| 書(shū)目名稱(chēng) | Fundamental Mathematical Analysis | | 編輯 | Robert Magnus | | 視頻video | http://file.papertrans.cn/351/350002/350002.mp4 | | 概述 | Recognises and addresses student difficulties.A selection of special topics (“nuggets”) sets it apart from existing texts.Includes a large number of exercises with hints | | 叢書(shū)名稱(chēng) | Springer Undergraduate Mathematics Series | | 圖書(shū)封面 |  | | 描述 | This 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 ofsequence. 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, pro | | 出版日期 | Textbook 2020 | | 關(guān)鍵詞 | Differentiation; Integration; Sequences and series; Continuous function; Real analysis; Foundations of an | | 版次 | 1 | | doi | https://doi.org/10.1007/978-3-030-46321-2 | | isbn_softcover | 978-3-030-46320-5 | | isbn_ebook | 978-3-030-46321-2Series ISSN 1615-2085 Series E-ISSN 2197-4144 | | issn_series | 1615-2085 | | copyright | The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Switzerl |
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