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OverviewThis book develops the theory of multivariable analysis, building on the single variable foundations established in the companion volume, Real Analysis: Foundations and Functions of One Variable. Together, these volumes form the first English edition of the popular Hungarian original, Valós Analízis I & II, based on courses taught by the authors at Eötvös Loránd University, Hungary, for more than 30 years. Numerous exercises are included throughout, offering ample opportunities to master topics by progressing from routine to difficult problems. Hints or solutions to many of the more challenging exercises make this book ideal for independent study, or further reading. Intended as a sequel to a course in single variable analysis, this book builds upon and expands these ideas into higher dimensions. The modular organization makes this text adaptable for either a semester or year-long introductory course. Topics include: differentiation and integration of functions of several variables; infinite numerical series; sequences and series of functions; and applications to other areas of mathematics. Many historical notes are given and there is an emphasis on conceptual understanding and context, be it within mathematics itself or more broadly in applications, such as physics. By developing the student’s intuition throughout, many definitions and results become motivated by insights from their context. Full Product DetailsAuthor: Miklós Laczkovich , Vera T. Sós , Gergely BálintPublisher: Springer-Verlag New York Inc. Imprint: Springer-Verlag New York Inc. Edition: Softcover reprint of the original 1st ed. 2017 Weight: 0.617kg ISBN: 9781493984640ISBN 10: 1493984640 Pages: 392 Publication Date: 30 August 2018 Audience: Professional and scholarly , Professional & Vocational Format: Paperback Publisher's Status: Active Availability: Manufactured on demand  We will order this item for you from a manufactured on demand supplier. Language: English Table of ContentsFunctions of Several Variables.- 1. R^p → R functions.- 2. R^p → R^q functions.- 3. The Jordan Measure.- 4. The Integral of Multivariable Functions I.- 5. The Integral of Multivariable Functions II.- 6. Infinite Series.- 7. Sequences and Series of Functions.- 8. Miscellaneous Topics.- 9. Hint, Solutions.- References.- Index.- Notation.ReviewsThe explicit intent of the authors is to present material gradually, and to develop precision based on intuition with the help of well-designed examples. The book contains 600 exercises. In my opinion this interesting book represents an alternative viewpoint in real analysis. (Zbigniew Grande, Mathematical Reviews, August, 2018) Author InformationMiklós Laczkovich is a member of the Hungarian Academy of Sciences and professor emeritus at Eötvös Loránd University Budapest and University College London. He was awarded the Ostrowski Prize in 1993 and the Széchenyi Prize in 1998. Vera T. Sós is a member of the Hungarian Academy of Sciences and professor emeritus at Eötvös Loránd Univesity Budapest and the Alfred Renyi Mathematical Institute of the Hungarian Academy of Sciences. She was awarded the Széchenyi Prize in 1997. Tab Content 6Author Website:Countries AvailableAll regions |
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