ABSTRACT
52In this chapter, some mathematical preliminaries and a review of solid mechanics and optics are presented. The mathematics sections cover the topics of elementary trigonometry, linear algebra, vector algebra, Taylor series, Fourier series and statistics. The solid mechanics section introduces the concepts of stress, strain, linear elastic constitutive relationships, elementary beam theory and Mohr’s circle. In addition, the Hertz contact theory is also briefly reviewed. In the optics section, the wave representation of light is presented along with the laws of reflection, refraction, the thin-lens formula and diffraction. While the chapter is self-contained and meant to serve as a quick reference for many of the mathematical and physical concepts used in the rest of the book, the reader interested in learning these topics in a more thorough fashion is referred to the references provided at the end of the chapter.
