Mathematical Methods in Science and Engineering (Applications in Optics and Photonics) (First Edition)

Book excerpt: Mathematical Methods in Science and Engineering: Applications in Optics and Photonics helps students build a conceptual appreciation for critical mathematical methods, as well as the physical feel and intuition for select mathematical ideas. Throughout the text, examples are provided from the field of optics and photonics to clarify key concepts. The book features 13 targeted chapters that begin with a brief introduction to the topical area and then dive directly into the subject matter. Students learn about properties of numbers, methods of mathematical reasoning, Euclidean geometry, the fundamentals of complex number theory, and techniques to deal with finite as well as infinite sums and products. Dedicated chapters speak to key concepts of multivariate calculus, the properties of analytic functions of a complex variable, Fourier transformation, methods of solving partial differential equations, the Sturm-Liouville theory, and special functions, including Euler's gamma function, Riemann's zeta function, and the Airy and Bessel functions. Elementary matrix algebra, vector calculus, and probability, random variables, and stochastic processes are addressed. Mathematical Methods in Science and Engineering is well suited for graduate-level courses in optical sciences, physics, and engineering.