From Calculus to Analysis
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Beschreibung
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.
Key features:
* Contains numerous exercises;
* Provides unique examples, such as many ways to estimate the number Pi;
* Introduces the basic principles of analysis;
* Offers a straightforward introduction to the calculus basics such as number systems, sequences, and series;
* Carefully written book with a thoughtful perspective for students.
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 findthis text a useful and pleasant experience in the classroom or as a self-study guide. The only prerequisite is a standard calculus course.
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.
Contains excellent exercise sets Introduces the principles of real analysis, as a formidable counterpart to calculus Places appropriate emphasis on techniques and definitions Carefully written book with a thoughtful perspective for students Includes supplementary material: sn.pub/extras
Autor*in
Rinaldo B. Schinazi
Themen in »From Calculus to Analysis«
Bolzaano-Weirestrass theorem Euler's formula Stirling's formula Wallis' integrals absolute convergence
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“The goal of this very readable text which is accompanied by a wealth of exercises is to advance the students technical experience, in particular in estimating algebraic expressions, and at the same time to enhance their mathematical culture.” (R. Steinbauer, Monatshefte für Mathematik, 2016)
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