The differential equations in Cartesian geometry are solved for the magnetoacoustic waves in a magnetic slab. The case of a field-free environment is also investigated as is the $\beta = 0$ plasma. Sausage and kink waves arise and their properties are described. The notion of surface waves and body waves is introduced. Dispersion diagrams are displayed under two sets of conditions, the photospheric medium and the coronal medium. Impulsive waves are examined. Also, waves in smoothly varying profiles are explored, especially the Epstein profile. Cutoff frequencies are obtained for a range of profiles.