Change and variations : a history of differential equations to 1900 /
This book presents a history of differential equations, both ordinary and partial, as well as the calculus of variations, from the origins of the subjects to around 1900. Topics treated include the wave equation in the hands of d’Alembert and Euler; Fourier’s solutions to the heat equation and the c...
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| Format: | Book |
| Language: | English |
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Cham, Switzerland :
Springer,
[2021]
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| Edition: | 1st ed. 2021 |
| Series: | Springer undergraduate mathematics series
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| Subjects: |
Table of Contents:
- 1 The First Ordinary Differential Equations
- 2 Variational Problems and the Calculus
- 3 The Partial Differential Calculus
- 4 Rational Mechanics
- 5 Partial Differential Equations
- 6 Lagrange's General Theory
- 7 The Calculus of Variations
- 8 Monge and Solutions to Partial Differential Equations
- 9 Revision
- 10 The Heat Equation
- 11 Gauss and the Hypergeometric Equation
- 12 Existence Theorem
- 13 Riemann and Complex Function Theory
- 14 Riemann and the Hypergeometric Equation
- 15 Schwarz and the Complex Hypergeometric Equation
- 16 Complex Ordinary Differential Equations: Poincaré
- 17 More General Partial Differential Equations
- 18 Green's Functions and Dirichlet's Principle
- 19 Attempts on Laplace's Equation
- 20 Applied Wave Equations
- 21 Revision
- 22 Riemann's Shock Wave Paper
- 23 The Example of Minimal Surfaces
- 24 Partial Differential Equations and Mechanics
- 25 Geometrical Interpretations of Mechanics
- 26 The Calculus of Variations in the 19th Century
- 27 Poincaré and Mathematical Physics
- 28 Elliptic Equations and Regular Variational Problems
- 29 Hyperbolic Equations
- 30 Revision
- 32 Translations
- A Newton's Principia Mathematica
- B Characteristics
- C First-order Non-linear Equations
- D Green's Theorem and Heat Conduction
- E Complex Analysis
- F Möbius Transformations
- G Lipschitz and Picard
- H The Assessment
- Bibliography
- Index