Andrew Russell Forsyth (1858–1942) was an influential Scottish mathematician notable for incorporating the advances of Continental mathematics within the British tradition. Originally published in 1906, this book constitutes the fifth of six volumes in Forsyth's Theory of Differential Equations series, concentrating specifically on partial differential equations. The text contains detailed information on the development of this area and substantial contributions made to it. All sources are quoted in their proper connection and a few fresh investigations are added. Examples are given, where necessary, in order to provide illustrations of various methods. This book will be of value to anyone with an interest in differential equations and the history of mathematics.
Contents
1. Introduction: two existence-theorems; 2. Cauchy's theorem; 3. Linear equations and complete linear systems; 4. Non-linear equations: Jacobi's second method, with Mayer's developments; 5. Classes of integrals possessed by equations of the first order: generalisation of integrals; 6. The method of characteristics for equations in two independent variables: geometrical relations of the various integrals; 7. Singular integrals and their geometrical properties: singularities of the characteristics; 8. The method of characteristics in any number of independent variables; 9. Lie's methods applied to equations of the first order; 10. The equations of theoretical dynamics; 11. Simultaneous equations of the first order.
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