This second English edition of a very popular two-volume work presents a thorough first course in analysis, leading from real numbers to such advanced topics as differential forms on manifolds; asymptotic methods; Fourier, Laplace, and Legendre transforms; elliptic functions; and distributions. Especially notable in this course are the clearly expressed orientation toward the natural sciences and the informal exploration of the essence and the roots of the basic concepts and theorems of calculus. Clarity of exposition is matched by a wealth of instructive exercises, problems, and fresh applications to areas seldom touched on in textbooks on real analysis. The main difference between the second and first English editions is the addition of a series of appendices to each volume. There are six of them in the first volume and five in the second. The subjects of these appendices are diverse. They are meant to be useful to both students (in mathematics and physics) and teachers, who may be motivated by different goals. Some of the appendices are surveys, both prospective and retrospective. The final survey establishes important conceptual connections between analysis and other parts of mathematics. This second volume presents classical analysis in its current form as part of a unified mathematics. It shows how analysis interacts with other modern fields of mathematics such as algebra, differential geometry, differential equations, complex analysis, and functional analysis. This book provides a firm foundation for advanced work in any of these directions.

This second edition of a very popular two-volume work presents a thorough first course in analysis, leading from real numbers to such advanced topics as differential forms on manifolds; asymptotic methods; Fourier, Laplace, and Legendre transforms; elliptic functions; and distributions. Especially notable in this course are the clearly expressed orientation toward the natural sciences and the informal exploration of the essence and the roots of the basic concepts and theorems of calculus. Clarity of exposition is matched by a wealth of instructive exercises, problems, and fresh applications to areas seldom touched on in textbooks on real analysis. The main difference between the second and first editions is the addition of a series of appendices to each volume. There are six of them in the first volume and five in the second. The subjects of these appendices are diverse. They are meant to be useful to both students (in mathematics and physics) and teachers, who may be motivated by different goals. Some of the appendices are surveys, both prospective and retrospective. The final survey establishes important conceptual connections between analysis and other parts of mathematics. The first volume constitutes a complete course in one-variable calculus along with the multivariable differential calculus elucidated in an up-to-date, clear manner, with a pleasant geometric and natural sciences flavor.

This second English edition of a very popular two-volume work presents a thorough first course in analysis, leading from real numbers to such advanced topics as differential forms on manifolds; asymptotic methods; Fourier, Laplace, and Legendre transforms; elliptic functions; and distributions. Especially notable in this course are the clearly expressed orientation toward the natural sciences and the informal exploration of the essence and the roots of the basic concepts and theorems of calculus. Clarity of exposition is matched by a wealth of instructive exercises, problems, and fresh applications to areas seldom touched on in textbooks on real analysis. The main difference between the second and first English editions is the addition of a series of appendices to each volume. There are six of them in the first volume and five in the second. The subjects of these appendices are diverse. They are meant to be useful to both students (in mathematics and physics) and teachers, who may be motivated by different goals. Some of the appendices are surveys, both prospective and retrospective. The final survey establishes important conceptual connections between analysis and other parts of mathematics. This second volume presents classical analysis in its current form as part of a unified mathematics. It shows how analysis interacts with other modern fields of mathematics such as algebra, differential geometry, differential equations, complex analysis, and functional analysis. This book provides a firm foundation for advanced work in any of these directions.

This second edition of a very popular two-volume work presents a thorough first course in analysis, leading from real numbers to such advanced topics as differential forms on manifolds; asymptotic methods; Fourier, Laplace, and Legendre transforms; elliptic functions; and distributions. Especially notable in this course are the clearly expressed orientation toward the natural sciences and the informal exploration of the essence and the roots of the basic concepts and theorems of calculus. Clarity of exposition is matched by a wealth of instructive exercises, problems, and fresh applications to areas seldom touched on in textbooks on real analysis. The main difference between the second and first editions is the addition of a series of appendices to each volume. There are six of them in the first volume and five in the second. The subjects of these appendices are diverse. They are meant to be useful to both students (in mathematics and physics) and teachers, who may be motivated by different goals. Some of the appendices are surveys, both prospective and retrospective. The final survey establishes important conceptual connections between analysis and other parts of mathematics. The first volume constitutes a complete course in one-variable calculus along with the multivariable differential calculus elucidated in an up-to-date, clear manner, with a pleasant geometric and natural sciences flavor.

