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 1890, this book constitutes the first of six volumes in Forsyth's Theory of Differential Equations series, concentrating specifically on exact equations and Pfaff's problem. The text contains detailed information on the development of these areas and substantial contributions made to them. 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. Single exact equation; 2. System of exact equations; 3. Historical summary of methods of treating Pfaff's problem; 4. Pfaff's reduction, completed as by Gauss and Jacobi; 5. Grassmann's method; 6. Natani's method; 7. Application to partial differential equations of the first order; 8. Clebsch's method; 9. Tangenital transformations; 10. Lie's method; 11. Frobenius' method; 12. Abstract of Darboux's method; 13. Systems of Pfaffians; Index.
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