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Michael Steele describes the fundamental topics in mathematical inequalities and their uses. Using the Cauchy-Schwarz inequality as a guide, Steele presents a fascinating collection of problems related to inequalities and coaches readers through solutions, in a style reminiscent of George Polya, by teaching basic concepts and sharpening problem solving skills at the same time. Undergraduate and beginning graduate students in mathematics, theoretical computer science, statistics, engineering, and economics will find the book appropriate for self-study.

Michael Steele describes the fundamental topics in mathematical inequalities and their uses. Using the Cauchy-Schwarz inequality as a guide, Steele presents a fascinating collection of problems related to inequalities and coaches readers through solutions, in a style reminiscent of George Polya, by teaching basic concepts and sharpening problem solving skills at the same time. Undergraduate and beginning graduate students in mathematics, theoretical computer science, statistics, engineering, and economics will find the book appropriate for self-study.

Très bon état général. Envoi rapide et soigné avec suivi. (C23-1)

This clearly written, self-contained volume studies the basic equations of kinetic theory in all of space. It contains up-to-date, state-of-the-art treatments of initial-value problems for the major kinetic equations, including the Boltzmann equation (from rarefied gas dynamics) and the Vlasov-Poisson/Vlasov-Maxwell systems (from plasma physics). This is the only existing book to treat Boltzmann-type problems and Vlasov-type problems together. Although these equations describe very different phenomena, they share the same streaming term. The author proves that solutions starting from a given configuration at an initial time exist for all future times by imposing appropriate hypotheses on the initial values in several important cases. He emphasizes those questions that a mathematician would ask first: Is there a solution to this problem? Is it unique? Can it be numerically approximated?

This book is a complete English translation of Augustin-Louis Cauchy's historic 1823 text (his first devoted to calculus), Résumé des leçons sur le calcul infinitésimal, "Summary of Lectures on the Infinitesimal Calculus," originally written to benefit his École Polytechnique students in Paris. Within this single text, Cauchy succinctly lays out and rigorously develops all of the topics one encounters in an introductory study of the calculus, from his classic definition of the limit to his detailed analysis of the convergence properties of infinite series. In between, the reader will find a full treatment of differential and integral calculus, including the main theorems of calculus and detailed methods of differentiating and integrating a wide variety of functions. Real, single variable calculus is the main focus of the text, but Cauchy spends ample time exploring the extension of his rigorous development to include functions of multiple variables as well as complex functions.This translation maintains the same notation and terminology of Cauchy's original work in the hope of delivering as honest and true a Cauchy experience as possible so that the modern reader can experience his work as it may have been like 200 years ago. This book can be used with advantage today by anyone interested in the history of the calculus and analysis. In addition, it will serve as a particularly valuable supplement to a traditional calculus text for those readers who desire a way to create more texture in a conventional calculus class through the introduction of original historical sources. 

This book is a complete English translation of Augustin-Louis Cauchy's historic 1823 text (his first devoted to calculus), Résumé des leçons sur le calcul infinitésimal, "Summary of Lectures on the Infinitesimal Calculus," originally written to benefit his École Polytechnique students in Paris. Within this single text, Cauchy succinctly lays out and rigorously develops all of the topics one encounters in an introductory study of the calculus, from his classic definition of the limit to his detailed analysis of the convergence properties of infinite series. In between, the reader will find a full treatment of differential and integral calculus, including the main theorems of calculus and detailed methods of differentiating and integrating a wide variety of functions. Real, single variable calculus is the main focus of the text, but Cauchy spends ample time exploring the extension of his rigorous development to include functions of multiple variables as well as complex functions.This translation maintains the same notation and terminology of Cauchy's original work in the hope of delivering as honest and true a Cauchy experience as possible so that the modern reader can experience his work as it may have been like 200 years ago. This book can be used with advantage today by anyone interested in the history of the calculus and analysis. In addition, it will serve as a particularly valuable supplement to a traditional calculus text for those readers who desire a way to create more texture in a conventional calculus class through the introduction of original historical sources. 

