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Author: Robert E. Bradley
Publisher: Springer Science & Business Media
ISBN: 1441905499
Category : Mathematics
Languages : en
Pages : 416
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Book Description
In 1821, Augustin-Louis Cauchy (1789-1857) published a textbook, the Cours d’analyse, to accompany his course in analysis at the Ecole Polytechnique. It is one of the most influential mathematics books ever written. Not only did Cauchy provide a workable definition of limits and a means to make them the basis of a rigorous theory of calculus, but he also revitalized the idea that all mathematics could be set on such rigorous foundations. Today, the quality of a work of mathematics is judged in part on the quality of its rigor, and this standard is largely due to the transformation brought about by Cauchy and the Cours d’analyse. For this translation, the authors have also added commentary, notes, references, and an index.
Author: Robert E. Bradley
Publisher: Springer Science & Business Media
ISBN: 1441905499
Category : Mathematics
Languages : en
Pages : 416
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Book Description
In 1821, Augustin-Louis Cauchy (1789-1857) published a textbook, the Cours d’analyse, to accompany his course in analysis at the Ecole Polytechnique. It is one of the most influential mathematics books ever written. Not only did Cauchy provide a workable definition of limits and a means to make them the basis of a rigorous theory of calculus, but he also revitalized the idea that all mathematics could be set on such rigorous foundations. Today, the quality of a work of mathematics is judged in part on the quality of its rigor, and this standard is largely due to the transformation brought about by Cauchy and the Cours d’analyse. For this translation, the authors have also added commentary, notes, references, and an index.
Author: Panos M Pardalos
Publisher: World Scientific
ISBN: 9811267057
Category : Mathematics
Languages : en
Pages : 958
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Book Description
This comprehensive volume presents essential mathematical results devoted to topics of mathematical analysis, differential equations and their various applications. It focuses on differential operators, Wardowski maps, low-oscillation functions, Galois and Pataki connections, Hardy-type inequalities, to name just a few.Effort has been made for this unique title to have an interdisciplinary flavor and features several applications such as in tomography, elastic scattering, fluid mechanics, etc.This work could serve as a useful reference text to benefit professionals, academics and graduate students working in theoretical computer science, computer mathematics, and general applied mathematics.
Author: Enrique A. González-Velasco
Publisher: Springer Science & Business Media
ISBN: 0387921540
Category : Mathematics
Languages : en
Pages : 479
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Book Description
This book offers an accessible and in-depth look at some of the most important episodes of two thousand years of mathematical history. Beginning with trigonometry and moving on through logarithms, complex numbers, infinite series, and calculus, this book profiles some of the lesser known but crucial contributors to modern day mathematics. It is unique in its use of primary sources as well as its accessibility; a knowledge of first-year calculus is the only prerequisite. But undergraduate and graduate students alike will appreciate this glimpse into the fascinating process of mathematical creation. The history of math is an intercontinental journey, and this book showcases brilliant mathematicians from Greece, Egypt, and India, as well as Europe and the Islamic world. Several of the primary sources have never before been translated into English. Their interpretation is thorough and readable, and offers an excellent background for teachers of high school mathematics as well as anyone interested in the history of math.
Author: Dean Corbae
Publisher: Princeton University Press
ISBN: 1400833086
Category : Business & Economics
Languages : en
Pages : 696
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Book Description
Providing an introduction to mathematical analysis as it applies to economic theory and econometrics, this book bridges the gap that has separated the teaching of basic mathematics for economics and the increasingly advanced mathematics demanded in economics research today. Dean Corbae, Maxwell B. Stinchcombe, and Juraj Zeman equip students with the knowledge of real and functional analysis and measure theory they need to read and do research in economic and econometric theory. Unlike other mathematics textbooks for economics, An Introduction to Mathematical Analysis for Economic Theory and Econometrics takes a unified approach to understanding basic and advanced spaces through the application of the Metric Completion Theorem. This is the concept by which, for example, the real numbers complete the rational numbers and measure spaces complete fields of measurable sets. Another of the book's unique features is its concentration on the mathematical foundations of econometrics. To illustrate difficult concepts, the authors use simple examples drawn from economic theory and econometrics. Accessible and rigorous, the book is self-contained, providing proofs of theorems and assuming only an undergraduate background in calculus and linear algebra. Begins with mathematical analysis and economic examples accessible to advanced undergraduates in order to build intuition for more complex analysis used by graduate students and researchers Takes a unified approach to understanding basic and advanced spaces of numbers through application of the Metric Completion Theorem Focuses on examples from econometrics to explain topics in measure theory
Author: Craig Smorynski
Publisher: Springer
ISBN: 3319529560
Category : Mathematics
Languages : en
Pages : 504
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Book Description
This book is about the rise and supposed fall of the mean value theorem. It discusses the evolution of the theorem and the concepts behind it, how the theorem relates to other fundamental results in calculus, and modern re-evaluations of its role in the standard calculus course. The mean value theorem is one of the central results of calculus. It was called “the fundamental theorem of the differential calculus” because of its power to provide simple and rigorous proofs of basic results encountered in a first-year course in calculus. In mathematical terms, the book is a thorough treatment of this theorem and some related results in the field; in historical terms, it is not a history of calculus or mathematics, but a case study in both. MVT: A Most Valuable Theorem is aimed at those who teach calculus, especially those setting out to do so for the first time. It is also accessible to anyone who has finished the first semester of the standard course in the subject and will be of interest to undergraduate mathematics majors as well as graduate students. Unlike other books, the present monograph treats the mathematical and historical aspects in equal measure, providing detailed and rigorous proofs of the mathematical results and even including original source material presenting the flavour of the history.
