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Calculus reordered : a history of the big ideas /
Calculus Reordered takes readers on a remarkable journey through hundreds of years to tell the story of how calculus grew to what we know today. David Bressoud explains why calculus is credited to Isaac Newton and Gottfried Leibniz in the seventeenth century, and how its current structure is based o...
| Clasificación: | Libro Electrónico |
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| Autor principal: | |
| Formato: | Electrónico eBook |
| Idioma: | Inglés |
| Publicado: |
Princeton, New Jersey :
Princeton University Press,
[2019]
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| Temas: | |
| Acceso en línea: | Texto completo |
Tabla de Contenidos:
- Cover; Contents; Preface; Chapter 1. Accumulation; 1.1. Archimedes and the Volume of the Sphere; 1.2. The Area of the Circle and the Archimedean Principle; 1.3. Islamic Contributions; 1.4. The Binomial Theorem; 1.5. Western Europe; 1.6. Cavalieri and the Integral Formula; 1.7. Fermat's Integral and Torricelli's Impossible Solid; 1.8. Velocity and Distance; 1.9. Isaac Beeckman; 1.10. Galileo Galilei and the Problem of Celestial Motion; 1.11. Solving the Problem of Celestial Motion; 1.12. Kepler's Second Law; 1.13. Newton's Principia; Chapter 2. Ratios of Change; 2.1. Interpolation
- 2.2. Napier and the Natural Logarithm; 2.3. The Emergence of Algebra; 2.4. Cartesian Geometry; 2.5. Pierre de Fermat; 2.6. Wallis's Arithmetic of Infinitesimals; 2.7. Newton and the Fundamental Theorem; 2.8. Leibniz and the Bernoullis; 2.9. Functions and Differential Equations; 2.10. The Vibrating String; 2.11. The Power of Potentials; 2.12. The Mathematics of Electricity and Magnetism; Chapter 3. Sequences of Partial Sums; 3.1. Series in the Seventeenth Century; 3.2. Taylor Series; 3.3. Euler's Influence; 3.4. D'Alembert and the Problem of Convergence; 3.5. Lagrange Remainder Theorem
- Teaching Series as Sequences of Partial Sums; Teaching Limits as the Algebra of Inequalities; The Last Word; Notes; Bibliography; Index; Image Credits