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Record Nr. |
UNINA9910765493503321 |
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Autore |
Mercer Peter R. |
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Titolo |
A Compact Capstone Course in Classical Calculus / / by Peter R. Mercer |
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Pubbl/distr/stampa |
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Cham : , : Springer Nature Switzerland : , : Imprint : Birkhäuser, , 2023 |
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ISBN |
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Edizione |
[1st ed. 2023.] |
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Descrizione fisica |
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1 online resource (XI, 157 p. 43 illus.) |
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Collana |
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Compact Textbooks in Mathematics, , 2296-455X |
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Disciplina |
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Soggetti |
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Mathematics |
Functions of real variables |
General Mathematics |
Real Functions |
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Lingua di pubblicazione |
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Formato |
Materiale a stampa |
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Livello bibliografico |
Monografia |
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Nota di bibliografia |
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Includes bibliographical references and index. |
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Nota di contenuto |
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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. |
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Sommario/riassunto |
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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 |
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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. |
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