Theory of Differential Equations Ordinary Linear Equations Theory of Differential Equations 6 Volume Set Series

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 1902, this book constitutes the fourth of six volumes in Forsyth's Theory of Differential Equations series, concentrating specifically on ordinary linear 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. Linear equations: existence of synectic integrals: fundamental systems; 2. General form and properties of integrals near a singularity; 3. Regular equations: equation having all its integrals regular near a singularity; 4. Equations having their integrals regular in the vicinity of every singularity (including infinity); 5. Linear equations of the second and the third orders possessing algebraic integrals; 6. Equations having only some of their integrals regular near a singularity; 7. Normal integrals: subnormal integrals; 8. Infinite determinants, and their application to the solution of linear equations; 9. Equations with uniform periodic coefficients; 10. Equations having algebraic coefficients; Index to Part III.