This book explores the background of a major intellectual revolution: the rigorous reinterpretation of the calculus undertaken by Augustin-Louis Cauchy and his contemporaries in the first part of the 19th century. Their generation changed the calculus from a method of solving problems to a collection of theorems, based on precise definitions, about limits, continuity, series, derivatives, and integrals. The book shows how Cauchy reshaped inherited 18th-century concepts to create an approach to rigor that we still accept today. In so doing, The Origins of Cauchy's Rigorous Calculus provides fresh insights and a new perspective on the foundations of analysis. After defining rigor and describing the characteristics of 19th-century thinking about analysis, the book examines 18th-century views of the calculus and the manifest lack of interest in the foundations of analysis. The greater part of the book concerns itself with tracing how specific achievements of 18th-century mathematics were transformed by Cauchy into the basis of his rigorous calculus (especially the development of the algebra of inequalities: ideas on limits, continuity, and convergence; and certain 18th-century treatments of the derivative and integral), with the work of Joseph-Louis Lagrange shown to be crucial in the transition to new ways of thinking.

Would well repay study by most theoretical physicists."--Physics Today"An overwhelming influence on subsequent work on the wave equation."--Science Progress"One of the classical treatises on hyperbolic equations."--Royal Naval Scientific ServiceDelivered at Columbia University and the Universities of Rome and Zürich, these lectures represent a pioneering investigation. Jacques Hadamard based his research on prior studies by Riemann, Kirchhoff, and Volterra. He extended and improved Volterra's work, applying its theories relating to spherical and cylindrical waves to all normal hyperbolic equations instead of only to one. Topics include the general properties of Cauchy's problem, the fundamental formula and the elementary solution, equations with an odd number of independent variables, and equations with an even number of independent variables and the method of descent. 1923 ed.

This book explores the background of a major intellectual revolution: the rigorous reinterpretation of the calculus undertaken by Augustin-Louis Cauchy and his contemporaries in the first part of the 19th century. Their generation changed the calculus from a method of solving problems to a collection of theorems, based on precise definitions, about limits, continuity, series, derivatives, and integrals. The book shows how Cauchy reshaped inherited 18th-century concepts to create an approach to rigor that we still accept today. In so doing, The Origins of Cauchy's Rigorous Calculus provides fresh insights and a new perspective on the foundations of analysis. After defining rigor and describing the characteristics of 19th-century thinking about analysis, the book examines 18th-century views of the calculus and the manifest lack of interest in the foundations of analysis. The greater part of the book concerns itself with tracing how specific achievements of 18th-century mathematics were transformed by Cauchy into the basis of his rigorous calculus (especially the development of the algebra of inequalities: ideas on limits, continuity, and convergence; and certain 18th-century treatments of the derivative and integral), with the work of Joseph-Louis Lagrange shown to be crucial in the transition to new ways of thinking.

This is the fourth book of Math Contest Books Series. The book introduces the ways to use Cauchy's Inequalities to solve a variety of math contest problems. The book can be used by students preparing for math competitions such as AMC 10/12, ARML, AIME, and USAMO. Each chapter consists of (1) basic skill and knowledge section with examples, (2) exercise problems, and (3) detailed solutions to all problems. First book of Math Contest Books Series. The Mass Points Method: https://www.amazon.com/Mass-Points-Method-Yongcheng-Chen/dp/1523265884 9th book: Problem Solving Using Auxiliary Lineshttps://www.amazon.com/dp/1975681754 10th book: https://www.amazon.com/Problem-Solving-Using-Vietas-Theorem/dp/1542800056

A great difficulty facing a biographer of Cauchy is that of delineating the curious interplay between the man, his times, and his scientific endeavors. Professor Belhoste has succeeded admirably in meeting this challenge and has thus written a vivid biography that is both readable and informative. His subject stands out as one of the most brilliant, versatile, and prolific fig ures in the annals of science. Nearly two hundred years have now passed since the young Cauchy set about his task of clarifying mathematics, extending it, applying it wherever possible, and placing it on a firm theoretical footing. Through Belhoste's work we are afforded a detailed, rather personalized picture of how a first rate mathematician worked at his discipline - his strivings, his inspirations, his triumphs, his failures, and above all, his conflicts and his errors.

