macro equilibria. If an economy reaches an underemployment equilibrium, something is necessary to boost or stimulate demand to produce full employment. This something could be business investment but because of the logic and individualist nature of investment decisions, it is unlikely to rapidly restore full employment. Keynes logically seizes upon the public budget and government expenditures as the quickest way to restore full employment. Borrowing the * to finance the deficit from private households and businesses is a quick, direct way to restore full employment while at the same time, redirecting or siphoning
Book Synopsis Measure and Integration by : Leonard F. Richardson
Download or read book Measure and Integration written by Leonard F. Richardson and published by John Wiley & Sons. This book was released on 2009-07-01 with total page 255 pages. Available in PDF, EPUB and Kindle. Book excerpt: A uniquely accessible book for general measure and integration, emphasizing the real line, Euclidean space, and the underlying role of translation in real analysis Measure and Integration: A Concise Introduction to Real Analysis presents the basic concepts and methods that are important for successfully reading and understanding proofs. Blending coverage of both fundamental and specialized topics, this book serves as a practical and thorough introduction to measure and integration, while also facilitating a basic understanding of real analysis. The author develops the theory of measure and integration on abstract measure spaces with an emphasis of the real line and Euclidean space. Additional topical coverage includes: Measure spaces, outer measures, and extension theorems Lebesgue measure on the line and in Euclidean space Measurable functions, Egoroff's theorem, and Lusin's theorem Convergence theorems for integrals Product measures and Fubini's theorem Differentiation theorems for functions of real variables Decomposition theorems for signed measures Absolute continuity and the Radon-Nikodym theorem Lp spaces, continuous-function spaces, and duality theorems Translation-invariant subspaces of L2 and applications The book's presentation lays the foundation for further study of functional analysis, harmonic analysis, and probability, and its treatment of real analysis highlights the fundamental role of translations. Each theorem is accompanied by opportunities to employ the concept, as numerous exercises explore applications including convolutions, Fourier transforms, and differentiation across the integral sign. Providing an efficient and readable treatment of this classical subject, Measure and Integration: A Concise Introduction to Real Analysis is a useful book for courses in real analysis at the graduate level. It is also a valuable reference for practitioners in the mathematical sciences.
Book Synopsis Linear Integral Equations by : William Vernon Lovitt
Download or read book Linear Integral Equations written by William Vernon Lovitt and published by . This book was released on 1924 with total page 280 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Lectures on the Theory of Integration by : Ralph Henstock
Download or read book Lectures on the Theory of Integration written by Ralph Henstock and published by World Scientific. This book was released on 1988 with total page 224 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is intended to be self-contained, giving the theory of absolute (equivalent to Lebesgue) and non-absolute (equivalent to Denjoy-Perron) integration by using a simple extension of the Riemann integral. A useful tool for mathematicians and scientists needing advanced integration theory would be a method combining the ideas of the calculus of indefinite integral and Riemann definite integral in such a way that Lebesgue properties can be proved easily.Three important results that have not appeared in any other book distinguish this book from the rest. First a result on limits of sequences under the integral sign, secondly the necessary and sufficient conditions for the various limits under the integral sign and thirdly the application of these results to ordinary differential equations. The present book will give non-absolute integration theory just as easily as the absolute theory, and Stieltjes-type integration too.
