Fundamental Mathematical Analysis

Robert Magnus

ISBN 10: 3030463206 / ISBN 13: 9783030463205

Editore: Springer, Springer, 2020

Riguardo questo articolo

Druck auf Anfrage Neuware - Printed after ordering - 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 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.

Codice articolo 9783030463205

Dati bibliografici

• Titolo: Fundamental Mathematical Analysis
• Editore: Springer, Springer
• Data di pubblicazione: 2020
• Lingua: Inglese
• ISBN 10: 3030463206
• ISBN 13: 9783030463205
• Rilegatura: Taschenbuch
• Condizione: Neu
• Dimensioni: 235 L x 155 A x 25 P (millimetri) 235 millimetri di larghezza per 155 millimetri di altezza per 25 millimetri di profondità
• Peso: 686 grammi

Descrizione articolo

Riassunto

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 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.

Informazioni sull?autore

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.