Description
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 , 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.
About the Author
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.
Reviews
"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)
Book Information
ISBN 9783030463205
Author Robert Magnus
Format Paperback
Page Count 433
Imprint Springer Nature Switzerland AG
Publisher Springer Nature Switzerland AG
