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

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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

Annotated Table of Contents
Preface
IExhortation1
IIThe Field Axioms3
IIIThe Order Relation11
IVThe Natural Numbers16
VFinite and Infinite Sets23
VILong Division and Prime Factorization30
VIIThe Completeness Axiom and Sequences38
VIIIThree Heavy Theorems on Sequences46
IXAlternative Completeness Axioms52
XContinuous Functions55
XIUniform Continuity62
XIIClosed Sets; Compact Sets; Open Sets69
XIIIDerivatives75
XIVThe Darboux Integral85
XVThe Riemann Definition92
XVIlogx and e[superscript x]101
XVIIUnordered Sums and Infinite Series104
XVIIIThe Calculus of Series112
XIXSequences and Series of Functions120
XXTopology in R[superscript 2]130
XXICalculus of Two Variables137
XXIIComplex Numbers146
XXIIICurves in the Plane155
XXIVTrigonometric Functions162
XXVLine Integrals170
XXVIPower Series179
XXVIIThe Transcendental Functions187
XXVIIIAnalytic Functions192
XXIXCauchy's Integral Theorems202
XXXLebesgue Measure in (0, 1)215
XXXIMeasurable Sets220
XXXIIThe Lebesgue Integral228
XXXIIIMeasurable Functions235
XXXIVConvergence Theorems241
Index247

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