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200 12$aA Compact Capstone Course in Classical Calculus$b[electronic resource] /$fby Peter R. Mercer
205   $a1st ed. 2023.
210  1$aCham :$cSpringer Nature Switzerland :$cImprint: Birkhäuser,$d2023.
215   $a1 online resource (XI, 157 p. 43 illus.) 
225 1 $aCompact Textbooks in Mathematics,$x2296-455X
311 08$a9783031439131 
327   $aChapter 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.
330   $aThis textbook offers undergraduates a self-contained introduction to advanced topics not covered in a standard calculus sequence. The author?s enthusiastic and engaging style makes this material, which typically requires a substantial amount of study, accessible to students with minimal prerequisites. Readers will gain a broad knowledge of the area, with approaches based on those found in recent literature, as well as historical remarks that deepen the exposition. Specific topics covered include the binomial theorem, the harmonic series, Euler's constant, geometric probability, and much more. Over the fifteen chapters, readers will discover the elegance of calculus and the pivotal role it plays within mathematics. A Compact Capstone Course in Classical Calculus is ideal for exploring interesting topics in mathematics beyond the standard calculus sequence, particularly for undergraduates who may not be taking more advanced math courses. It would also serve as a useful supplement for a calculus course and a valuable resource for self-study. Readers are expected to have completed two one-semester college calculus courses.
410  0$aCompact Textbooks in Mathematics,$x2296-455X
606   $aMathematics
606   $aFunctions of real variables
606   $aGeneral Mathematics
606   $aReal Functions
615  0$aMathematics.
615  0$aFunctions of real variables.
615 14$aGeneral Mathematics.
615 24$aReal Functions.
676   $a510
700   $aMercer$b Peter R$4aut$4http://id.loc.gov/vocabulary/relators/aut$0722025
801  0$bMiAaPQ
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906   $aBOOK
912   $a9910765493503321
996   $aA Compact Capstone Course in Classical Calculus$93645541
997   $aUNINA