Appendix - Mathematical Background

Summary

We summarize here the most important mathematical results used in the text (and useful for solving some of the proposed exercises). Overall, this appendix is intended more as a selection of mathematical results relevant to stellar dynamics than an organic presentation of definitions and theorems. A good knowledge of linear algebra and calculus at the undergraduate level is assumed, and the interested reader is encouraged to refer to some of the excellent classical treatises of mathematical physics, such as Arfken and Weber (2005), Bender and Orszag (1978), Courant and Hilbert (1989), Dennery and Krzywicki (1967), Ince (1927), Jeffrey and Jeffrey (1950), Kahn (2004), and Morse and Feshbach (1953). To help with further study, in the following sections more specific references are sometimes also provided.