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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 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.
List of contents
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.
About the author
Peter R. Mercer is a Full Professor of Mathematics at Buffalo State University. He serves as an Editor for the journals
Journal of Mathematical Inequalities, and he have over 50 publications. He serves as an Associate Editor for
The College Mathematics Journal and
Australian Journal of Mathematical Analysis.
