An Introduction to Mathematical Analysis / Edition 1

An Introduction to Mathematical Analysis / Edition 1

by H. S. Bear
     
 

ISBN-10: 0120839407

ISBN-13: 9780120839407

Pub. Date: 04/28/1997

Publisher: Elsevier Science & Technology Books

An Introduction to Mathematical Analysis provides detailed explanations and exhaustive proofs, and follows

an axiomatic approach to presenting the material. The text assumes that the student has little background in mathematical

analysis; therefore, the initial pace is slowed down. The proofs are formal, complete, and augmented by an informal and

Overview

An Introduction to Mathematical Analysis provides detailed explanations and exhaustive proofs, and follows

an axiomatic approach to presenting the material. The text assumes that the student has little background in mathematical

analysis; therefore, the initial pace is slowed down. The proofs are formal, complete, and augmented by an informal and

heuristic explanation. The author presents the subject in clear and evocative language, and includes treatment of the Lebesgue

integral, a topic not usually found in texts of this level. Mathematical problems are included throughout the text and are designed

to get the student involved at every stage.

Product Details

ISBN-13:
9780120839407
Publisher:
Elsevier Science & Technology Books
Publication date:
04/28/1997
Pages:
252
Product dimensions:
6.27(w) x 9.31(h) x 0.91(d)

Table of Contents

Exhortation.

The Field Axioms.

The Order Relation.

The Natural Numbers.

Finite and Infinite Sets.

Long Division and Prime Factorization.

The Completeness Axiom and Sequences.

Three Heavy Theorems on Sequences.

Alternative Completeness Axioms. C

ontinuous Functions.

Uniform Continuity.

Closed Sets; Compact Sets; Open Sets.

Derivatives.

The Darboux Integral.

The Riemann Definition.

Log x and e<->x.

Unordered Sums and Infinite Series.

The Calculus of Series.

Sequences and Series of Functions.

Topology in (<->2.

Calculus of Two Variables.

Complex Numbers.

Curves in the Plane.

Trigonometric Functions.

Line Integrals.

Power Series.

The Transcendental Functions.

Analytic Functions.

Cauchys Integral Theorems.

Lebesgue Measure in (0, 1).

Measurable Sets.

The Lebesgue Integral.

Measurable Functions.

Convergence Theorems.

Subject Index.

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