For those new to musical sound synthesis, there are various other texts which are worth consulting:
The physics of musical instruments is covered in the texts by Fletcher and Rossing [86], Rossing, Moore and Wheeler, [184] and Campbell and Greated [40]. A more advanced treatment for many of the systems encountered in this book is given in the classic texts by Morse and Ingard [149], Graff [100] and Nayfeh and Mook [151]. Many interesting aspects of musical instrument physics are covered in the collection edited by Hirschberg, Kergomard and Weinreich [107].
For a general overview of digital sound synthesis, see the books by Roads [174], Dodge and Jerse [68], Miranda [145] and Moore [146], and various edited collections [175,65,176]. Special topics in physical modeling sound synthesis are covered in various texts. For an exhaustive presentation of digital waveguides, see the text by Smith [209], readily available on line, and certainly the best reference in existence on physical modeling. Functional transformation approaches, which are similar to modal synthesis methods, are discussed in Trautmann and Rabenstein [222]. A variety of sound synthesis techniques, including a good deal of material on both digital waveguides and modal methods are found in the book by Cook [57].
A good introduction to finite difference methods is the text by Strikwerda [210], which covers frequency domain analysis in great detail, and from a point of view that will be approachable to those with an audio signal processing background; the text of Gustaffson, Kreiss, and Oliger [102], which is written at a more advanced level, deals with energy techniques as well. The text by Ames [2], though much older, is an invaluable reference. That of Evans, Blackledge and Yardley [79] is an accessible introduction to finite element as well as finite difference methods. A lively reference on spectral methods, conceived around the use of Matlab, is the book by Trefethen [225].