ABSTRACT
This chapter first introduces maps that transform the phase-space coordinates of particles from the entrance to the exit of commonly found components in an accelerator. In many cases the maps are linear and can be represented by transfer-matrices, which provide a framework to describe both single particles and representations of distributions, the centroid and sigma-matrix. All operations are illustrated with Matlab code. In numerical experiments, the concepts of transverse beam optics, such as Twiss parameters, tunes, emittance, dispersion, chromaticity, and coupling are introduced and further explored. Matching, the adjustment of magnet parameters in order to fulfill constraints, is introduced in the Matlab code and used to set up and analyze a number of beam optical systems: telescopes, doublets, triplets, achromats, dispersion suppressors, interaction regions, and bunch compressors.
