From calculus to analysis

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This comprehensive textbook is intended for a two-semester sequence in analysis. The first four chapters present a practical introduction to analysis by using the tools and concepts of calculus. The last five chapters present a first course in analysis. The presentation is clear and concise, allowing students to master the calculus tools that are crucial in understanding analysis.

From Calculus to Analysis prepares readers for their first analysis course—important because many undergraduate programs traditionally require such a course. Undergraduates and some advanced high-school seniors will find this text a useful and pleasant experience in the classroom or as a self-study guide. The only prerequisite is a standard calculus course.

Author(s): Rinaldo B. Schinazi (auth.)
Edition: 1
Publisher: Birkhäuser Basel
Year: 2012

Language: English
Pages: 250
City: New York
Tags: Analysis; Sequences, Series, Summability; Approximations and Expansions; Measure and Integration

Front Matter....Pages I-X
Number Systems....Pages 1-32
Sequences and Series....Pages 33-63
Power Series and Special Functions....Pages 65-94
Fifty Ways to Estimate the Number π ....Pages 95-135
Continuity, Limits, and Differentiation....Pages 137-176
Riemann Integration....Pages 177-205
Convergence of Functions....Pages 207-219
Decimal Representation of Numbers....Pages 221-233
Countable and Uncountable Sets....Pages 235-244
Back Matter....Pages 245-250