Stories about Maxima and Minima
About this Title
V. M. Tikhomirov, Moscow State University, Moscow, Russia
Publication: Mathematical World
Publication Year
1991: Volume 1
ISBNs: 978-0-8218-0165-9 (print); 978-1-4704-2469-5 (online)
DOI: http://dx.doi.org/10.1090/mawrld/001
MathSciNet review: MR1152027
MSC: Primary 49-01; Secondary 00A05, 26-01, 52A40, 90C25
Table of Contents
Front/Back Matter
Chapters
- 1. Part One. Ancient Maximum and Minimum Problems
- 2. The first story. Why Do We Solve Maximum and Minimum Problems?
- 3. The second story. The Oldest Problem—Dido’s Problem
- 4. The third story. Maxima and Minima in Nature (Optics)
- 5. The fourth story. Maxima and Minima in Geometry
- 6. The fifth story. Maxima and Minima in Algebra and in Analysis
- 7. The sixth story. Kepler’s Problem
- 8. The seventh story. The Brachistochrone
- 9. The eighth story. Newton’s Aerodynamical Problem
- 10. Part Two. Methods of Solution of Extremal Problems
- 11. The ninth story. What is a Function?
- 12. The tenth story. What is an Extremal Problem?
- 13. The eleventh story. Extrema of Functions of One Variable
- 14. The twelfth story. Extrema of Functions of Many Variables. The Lagrange Principle
- 15. The thirteenth story. More Problem Solving
- 16. The fourteenth story. What Happened Later in the Theory of Extremal Problems?
- 17. The last story. More Accurately, a Discussion