# More Calculus of a Single Variable

Part of the Undergraduate Texts in Mathematics book series (UTM)

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Part of the Undergraduate Texts in Mathematics book series (UTM)

This book goes beyond the basics of a first course in calculus to reveal the power and richness of the subject. Standard topics from calculus — such as the real numbers, differentiation and integration, mean value theorems, the exponential function — are reviewed and elucidated before digging into a deeper exploration of theory and applications, such as the AGM inequality, convexity, the art of integration, and explicit formulas for π. Further topics and examples are introduced through a plethora of exercises that both challenge and delight the reader. While the reader is thereby exposed to the many threads of calculus, the coherence of the subject is preserved throughout by an emphasis on patterns of development, of proof and argumentation, and of generalization.

*More Calculus of a Single Variable* is suitable as a text for a course in advanced calculus, as a supplementary text for courses in analysis, and for self-study by students, instructors, and, indeed, all connoisseurs of ingenious calculations.

AGM inequality Taylor's theorem continuous functions mean value theorem

- DOI https://doi.org/10.1007/978-1-4939-1926-0
- Copyright Information Springer Science+Business Media New York 2014
- Publisher Name Springer, New York, NY
- eBook Packages Mathematics and Statistics
- Print ISBN 978-1-4939-1925-3
- Online ISBN 978-1-4939-1926-0
- Series Print ISSN 0172-6056
- Series Online ISSN 2197-5604
- Buy this book on publisher's site