The purpose is to provide development of the subject-matter which is well motivated, rigorous and at the same time not too pedantic. Most of the hard theorems which are either omitted or treated rather skimply in many texts in advanced analysis have been proved with care. Some of them are ordinarily considered too difficult for a standard course in calculus but too elementary for a course of analysis. With the inclusion of those theorems, the book attempts to fill the gap and to make the transfer from elementary calculus to advanced course in analysis as smooth as possible.
Sprache
Verlagsort
Zielgruppe
Für höhere Schule und Studium
Illustrationen
Maße
Höhe: 230 mm
Breite: 150 mm
Gewicht
ISBN-13
978-0-85226-575-8 (9780852265758)
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Schweitzer Klassifikation
Preface; Real Numbers; Limit Points: Open and Closed Sets; Real Sequences; Infinite Series; Functions of a Single Variable (I); Functions of a Single Variable (II); Applications of Taylor's Theorem; Functions; The Riemann Integral (Integration of Bounded Functions on R); The Riemann-Stieltjes Integral; Improper Integrals; Fourier Series; Uniform Convergence (Sequences and Series of Functions); Power Series; Functions of Several Variables; Implicit Functions; Integration on R2 (Line integrals, Double integrals); Integration on R3 (Line, Surface and Volume Integrals); Cantor's Theory of Real Numbers; The Lebesgue Integral; Bibliography; Index.
