Continuous Functions of Vector Variables / Edition 1

Continuous Functions of Vector Variables / Edition 1

by Alberto Guzman
     
 

ISBN-10: 0817642730

ISBN-13: 9780817642730

Pub. Date: 07/31/2002

Publisher: Birkhauser Verlag

This text is an axiomatic treatment of the properties of continuous multivariable functions and related results from topology. Viewing multiple real variables as members of vector spaces, the author covers boundedness, extreme values, and uniform continuity of functions, along with the connections between continuity and topological concepts such as connectedness

Overview

This text is an axiomatic treatment of the properties of continuous multivariable functions and related results from topology. Viewing multiple real variables as members of vector spaces, the author covers boundedness, extreme values, and uniform continuity of functions, along with the connections between continuity and topological concepts such as connectedness and compactness. The order of topics deliberately mimics the order of development in elementary calculus. This sequencing allows an elementary approach, with analogies to and generalizations from such familiar ideas as the Pythagorean Theorem. The reader is frequently reminded that the pictures suggested by geometry are powerful guides and tools. The definition-theorem-proof format resides within an informal exposition, containing numerous historical comments and questions within and between the proofs. The objective is to present precise proofs, but in a structure and tone that teach the student to plan and write proofs, both in general and specifically in a real analysis course. Applications are largely absent, except where they provide interesting illustrations of the principles and theorems presented. Problems, solutions, bibliography and index complete this book. Continuous Functions of Vector Variables is suitable for advanced undergraduates preparing for graduate programs in pure mathematics. Required background includes a course in the theory of one-variable calculus and the elements of linear algebra.

Product Details

ISBN-13:
9780817642730
Publisher:
Birkhauser Verlag
Publication date:
07/31/2002
Edition description:
2002
Pages:
210
Product dimensions:
9.21(w) x 6.14(h) x 0.46(d)

Table of Contents

Introduction
• Euclidian Space
• Sequences In Normed Spaces
• Limits and Continuity in Normed Spaces
• Characteristics of Continuous Functions
• Topology in Normed Spaces
• Answers
• Bibliography
• Index

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