Author: Dragoslav S. Mitrinovic
Publisher: Springer Science & Business Media
ISBN: 9401710430
Category : Mathematics
Languages : en
Pages : 739
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Book Description
This volume presents a comprehensive compendium of classical and new inequalities as well as some recent extensions to well-known ones. Variations of inequalities ascribed to Abel, Jensen, Cauchy, Chebyshev, Hölder, Minkowski, Stefferson, Gram, Fejér, Jackson, Hardy, Littlewood, Po'lya, Schwarz, Hadamard and a host of others can be found in this volume. The more than 1200 cited references include many from the last ten years which appear in a book for the first time. The 30 chapters are all devoted to inequalities associated with a given classical inequality, or give methods for the derivation of new inequalities. Anyone interested in equalities, from student to professional, will find their favorite inequality and much more.
Author: Jenny P. Glusker
Publisher: John Wiley & Sons
ISBN: 9780471185437
Category : Science
Languages : en
Pages : 876
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Book Description
Anhand verschiedener Beispiele zeigen die Autoren die Bedeutung der Kristallographie für Chemie und Biochemie auf und bieten somit eine gute Zusammenfassung der allgemeinen Prinzipien der Kristallstrukturanalyse. Zum einen sollen Interessierte, die diese Methode nicht selbst durchführen, in die Lage versetzt werden, deren Ergebnisse zu interpretieren. Zum anderen wird dem Leser deutlich gemacht, welche Bedeutung die ungeheure Datenmenge, die sich aus dieser Methode ergibt, einerseits für die Chemie sowie andererseits für die Biochemie hat. Das Buch ist verständlich geschrieben und mit zahlreichen Abbildungen versehen. Durch die Darstellung der Kristallstrukturanalyse im Vergleich zu anderen Methoden ist das Werk auch besonders für fortgeschrittene Studenten geeignet, die sich mit der Kristallographie vertraut machen wollen.
Author: Apostolos Doxiadis
Publisher: Princeton University Press
ISBN: 0691149046
Category : Mathematics
Languages : en
Pages : 592
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Book Description
Why narrative is essential to mathematics Circles Disturbed brings together important thinkers in mathematics, history, and philosophy to explore the relationship between mathematics and narrative. The book's title recalls the last words of the great Greek mathematician Archimedes before he was slain by a Roman soldier—"Don't disturb my circles"—words that seem to refer to two radically different concerns: that of the practical person living in the concrete world of reality, and that of the theoretician lost in a world of abstraction. Stories and theorems are, in a sense, the natural languages of these two worlds—stories representing the way we act and interact, and theorems giving us pure thought, distilled from the hustle and bustle of reality. Yet, though the voices of stories and theorems seem totally different, they share profound connections and similarities. A book unlike any other, Circles Disturbed delves into topics such as the way in which historical and biographical narratives shape our understanding of mathematics and mathematicians, the development of "myths of origins" in mathematics, the structure and importance of mathematical dreams, the role of storytelling in the formation of mathematical intuitions, the ways mathematics helps us organize the way we think about narrative structure, and much more. In addition to the editors, the contributors are Amir Alexander, David Corfield, Peter Galison, Timothy Gowers, Michael Harris, David Herman, Federica La Nave, G.E.R. Lloyd, Uri Margolin, Colin McLarty, Jan Christoph Meister, Arkady Plotnitsky, and Bernard Teissier.
Author: Ralph Henstock
Publisher: World Scientific
ISBN: 9814551805
Category : Mathematics
Languages : en
Pages : 223
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Book Description
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.
Author: George A. Jr. Baker
Publisher: Elsevier
ISBN: 0323156150
Category : Science
Languages : en
Pages : 319
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Book Description
Essentials of Padé Approximants
