Fundamental Mathematical Analysis

1. Auflage 2020
ISBN: 978-3-030-46320-5
Verlag: Springer International Publishing

Buch, Englisch, 433 Seiten, Paperback, Format (B × H): 155 mm x 235 mm, Gewicht: 686 g

Reihe: Springer Undergraduate Mathematics Series

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 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 p, 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.

Zielgruppe

Lower undergraduate

Autoren/Hrsg.

Magnus, Robert

Fachgebiete

• Mathematik | Informatik Mathematik Mathematische Analysis Elementare Analysis und Allgemeine Begriffe
• Mathematik | Informatik Mathematik Mathematische Analysis Reelle Analysis

Inhaltsverzeichnis

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.

Über Autor(innen)

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.