B. Mathematical background¶
This book assumes mathematical background knowledge at the level of an advanced undergraduate student in Physics or Astrophysics. This includes strong familiarity with differential calculus (derivatives, integrals, and ordinary differential equations), vectors and vector calculus, mathematical transformations such as Fourier and Laplace transformations, special functions, and basic probability theory. The aim of this appendix is not to give a comprehensive introduction to the required background knowledge, but rather to establish the specific notation that we use and to discuss aspects of the mathematical background that are particularly relevant to the study of galaxies and to the mathematical treatment in this book. Note that Fourier transforms are discussed in various places in the main text of the book (e.g., Chapter 7.3.1 and Chapter 17.1.4.1) and they are not discussed further here. We also do not discuss general numerical techniques for, e.g., integration; a good reference for this remains Press et al. (2007). Not every possible aspect of the required mathematical background is covered in this appendix; enough information on topics not covered here can usually be obtained using a quick web search.
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