This softcover edition of a very popular two-volume work presents a thorough first course in analysis, leading from real numbers to such advanced topics as differential forms on manifolds, asymptotic methods, Fourier, Laplace, and Legendre transforms, elliptic functions and distributions. Especially notable in this course is the clearly expressed orientation toward the natural sciences and its informal exploration of the essence and the roots of the basic concepts and theorems of calculus. Clarity of exposition is matched by a wealth of instructive exercises, problems and fresh applications to areas seldom touched on in real analysis books.

The first volume constitutes a complete course on one-variable calculus along with the multivariable differential calculus elucidated in an up-to-day, clear manner, with a pleasant geometric flavor.

Like all of Vladimir Arnold's books, this book is full of geometric insight. Arnold illustrates every principle with a figure. This book aims to cover the most basic parts of the subject and confines itself largely to the Cauchy and Neumann problems for the classical linear equations of mathematical physics, especially Laplace's equation and the wave equation, although the heat equation and the Korteweg-de Vries equation are also discussed. Physical intuition is emphasized. A large number of problems are sprinkled throughout the book, and a full set of problems from examinations given in Moscow are included at the end. Some of these problems are quite challenging! What makes the book unique is Arnold's particular talent at holding a topic up for examination from a new and fresh perspective. He likes to blow away the fog of generality that obscures so much mathematical writing and reveal the essentially simple intuitive ideas underlying the subject. No other mathematical writer does this quite so well as Arnold.

A searing Southern story about confronting the difference between the family you're born into and the family you choose, from the acclaimed author of How to Bury Your Brother Lex fled Memphis years ago, making ends meet with odd jobs teaching English around the world. She only returns when she has no choice, when her godmother presents her with a bargain she can't refuse. Lex has never understood her mother, who died tragically right before Lex's college graduation, but now she's got a chance to read her journals, to try and figure out what sent her mother spiraling all those years ago. The Memphis that Lex inhabits is more bourbon and bbq joint than sweet tea on front porches, and as she pieces together the Memphis her mother knew, seeing the lure of the world through her mother's lush writing, she must confront more of her own past and the people she left behind. Once all is laid bare, Lex must decide for herself: What is the true meaning of family?

A collection of new essays treating the most important aspects of the work of the most famous late Romantic, Heinrich Heine. As the most prominent German-Jewish Romantic writer, Heinrich Heine (1797-1856) became a focal point for much of the tension generated by the Jewish assimilation to German culture in a time marked by a growing emphasis on the shared ancestry of the German Volk. As both an ingenious composer of Romantic verse and the originator of modernist German prose, he defied nationalist-Romantic concepts of creative genius that grounded German greatness in an idealist tradition of Dichter und Denker. And as a brash, often reckless champion of freedom and social justice, he challenged not only the reactionary ruling powers of Restoration Germany but also the incipient nationalistideology that would have fateful consequences for the new Germany--consequences he often portended with a prophetic vision born of his own experience. Reaching to the heart of the `German question,' the controversies surrounding Heine have been as intense since his death as they were in his own lifetime, often serving as an acid test for important questions of national and social consciousness. This new volume of essays by scholars from Germany, Britain, Canada, and the United States offers new critical insights on key recurring issues in his work: the symbiosis of German and Jewish culture; emerging nationalism among the European peoples; critical views of Romanticism and modern philosophy; European culture on the threshold to modernity; irony, wit, and self-critique as requisite elements of a modern aesthetic; changing views on teleology and the dialectics of history; and final thoughts and reconsiderations from his last, prolonged years in a sickbed. Contributors: Michael Perraudin, Paul Peters, Roger F. Cook, Willi Goetschel, Gerhard Hoehn, Paul Reitter, Robert C. Holub, Jeffrey Grossman, Anthony Phelan, Joseph A. Kruse, and George F. Peters. Roger F. Cook is Professor of German at the University of Missouri, Columbia.

