Theory of Differential Equations
Partial Differential Equations

The fifth of six volumes in Andrew Russell Forsyth's Theory of Differential Equations series, concentrating specifically on partial differential equations.

Andrew Russell Forsyth (Author)

9781107660144, Cambridge University Press

Paperback / softback, published 19 July 2012

500 pages
21.6 x 14 x 2.8 cm, 0.63 kg

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.

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.

Subject Areas: Calculus & mathematical analysis [PBK]