al are solved-for by electrical engineers through Laplace transform analysis (pp. 1-9 et seq.), which in turn typically requires use of the partial-fraction expansion method (pp. 1-3 and -4), which is exactly analogous to positional numbering systems described under real numbers, back at page 1-1. This manner of building topics one upon another is successfully followed throughout the book.
Following most directly from the discussion of real numbers is that of complex numbers (involving the square root of -1) (pp. 1-1 to -3). Then, reviews are given of basic algebra (pp. 1-3 and -4); trigonometric identities (p. 1-4); analytic geometry (pp. 1-4 and -5); differential calculus (p. 1-5); and integral calculus (pp. 1-5 and -6).
Next, Yarbrough gives methods to solve first- and second-order differential equations, by the "classical methods" (pp. 1-6 to -8), by Fourier analyses (pp. 1-8 and -9), and by Laplace transforms (pp. 1-9 to -11). Differential equations of these orders "often occur in DC switching problems" (p. 1-6).
Yarbrough then introduces (for the first time in this Edition) the concept of the fast Fourier transform, an efficient evaluation method for finite Fourier series--reducing computation times by "a factor of 100 or more" (p. 1-13). The chapter concludes with the Fourier transform (pp. 1-14 to -16), determinants and their manipulation (pp 1-16 and -17), and solutions to linear simultaneous equations (pp. 1-17 and -18).
2. Linear Circuit Analysis. This chapter flows generally from the relationship between voltage (V) and current (I) in a simple wire circuit with resistance (R) (Ohm's law: V =IR) (p.2-5), to the analysis of complex networks of circuits (pp. 2-22 to -26). Following that, there is a concentration on circuits based on analyses of the impedances therein (pp. 2-26 and -27); and the chapter concludes with algebraic and free-body-diagram summaries of a number of "commonly encountered impedances" ...