MATLAB (Matrix Laboratory), the numerical computing environment, is used heavily in engineering and mathematics, but it also allows us to use it as an outstanding tool for learning numerical weather prediction techniques. In this presentation, MATLAB is used to solve the linearized shallow water equations using a variety of different numerical methods. These methods include finite difference methods as well as spectral and pseudo-spectral methods using MATLAB's built in Fast Fourier Transform (FFT) capabilities. Comparisons are made between the different numerical methods. The linear equations are then generalized to the f-plane and used to examine the geostrophic adjustment process (how winds and pressure fields come to balance) for a variety of unbalanced initial conditions.