Lectures on Differential Equations provides a clear and concise presentation of differential equations for undergraduates and beginning graduate students. There is more than enough material here for a year-long course. In fact, the text developed from the author's notes for three courses: the undergraduate introduction to ordinary differential equations, the undergraduate course in Fourier analysis and partial differential equations, and a first graduate course in differential equations. The first four chapters cover the classical syllabus for the undergraduate ODE course leavened by a modern...