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This text places the basic ideas of real analysis and numerical analysis together in an applied setting that is both accessible and motivational to young students. The essentials of real analysis are presented in the context of a fundamental problem of applied mathematics, which is to approximate the solution of a physical model. The framework of existence, uniqueness, and methods to approximate solutions of model equations is sufficiently broad to introduce and motivate all the basic ideas of real analysis. The book includes background and review material, numerous examples, visualizations and alternate explanations of some key ideas, and a variety of exercises ranging from simple computations to analysis and estimates to computations on a computer.
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This book attempts to place the basic ideas of real analysis and numerical analysis together in an applied setting that is both accessible and motivational to young students. The essentials of real analysis are presented in the context of a fundamental problem of applied mathematics, which is to approximate the solution of a physical model. The framework of existence, uniqueness, and methods to approximate solutions of model equations is sufficiently broad to introduce and motivate all the basic ideas of real analysis. The book includes background and review material, numerous examples, visualizations and alternate explanations of some key ideas, and a variety of exercises ranging from simple computations to analysis and estimates to computations on a computer. The book can be used in an honor calculus sequence typically taken by freshmen planning to major in engineering, mathematics, and science, or in an introductory course in rigorous real analysis offered to mathematics majors.
Donald Estep is Professor of Mathematics at Colorado State University. He is the author of Computational Differential Equations, with K. Eriksson, P. Hansbo and C. Johnson (Cambridge University Press 1996) and Estimating the Error of Numerical Solutions of Systems of Nonlinear Reaction-Diffusion Equations with M. Larson and R. Williams (A.M.S. Memoirs, 2000), and recently co-edited Collected Lectures on the Preservation of Stability under Discretization, with Simon Tavener (S.I.A.M., 2002), as well as numerous research articles. His research interests include computational error estimation and adaptive finite element methods, numerical solution of evolutionary problems, and computational investigation of physical models.
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Practical Analysis in One Variable (Undergraduate Texts in Mathematics)
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Condizione: New. Dieser Artikel ist ein Print on Demand Artikel und wird nach Ihrer Bestellung fuer Sie gedruckt. This text places the basic ideas of real analysis and numerical analysis together in an applied setting that is both accessible and motivational to young students. The essentials of real analysis are presented in the context of a fundamental problem of appl. Codice articolo 5912563
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Buch. Condizione: Neu. This item is printed on demand - it takes 3-4 days longer - Neuware -This book attempts to place the basic ideas of real analysis and numerical analysis together in an applied setting that is both accessible and motivational to young students. The essentials of real analysis are presented in the context of a fundamental problem of applied mathematics, which is to approximate the solution of a physical model. The framework of existence, uniqueness, and methods to approximate solutions of model equations is sufficiently broad to introduce and motivate all the basic ideas of real analysis. The book includes background and review material, numerous examples, visualizations and alternate explanations of some key ideas, and a variety of exercises ranging from simple computations to analysis and estimates to computations on a computer. The book can be used in an honor calculus sequence typically taken by freshmen planning to major in engineering, mathematics, and science, or in an introductory course in rigorous real analysis offered to mathematics majo rs. Students who work through the proofs and solve the practical problems in this book will develop a 'hands-on' understanding of analysis that will serve them well in the future. 652 pp. Englisch. Codice articolo 9780387954844
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Practical Analysis in One Variable
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Springer New York, Springer US Okt 2002, 2002
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Buch. Condizione: Neu. Neuware -Background I was an eighteen-year-old freshman when I began studying analysis. I had arrived at Columbia University ready to major in physics or perhaps engineering. But my seduction into mathematics began immediately with Lipman Bers¿ calculus course, which stood supreme in a year of exciting classes. Then after the course was over, Professor Bers called me into his o ce and handed me a small blue book called Principles of Mathematical Analysis by W. Rudin. He told me that if I could read this book over the summer,understandmostofit,andproveitbydoingmostoftheproblems, then I might have a career as a mathematician. So began twenty years of struggle to master the ideas in ¿Little Rudin. ¿ I began because of a challenge to my ego but this shallow reason was quickly forgotten as I learned about the beauty and the power of analysis that summer. Anyone who recalls taking a ¿serious¿ mathematics course for the rst time will empathize with my feelings about this new world into which I fell. In school, I restlessly wandered through complex analysis, analyticnumbertheory,andpartialdi erentialequations,beforeeventually settling in numerical analysis. But underlying all of this indecision was an ever-present and ever-growing appreciation of analysis. An appreciation thatstillsustainsmyintellectevenintheoftencynicalworldofthemodern academic professional. But developing this appreciation did not come easy to me, and the p- sentation in this book is motivated by my struggles to understand the viii Preface most basic concepts of analysis. To paraphrase J.Springer Verlag GmbH, Tiergartenstr. 17, 69121 Heidelberg 652 pp. Englisch. Codice articolo 9780387954844
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Buch. Condizione: Neu. Druck auf Anfrage Neuware - Printed after ordering - Background I was an eighteen-year-old freshman when I began studying analysis. I had arrived at Columbia University ready to major in physics or perhaps engineering. But my seduction into mathematics began immediately with Lipman Bers' calculus course, which stood supreme in a year of exciting classes. Then after the course was over, Professor Bers called me into his o ce and handed me a small blue book called Principles of Mathematical Analysis by W. Rudin. He told me that if I could read this book over the summer,understandmostofit,andproveitbydoingmostoftheproblems, then I might have a career as a mathematician. So began twenty years of struggle to master the ideas in 'Little Rudin. ' I began because of a challenge to my ego but this shallow reason was quickly forgotten as I learned about the beauty and the power of analysis that summer. Anyone who recalls taking a 'serious' mathematics course for the rst time will empathize with my feelings about this new world into which I fell. In school, I restlessly wandered through complex analysis, analyticnumbertheory,andpartialdi erentialequations,beforeeventually settling in numerical analysis. But underlying all of this indecision was an ever-present and ever-growing appreciation of analysis. An appreciation thatstillsustainsmyintellectevenintheoftencynicalworldofthemodern academic professional. But developing this appreciation did not come easy to me, and the p- sentation in this book is motivated by my struggles to understand the viii Preface most basic concepts of analysis. To paraphrase J. Codice articolo 9780387954844
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