Part explanation of important recent work, and part introduction to some of the techniques of modern partial differential equations, this monograph is a self-contained exposition of the Neumann problem for the Cauchy-Riemann complex and certain of its applications. The authors prove the main existence and regularity theorems in detail, assuming only a knowledge of the basic theory of differentiable manifolds and operators on Hilbert space. They discuss applications to the theory of several complex variables, examine the associated complex on the boundary, and outline other techniques relevant to these problems. In an appendix they develop the functional analysis of differential operators in terms of Sobolev spaces, to the extent it is required for the monograph.

Part explanation of important recent work, and part introduction to some of the techniques of modern partial differential equations, this monograph is a self-contained exposition of the Neumann problem for the Cauchy-Riemann complex and certain of its applications. The authors prove the main existence and regularity theorems in detail, assuming only a knowledge of the basic theory of differentiable manifolds and operators on Hilbert space. They discuss applications to the theory of several complex variables, examine the associated complex on the boundary, and outline other techniques relevant to these problems. In an appendix they develop the functional analysis of differential operators in terms of Sobolev spaces, to the extent it is required for the monograph.

This is the fourth book of Math Contest Books Series. The book introduces the ways to use Cauchy's Inequalities to solve a variety of math contest problems. The book can be used by students preparing for math competitions such as AMC 10/12, ARML, AIME, and USAMO. Each chapter consists of (1) basic skill and knowledge section with examples, (2) exercise problems, and (3) detailed solutions to all problems. First book of Math Contest Books Series. The Mass Points Method: https://www.amazon.com/Mass-Points-Method-Yongcheng-Chen/dp/1523265884 9th book: Problem Solving Using Auxiliary Lineshttps://www.amazon.com/dp/1975681754 10th book: https://www.amazon.com/Problem-Solving-Using-Vietas-Theorem/dp/1542800056

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Presents applications as well as the basic theory of analytic functions of one or several complex variables. The first volume discusses applications and basic theory of conformal mapping and the solution of algebraic and transcendental equations. Volume Two covers topics broadly connected with ordinary differental equations: special functions, integral transforms, asymptotics and continued fractions. Volume Three details discrete fourier analysis, cauchy integrals, construction of conformal maps, univalent functions, potential theory in the plane and polynomial expansions.

Occasion - Bon Etat - Résumé des leçons données à l'École royale polytechnique sur le calcul infinitésimal : Tome premier (1994) - Grand Format

Now in paperback, this remains one of the classic expositions of the theory of wavelets from two of the subject's leading experts. This volume discusses the theory of paradifferential operators and the Cauchy kernel on Lipschitz curves with the emphasis firmly on their connection with wavelet bases. Sparse matrix representations of these operators can be given in terms of wavelet bases that have important applications in image processing and numerical analysis. This method is now widely studied and can be used to tackle a wide variety of problems arising in science and engineering. Put simply, this is an essential purchase for anyone researching the theory of wavelets.

This practical textbook offers solid discussions of the mathematics, clear expositions and wide selection of applications for complex variables. It introduces Cauchy's theorems for polynomials and rational functions in the first chapter, allowing students to progress quickly to applications. Providing a variety of exercises labelled according their level of difficulty, this text: furnishes a systematic treatment of applications to potential theory of particular value to science and engineering students; defines exponential and trigonometric functions as infinite series to display their connection with the corresponding real-valued functions of elementary calculus; clarifies the many values of the logarithm by introducing it as an integral early in the book; and examines Laplace transforms, differential equations, conformal mapping, analytic continuations and Riemann surfaces.;Complex Variables is intended for all undergraduate mathematics, science and engineering students in one-semester courses on complex variables.;A solutions manual is available to instructors only. Requests must be made on official school stationery.

The definitive reference for statistical distributions Continuous Univariate Distributions, Volume 1 offers comprehensive guidance toward the most commonly used statistical distributions, including normal, lognormal, inverse Gaussian, Pareto, Cauchy, gamma distributions and more. Each distribution includes clear definitions and properties, plus methods of inference, applications, algorithms, characterizations, and reference to other related distributions. Organized for easy navigation and quick reference, this book is an invaluable resource for investors, data analysts, or anyone working with statistical distributions on a regular basis.