A Companion to Analysis

Erscheinungsjahr 2003
ISBN: 978-0-8218-3447-3
Verlag: American Mathematical Society

Buch, Englisch, 590 Seiten

Roughly corresponding to 60 to 70 hours worth of lectures on rigorous analysis at Cambridge (UK), this mathematical treatise aims to provide the foundations for later courses in functional analysis, differential geometry, and measure theory. Approaching the topic from the perspective of pure mathema

Many students acquire knowledge of a large number of theorems and methods of calculus without being able to say how they work together. This book provides those students with the coherent account that they need. A Companion to Analysis explains the proble

The real line; A first philosophical interlude; Other versions of the fundamental axiom; Higher dimensions; Sums and suchlike; Differentiation; Local Taylor theorems; The Riemann integral; Developments and limitations of the Riemann integral; Metric spaces; Complete metric spaces; Contraction mappings and differential equations; Inverse and implicit functions; Completion; Appendices; Executive summary; Exercises; Bibliography; Index; The real line; A first philosophical interlude; Other versions of the fundamental axiom; Higher dimensions; Sums and suchlike; Differentiation; Local Taylor theorems; The Riemann integral; Developments and limitations of the Riemann integral; Metric spaces; Complete metric spaces; Contraction mappings and differential equations; Inverse and implicit functions; Completion; Appendices; Executive summary; Exercises; Bibliography; Index

Autoren/Hrsg.

K¿rner, T. W.

Fachgebiete

• Mathematik | Informatik Mathematik Mathematische Analysis Funktionentheorie, Komplexe Analysis
• Mathematik | Informatik Mathematik Mathematische Analysis Elementare Analysis und Allgemeine Begriffe
• Mathematik | Informatik Mathematik Mathematische Analysis Funktionalanalysis