Readable and systematic, this volume offers coherent presentations of not only the general theory of linear equations with a single integration, but also of applications to differential equations, the calculus of variations, and special areas in mathematical physics. Topics include the solution of Fredholm’s equation expressed as a ratio of two integral series in lambda, free and constrained vibrations of an elastic string, and auxiliary theorems on harmonic functions. Discussion of the Hilbert-Schmidt theory covers boundary problems for ordinary linear differential equations, vibration problems, and flow of heat in a bar. 1924 ed.
Here's a sample of other books in this Dover category
Hill's Equation by Wilhelm Magnus, Stanley Winkler This two-part treatment explains basic theory and details, including oscillatory solutions, intervals of stability and instability, discriminants, and coexistence. Particular attention to stability problems and coexistence of periodic solutions. 1966 edition.
Theory of the Integral by Stanislaw Saks An excellent introduction to modern real variable theorem, this volume covers all the standard topics such as theory, theory of measure, functions with general properties, and theory of integration.
The Finite Element Method: Linear Static and Dynamic Finite Element Analysis by Thomas J. R. Hughes Text for students without in-depth mathematical training, this text includes a comprehensive presentation and analysis of algorithms of time-dependent phenomena plus beam, plate, and shell theories. Solution guide available upon request.
