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Title
A compact capstone course in classical calculus / Peter R. Mercer.
ISBN
9783031439148 electronic book
3031439147 electronic book
3031439139
9783031439131
Published
Cham : Birkhäuser, 2023.
Language
English
Description
1 online resource
Item Number
10.1007/978-3-031-43914-8 doi
Call Number
QA303.2 .M47 2023
Dewey Decimal Classification
515
Summary
This textbook offers undergraduates a self-contained introduction to advanced topics not covered in a standard calculus sequence. The authors 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.
Bibliography, etc. Note
Includes bibliographical references and index.
Access Note
Access limited to authorized users.
Source of Description
Online resource; title from PDF title page (SpringerLink, viewed December 7, 2023).
Series
Compact textbooks in mathematics.
Available in Other Form
Print version: 9783031439131
Chapter 1. Prelude: Vi`etes Product
Chapter. 2. Calculus Warm-up
Chapter. 3. The Probability Integral & Gamma Function
Chapter. 4. Walliss 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. Stirlings Formula
Chapter. 14. Eulers Sine Product
Chapter. 15. Postlude: Stirlings Formula Again
Index.
