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1 The First Ordinary Differential Equations |
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2 Variational Problems and the Calculus |
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3 The Partial Differential Calculus |
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4 Rational Mechanics |
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5 Partial Differential Equations |
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6 Lagrange's General Theory |
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7 The Calculus of Variations |
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8 Monge and Solutions to Partial Differential Equations |
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9 Revision |
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10 The Heat Equation |
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11 Gauss and the Hypergeometric Equation |
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12 Existence Theorem |
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13 Riemann and Complex Function Theory |
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14 Riemann and the Hypergeometric Equation |
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15 Schwarz and the Complex Hypergeometric Equation |
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16 Complex Ordinary Differential Equations: Poincaré |
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17 More General Partial Differential Equations |
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18 Green's Functions and Dirichlet's Principle |
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19 Attempts on Laplace's Equation |
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20 Applied Wave Equations |
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21 Revision |
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22 Riemann's Shock Wave Paper |
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23 The Example of Minimal Surfaces |
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24 Partial Differential Equations and Mechanics |
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25 Geometrical Interpretations of Mechanics |
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26 The Calculus of Variations in the 19th Century |
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27 Poincaré and Mathematical Physics |
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28 Elliptic Equations and Regular Variational Problems |
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29 Hyperbolic Equations |
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30 Revision |
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32 Translations |
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A Newton's Principia Mathematica |
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B Characteristics |
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C First-order Non-linear Equations |
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D Green's Theorem and Heat Conduction |
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E Complex Analysis |
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F Möbius Transformations |
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G Lipschitz and Picard |
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H The Assessment |
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Bibliography |
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Index |
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1 The First Ordinary Differential Equations |
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2 Variational Problems and the Calculus |
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3 The Partial Differential Calculus |
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