Table of contents
About this book
Based on courses given at Eötvös Loránd University (Hungary) over the past 30 years, this introductory textbook develops the central concepts of the analysis of functions of one variable - systematically, with many examples and illustrations, and in a manner that builds upon, and sharpens, the students' mathematical intuition.
The modular organization of the book makes it adaptable for either semester or year-long introductory courses, while the wealth of material allows for it to be used at various levels of student sophistication in all programs where analysis is a part of the curriculum, including teachers' education.
In the spirit of learning-by-doing, Real Analysis includes more than 500 engaging exercises for the student keen on mastering the basics of analysis. There are frequent hints and occasional complete solutions provided for the more challenging exercises making it an ideal choice for independent study.
The book includes a solid grounding in the basics of logic and proofs, sets, and real numbers, in preparation for a rigorous study of the main topics: limits, continuity, rational functions and transcendental functions, differentiation, and integration. Numerous historical notes and applications to other areas of mathematics, and to physics, are given, thereby demonstrating the practical scope and power of mathematical analysis.
- Book Title Real Analysis
- Book Subtitle Foundations and Functions of One Variable
- Series Title Undergraduate Texts in Mathematics
- Series Abbreviated Title Undergraduate Texts Mathematics
- DOI https://doi.org/10.1007/978-1-4939-2766-1
- Copyright Information Springer New York 2015
- Publisher Name Springer, New York, NY
- eBook Packages Mathematics and Statistics Mathematics and Statistics (R0)
- Hardcover ISBN 978-1-4939-2765-4
- Softcover ISBN 978-1-4939-4222-0
- eBook ISBN 978-1-4939-2766-1
- Series ISSN 0172-6056
- Series E-ISSN 2197-5604
- Edition Number 1
- Number of Pages X, 483
- Number of Illustrations 94 b/w illustrations, 0 illustrations in colour
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