Fundamental Mathematical Analysis
Springer International Publishing (Verlag)
978-3-030-46320-5 (ISBN)
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 pi, 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.
Robert Magnus was born in the UK and studied mathematics at the Universities of Cambridge and Sussex. He has taught nearly all subjects associated with analysis and has published papers in the areas of bifurcation theory, catastrophe theory, analytic operator functions and non-linear partial differential equations. Since 1977 he has lived and worked in Iceland.
1 Introduction.- 2 Real Numbers.- 3 Sequences and Series.- 4 Functions and Continuity.- 5 Derivatives and Differentiation.- 6 Integrals and Integration.- 7 The Elementary Transcendental Functions.- 8 The Techniques of Integration.- 9 Complex Numbers.- 10 Complex Sequences and Series.- 11 Function Sequences and Function Series.- 12 Improper Integrals.- Index.
"Fundamental Mathematical Analysis is a complete and wide-ranging text that offers a rigorous introduction to the analysis of real-valued, single-variable functions. This text is well organized and peppered with insight and mathematical nuggets. ... I found it an enjoyable read and am confident that a well-prepared student would gain a tremendous deal from this text." (John Ross, MAA Reviews, May 29, 2021)
| Erscheinungsdatum | 18.07.2020 |
|---|---|
| Reihe/Serie | Springer Undergraduate Mathematics Series |
| Zusatzinfo | XX, 433 p. 35 illus., 11 illus. in color. |
| Verlagsort | Cham |
| Sprache | englisch |
| Maße | 155 x 235 mm |
| Gewicht | 694 g |
| Themenwelt | Mathematik / Informatik ► Mathematik ► Analysis |
| Schlagworte | continuous function • Differentiation • Foundations of analysis • functions of a real variable • Integration • Real analysis • Sequences and Series |
| ISBN-10 | 3-030-46320-6 / 3030463206 |
| ISBN-13 | 978-3-030-46320-5 / 9783030463205 |
| Zustand | Neuware |
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