The Heart of Calculus
Explorations and Applications

Accessible enrichment material for talented undergraduate students taking courses in calculus, differential equations, modelling, and real analysis.

Philip M. Anselone (Author), John Lee (Author)

9780883857878, The Mathematical Association of America

Hardback, published 13 August 2015

245 pages
26.1 x 18.2 x 1.8 cm, 0.6 kg

Targeting talented students who seek a deeper understanding of calculus and its applications, this book contains enrichment material for courses in first- and second-year calculus, differential equations, modelling, and introductory real analysis. Maintaining a high level of rigour whilst avoiding epsilons and deltas, the explorations, problems, and projects in the book impart a deeper understanding of the mathematical reasoning that lies at the heart of calculus and conveys its beauty and depth. The presentation is friendly and accessible to students at various levels of mathematical maturity, requiring only basic logical reasoning skills as a prerequisite. The sixteen largely independent chapters, divided equally between pure and applied mathematics, present material that includes fundamentals of differential calculus and celestial motion and gravitation, along with other significant topics chosen for their intrinsic interest, historical influence, and continuing importance.

Preface
The foundation on which calculus stands
1. Critical points and graphing
2. Inverse functions
3. Exponential and logarithmic functions
4. Linear approximation and Newton's method
5. Taylor polynomial approximation
6. Global extreme values
7. Angular velocity and curvature
8. π and e are irrational
9. Hanging cables
10. The Buffon needle problem
11. Optimal location
12. Energy
13. Springs and pendulums
14. Kepler's laws of planetary motion
15. Newton's law of universal gravitation
16. From Newton to Kepler and beyond
Index.

Subject Areas: Integral calculus & equations [PBKL], Differential calculus & equations [PBKJ], Complex analysis, complex variables [PBKD], Real analysis, real variables [PBKB], Calculus & mathematical analysis [PBK], Mathematics [PB]