Mercer P. A Compact Capstone Course in Classical Calculus 2023

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Mercer P. A Compact Capstone Course in Classical Calculus 2023

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Textbook in PDF format 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. Preface Acknowledgments Prelude: Viete's Product Calculus Warm-Up The Probability Integral and Gamma Function Wallis's Product Interlude: How Big Is a Ball? Convexity—Tangents Some Important Series Geometric Probability Convexity—Chords Interlude: Minkowski Distance The Basel Problem Interlude: Beyond Basel Stirling's Formula Euler's Sine Product Postlude: Stirling's Formula Again 15.1 Prep Work Index