ABSTRACT
Infinite series of numbers and of functions can be employed in many different contexts. This chapter examines a number of additional but rather specialized applications of series. Brook Taylor series expansions are useful in the calculation of certain limits. Taylor expansions can be of decided use in approximating definite integrals in cases where it is difficult or impossible to find anti-derivatives. Bessel functions arise naturally in studies involving fluid motion, wave propagation and elasticity. The literature on Bessel functions is enormous; Watson's "A Treatise on the Theory of Bessel Functions," itself a book of 752 pages, includes a 36-page bibliography. The chapter illustrates how systems of equations can arise in physical problems. A number of interesting models have been developed through the application of mathematics to biology. The chapter considers a simplified model that might be used in connection with the diffusion of a compound across a series of cell walls.
