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This award-winning text carefully leads the student through the basic topics of Real Analysis. Topics include metric spaces, open and closed sets, convergent sequences, function limits and continuity, compact sets, sequences and series of functions, power series, differentiation and integration, Taylor's theorem, total variation, rectifiable arcs, and sufficient conditions of integrability. Well over 500 exercises (many with extensive hints) assist students through the material.
For students who need a review of basic mathematical concepts before beginning "epsilon-delta"-style proofs, the text begins with material on set theory (sets, quantifiers, relations and mappings, countable sets), the real numbers (axioms, natural numbers, induction, consequences of the completeness axiom), and Euclidean and vector spaces; this material is condensed from the author's Basic Concepts of Mathematics, the complete version of which can be used as supplementary background material for the present text.
Mathematical Analysis II completes this series with material on measure and integration and calculus on normed linear spaces.
There is a list of errata that records changes made to the text since the version of May 20, 2004. Other pdf formats available at trillia.com
This work is a sequel of Basic Concepts of Mathematics.
Mathematical Analysis II is a sequel of this work.
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Keywords
- Mathematics
- Mathematics / Mathematical Analysis
- Textbooks
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web: http://www.trillia.com/zakon-analysisI.htmlEditions