What is a differential equation? -- Second-order linear equations -- Power series solutions and special functions -- Sturm-Liouville problems and boundary value problems -- Numerical methods -- Fourier series : basic concepts -- Laplace transforms -- Distributions -- Wavelets -- Partial differential equations and boundary value problems.
Summary
"This new book from one of the most published authors in all of mathematics is an attempt to offer a new, more modern take on the Differential Equations course. Because of the theory of wavelets, Fourier analysis is ever more important and central and applications are a driving force behind mathematics"--