000			02295nam a22002897a 4500
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020			_a9783030463205
040			_aNISER LIBRARY _beng _cNISER LIBRARY
041			_aEnglish
082			_a517 _bMAG-F
100			_aMagnus, Robert
245			_aFundamental mathematical analysis
260			_aSwitzerland : _bSpringer, _c2020.
300			_axx, 433p.
490			_aSpringer undergraduate mathematics series _x1615-2085
504			_aIncludes index
520			_aThis textbook offers a comprehensive undergraduate course in real analysis in one variable. Taking the view that analysis can only be properly appreciated as a rigorous theory, the book recognises the difficulties that students experience when encountering this theory for the first time, carefully addressing them throughout. Historically, it was the precise description of real numbers and the correct definition of limit that placed analysis on a solid foundation. The book therefore begins with these crucial ideas and the fundamental notion of sequence. Infinite series are then introduced, followed by the key concept of continuity. These lay the groundwork for differential and integral calculus, which are carefully covered in the following chapters. Pointers for further study are included throughout the book, and for the more adventurous there is a selection of "nuggets", exciting topics not commonly discussed at this level. Examples of nuggets include Newton's method, the irrationality of π, Bernoulli numbers, and the Gamma function. Based on decades of teaching experience, this book is written with the undergraduate student in mind. A large number of exercises, many with hints, provide the practice necessary for learning, while the included "nuggets" provide opportunities to deepen understanding and broaden horizons.
650			_aMathematical analysis
650			_aFunctions of a real variable
650			_aFoundations of analysis
650			_aReal analysis
856			_3Table of contents _uhttps://link.springer.com/content/pdf/bfm:978-3-030-46321-2/1
856			_3Reviews _uhttps://www.goodreads.com/book/show/57190259-fundamental-mathematical-analysis#CommunityReviews
942			_2udc _cBK
999			_c35419 _d35419