Basic Real Analysis Along with a companion volume Advanced Real Analysis /

• Main Author: Knapp, Anthony W. (Author)
• Corporate Author: SpringerLink (Online service)
• Format: Electronic eBook
• Language: English
• Published: Boston, MA : Birkhäuser Boston, 2005.
• Series: Cornerstones
• Subjects: Mathematics.; Mathematical analysis.; Analysis (Mathematics).; Fourier analysis.; Measure theory.; Differential equations.; Functions of real variables.; Topology.; Analysis.; Measure and Integration.; Real Functions.; Fourier Analysis.; Ordinary Differential Equations.

Basic Real Analysis and Advanced Real Analysis (available separately or together as a Set) systematically develop those concepts and tools in real analysis that are vital to every mathematician, whether pure or applied, aspiring or established. These works present a comprehensive treatment with a gl...

Table of Contents:

• Theory of Calculus in One Real Variable
• Metric Spaces
• Theory of Calculus in Several Real Variables
• Theory of Ordinary Differential Equations and Systems
• Lebesgue Measure and Abstract Measure Theory
• Measure Theory for Euclidean Space
• Differentiation of Lebesgue Integrals on the Line
• Fourier Transform in Euclidean Space
• Lp Spaces
• Topological Spaces
• Integration on Locally Compact Spaces
• Hilbert and Banach Spaces.