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Transcendental curves in the Leibnizian Calculus /
| Clasificación: | Libro Electrónico |
|---|---|
| Autor principal: | |
| Formato: | Electrónico eBook |
| Idioma: | Inglés |
| Publicado: |
San Diego :
Academic Press,
2017.
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| Colección: | Studies in the History of Mathematical Inquiry.
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| Temas: | |
| Acceso en línea: | Texto completo |
Tabla de Contenidos:
- Front Cover; Transcendental Curves in the Leibnizian Calculus; Copyright; Contents ; Acknowledgments ; Chapter 1 Preliminary matters; 1.1. Purpose and scope of the present work; 1.2. Previous scholarship related to the present work; 1.3. What is new in the present work; 1.4. Conventions adopted in this work; 1.5. Some key terms; Chapter 2 Introduction; 2.1. The problem of transcendental curves; 2.2. Fundamental conflict between analytic and construction-based paradigms; 2.3. Implications of this story for the general historiography of the period.
- Chapter 3 The classical basis of 17th-century philosophy of mathematics3.1. Introduction; 3.2. Greek geometry; 3.3. 17th-century philosophy of geometry; Chapter 4 Mathematical context; 4.1. Introduction; 4.2. The early calculus according to Leibniz; 4.3. Transcendental curves in the early work of Huygens; 4.4. Johann Bernoulli's lectures on the calculus; Chapter 5 Transcendental curves by curve tracing; 5.1. Introduction; 5.2. The tractrix; 5.3. Johann Bernoulli's generalised tractrix; 5.4. Leibniz's construction by tractional motion of any curve given by dy/dx.
- 5.5. Jacob Bernoulli's tractional method5.6. Johann Bernoulli's crawling curves; Chapter 6 Transcendental curves analytically: exponentials and power series; 6.1. Introduction; 6.2. The problem with power series; 6.3. Exponentials; Chapter 7 Transcendental curves by the reduction of quadratures; 7.1. Introduction; 7.2. Computational reduction of quadratures; 7.3. The rectification of quadratures; Chapter 8 Transcendental curves in physics; 8.1. Introduction; 8.2. The elastica; 8.3. The paracentric isochrone; 8.4. The brachistochrone; 8.5. Forces and tangents.
- Chapter 9 A view from the 18th century9.1. Introduction; 9.2. The epistemological miracle of analytical methods; 9.3. Euler's analytical calculus; 9.4. Lagrange's analytical calculus; 9.5. Lagrange's analytical mechanics; Chapter 10 Concluding overview; Notes; References; Index; Back Cover.