The Heart of Calculus: Explorations and Applications (Hardcover)

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.