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Full Description
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 sixth and final volume 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
12. General integrals of equations of orders higher than the first; 13. Linear equations of the second order in two independent variables: the Laplace-transformations; 14. Adjoint equations: linear equations having equal invariants; 15. Forms of equations of the second order in two independent variables having their general integrals in explicit finite form; 16. Equations of the second order in two independent variables having an intermediate integral; 17. Ampère's method applied to equations of the second order in two independent variables; 18. Darboux's method and other methods for equations of the second order in two independent variables; 19. Generalisation of integrals; 20. Characteristics of equations of second order: intermediate integrals; 21. General transformation of equations of the second order; 22. Equations of the third and higher orders, in two independent variables; 23. Equations of the second order in more than two independent variables, having an intermediate integral; 24. Equations of the second order in three independent variables, not necessarily having an intermediate integral; Index to Part IV.
