Coleman (Fairfield University) reveals fundamentals of partial differential equations (PDEs), covering characteristics, integral transforms, Green's functions, and Fourier series. He examines the heat, wave, and Laplace equations and explains how these and other PDEs on finite intervals can be solved using the Fourier series for arbitrary initial and boundary conditions. Students will use MATLAB software for solving exercises. The text is suitable for a two- semester introduction to PDEs and Fourier series for students who have had basic courses in multivariable calculus and ODEs.