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＜電子ブック＞
A Compact Capstone Course in Classical Calculus / by Peter R. Mercer
(Compact Textbooks in Mathematics. ISSN:2296455X)

版	1st ed. 2023.
出版者	Cham : Springer Nature Switzerland : Imprint: Birkhäuser
出版年	2023
本文言語	英語
大きさ	XI, 157 p. 43 illus : online resource
著者標目	*Mercer, Peter R author SpringerLink (Online service)
件　名	LCSH:Mathematics LCSH:Functions of real variables FREE:General Mathematics FREE:Real Functions
一般注記	Chapter 1. Prelude: Vi`ete’s Product -- Chapter. 2. Calculus Warm-up -- Chapter. 3. The Probability Integral & Gamma Function -- Chapter. 4. Wallis’s Product -- Chapter. 5. Interlude: How Big is a Ball ? -- Chapter. 6. Convexity – Tangents -- Chapter. 7. Some Important Series -- Chapter. 8. Geometric Probability -- Chapter. 9. Convexity – Chords -- Chapter. 10. Interlude: Minkowski Distance -- Chapter. 11. The Basel Problem -- Chapter. 12. Interlude: Beyond Basel -- Chapter. 13. Stirling’s Formula -- Chapter. 14. Euler’s Sine Product -- Chapter. 15. Postlude: Stirling’s Formula Again -- Index This textbook offers undergraduates a self-contained introduction to advanced topics not covered in a standard calculus sequence. The author’s enthusiastic and engaging style makes this material, which typically requires a substantial amount of study, accessible to students with minimal prerequisites. Readers will gain a broad knowledge of the area, with approaches based on those found in recent literature, as well as historical remarks that deepen the exposition. Specific topics covered include the binomial theorem, the harmonic series, Euler's constant, geometric probability, and much more. Over the fifteen chapters, readers will discover the elegance of calculus and the pivotal role it plays within mathematics. A Compact Capstone Course in Classical Calculus is ideal for exploring interesting topics in mathematics beyond the standard calculus sequence, particularly for undergraduates who may not be taking more advanced math courses. It would also serve as a useful supplement for a calculus course and a valuable resource for self-study. Readers are expected to have completed two one-semester college calculus courses HTTP:URL=https://doi.org/10.1007/978-3-031-43914-8

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