B Appendix B Fourier facts
B.1 The delta function
. . . [E]ven the most precise sciences normally work with more or less ill-understood approximations toward which the scientist must maintain an appropriate skepticism . . . . The physicist rightly dreads precise argument, since an argument which is only convincing if precise loses all its force if the assumptions upon which it is based are slightly changed, while an argument which is convincing though imprecise may well be stable under small perturbations of its underlying axioms. (Jack Schwartz, The Pernicious Influence of Mathematics on Science)
In this appendix, we review some techniques ...