# Mathematical Analysis I

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About *Mathematical Analysis I:*

Excerpts from site and book:

Description: This 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.

This text is designed to be used as early as possible in the undergraduate mathematics curriculum; indeed, it was used for many years as the text for a two-semester class for second-year mathematics majors at the University of Windsor. If desired, the material can easily be specialized to n-dimensional (or even two-dimensional) Euclidean space.

Mathematical Analysis II (in preparation) completes this series with material on measure and integration and calculus on normed linear spaces.

Audience: This text is appropriate for any undergraduate mathematics course in real analysis or mathematical analysis, or for a preparatory class for beginning mathematics graduate students who will later advance to courses in measure theory and functional analysis. Knowledge of this material will also be of benefit to graduate students in economics, signal and image processing, fluid and structural mechanics, etc.

This text covers similar material to the books (we give US list prices for current hardcover editions at Amazon on July 10, 2006): Principles of Mathematical Analysis by W. Rudin ($130.00); Introductory Real Analysis by F. D'Angelo and M. Seyfried ($137.56); Introduction to Real Analysis by R. Bartle and D. Sherbert ($125.95); Real Analysis by H. Royden ($124.80); etc.

Description: This 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.

This text is designed to be used as early as possible in the undergraduate mathematics curriculum; indeed, it was used for many years as the text for a two-semester class for second-year mathematics majors at the University of Windsor. If desired, the material can easily be specialized to n-dimensional (or even two-dimensional) Euclidean space.

Mathematical Analysis II (in preparation) completes this series with material on measure and integration and calculus on normed linear spaces.

Audience: This text is appropriate for any undergraduate mathematics course in real analysis or mathematical analysis, or for a preparatory class for beginning mathematics graduate students who will later advance to courses in measure theory and functional analysis. Knowledge of this material will also be of benefit to graduate students in economics, signal and image processing, fluid and structural mechanics, etc.

This text covers similar material to the books (we give US list prices for current hardcover editions at Amazon on July 10, 2006): Principles of Mathematical Analysis by W. Rudin ($130.00); Introductory Real Analysis by F. D'Angelo and M. Seyfried ($137.56); Introduction to Real Analysis by R. Bartle and D. Sherbert ($125.95); Real Analysis by H. Royden ($124.80); etc.