1876/12/31 by William Thomson · 3 citations
Engineering · Mathematics · #Dynamics and Control of Mechanical Systems #Vibration and Dynamic Analysis #Mechanical and Thermal Properties Analysis #Differential equation #Mathematical analysis #Linear differential equation #Laplace transform #Mathematics #Order (exchange) #Variable (mathematics) #Function (biology) #Thermal conduction #Laplace's equation #Physics #Thermodynamics
paper · doi:10.1098/rspl.1875.0035
openalex publication_date 1876/12/31 · openalex created_date 2016/06/24 · openalex updated_date 2026/05/21
Abstract Every linear differential equation of the second order may, as is known, be reduced to the form d/dx (1/P du/dx) = u, . . . . . . (1) where P is any given function of x. On account of the great importance of this equation in mathematical physics (vibrations of a non-uniform stretched cord, of a hanging chain, water in a canal of non-uniform breadth and depth, of air in a pipe of non-uniform sectional area, conduction of heat along a bar of non-uniform fiction or non-uniform conductivity, Laplace’s differential equation of the tides, &c. &c.), I have long endeavoured to obtain a means of faciliiting its practical solution.