Introduction to Real Analysis

ISBN-13: 9780471853916 / Angielski / Miękka / 1991 / 368 str.

John DePree;DePree;Swartz

Opis

Assuming minimal background on the part of students, this text gradually develops the principles of basic real analysis and presents the background necessary to understand applications used in such disciplines as statistics, operations research, and engineering.

Spis treści

Preliminaries.

Real Numbers.

Sequences.

Infinite Series.

Euclidean Spaces.

Limits of Functions.

Continuity and Uniform Continuity.

Sequences of Functions.

The Riemann Integral Reviewed.

The Gauge Integral.

The Gauge Integral Over Unbounded Intervals.

Convergence Theorems.

Multiple Integrals.

Convolution and Approximation.

Metric Spaces.

Topology in Metric Spaces.

Continuity.

Complete Metric Spaces.

Contraction Mappings.

The Baire Category Theorem.

Compactness.

Connectedness.

The Stone–Weierstrass Theorem.

Differentiation of Vector–valued Functions.

Mapping Theorems.

Bibliography.

Index.