The Soviet school, one of the glories of twentieth-century mathematics, faced a serious crisis in the summer of 1936. It was suffering from internal strains due to generational conflicts between the young talents and the old establishment. At the same time, Soviet leaders (including Stalin himself) were bent on ``Sovietizing'' all of science in the USSR by requiring scholars to publish their works in Russian in the Soviet Union, ending the nearly universal practice of publishing in the West. A campaign to ``Sovietize'' mathematics in the USSR was launched with an attack on Nikolai Nikolaevich Luzin, the leader of the Soviet school of mathematics, in Pravda. Luzin was fortunate in that only a few of the most ardent ideologues wanted to destroy him utterly. As a result, Luzin, though humiliated and frightened, was allowed to make a statement of public repentance and then let off with a relatively mild reprimand. A major factor in his narrow escape was the very abstractness of his research area (descriptive set theory), which was difficult to incorporate into a propaganda campaign aimed at the broader public. The present book contains the transcripts of five meetings of the Academy of Sciences commission charged with investigating the accusations against Luzin, meetings held in July of 1936. Ancillary material from the Soviet press of the time is included to place these meetings in context.

This book has three main goals. First, it explores a selection of topics from the early period of the theory of relativity, focusing on particular aspects that are interesting or unusual. These include the twin paradox; relativistic mechanics and its interaction with Maxwell's laws; the earliest triumphs of general relativity relating to the orbit of Mercury and the deflection of light passing near the sun; and the surprising bizarre metric of Kurt Goedel, in which time travel is possible. Second, it provides an exposition of the differential geometry needed to understand these topics on a level that is intended to be accessible to those with just two years of university-level mathematics as background. Third, it reflects on the historical development of the subject and its significance for our understanding of what reality is and how we can know about the physical universe. The book also takes note of historical prefigurations of relativity, such as Euler's 1744 result that a particle moving on a surface and subject to no tangential acceleration will move along a geodesic, and the work of Lorentz and Poincare on space-time coordinate transformations between two observers in motion at constant relative velocity. The book is aimed at advanced undergraduate mathematics, science, and engineering majors (and, of course, at any interested person who knows a little university-level mathematics). The reader is assumed to know the rudiments of advanced calculus, a few techniques for solving differential equations, some linear algebra, and basics of set theory and groups.

Probabilistic risk analysis aims to quantify the risk caused by high technology installations in situations where classical statistical analysis is difficult or impossible. This book discusses the fundamental notion of uncertainty, its relationship with probability, and the limits to the quantification of uncertainty. Drawing on extensive experience in the theory and applications of risk analysis, the authors focus on the conceptual and mathematical foundations underlying the quantification, interpretation and management of risk. They cover standard topics as well as important new subjects such as the use of expert judgment and uncertainty propagation.

As the most prominent German-Jewish Romantic writer, Heinrich Heine (1797-1856) became a focal point for much of the tension generated by the Jewish assimilation to German culture in a time marked by a growing emphasis on the shared ancestry of the German Volk. As both an ingenious composer of Romantic verse and the originator of modernist German prose, he defied nationalist-Romantic concepts of creative genius that grounded German greatness in an idealist tradition of Dichter und Denker. And as a brash, often reckless champion of freedom and social justice, he challenged not only the reactionary ruling powers of Restoration Germany but also the incipient nationalist ideology that would have fateful consequences for the new Germany--consequences he often portended with a prophetic vision born of his own experience. Reaching to the heart of the German question, ' the controversies surrounding Heine have been as intense since his death as they were in his own lifetime, often serving as an acid test for important questions of national and social consciousness. This new volume of essays by scholars from Germany, Britain, Canada, and the United States offers new critical insights on key recurring issues in his work: the symbiosis of German and Jewish culture; emerging nationalism among the European peoples; critical views of Romanticism and modern philosophy; European culture on the threshold to modernity; irony, wit, and self-critique as requisite elements of a modern aesthetic; changing views on teleology and the dialectics of history; and final thoughts and reconsiderations from his last, prolonged years in a sickbed. Contributors: Michael Perraudin, Paul Peters, Roger F. Cook, Willi Goetschel, Gerhard Hohn, Paul Reitter, Robert C. Holub, Jeffrey Grossman, Anthony Phelan, Joseph A. Kruse, and George F. Peters. Roger F. Cook is professor of German at the University of Missouri, Columbia.