Essential Mathematics for the Physical Sciences, Volume 1: Homogenous Boundary Value Problems, Fourier Methods, and Special Functions

Physics is expressed in the language of mathematics; it is deeply ingrained in how physics is taught and how it's practiced.\n\nA study of the mathematics used in science is thus asound intellectual investment for training as scientists and engineers. This first volume of two is centered on methods of solving partial differential equations (PDEs) and the special functions introduced. Solving PDEs can't be done, however, outside of the context in which they apply to physical systems. The solutions to PDEs must conform to boundary conditions, a set of additional constraints in space or time to be satisfied at the boundaries of the system, that small part of the universe under study. The first volume is devoted to homogeneous boundary-value problems (BVPs), homogeneous implying a system lacking a forcing function, or source function. The second volume takes up (in addition to other topics) inhomogeneous problems where, in addition to the intrinsic PDE governing a physical field, source functions are an essential part of the system.This text is based on a course offered at the Naval Postgraduate School (NPS) and while produced for NPS needs, it will serve other universities well. It is based on the assumption that it follows a math review course, and was designed to coincide with the second quarter of student study, which is dominated by BVPs but also requires an understanding of special functions and Fourier analysis. Additional ISBNs 1681744848, 1643279173, 9781681744841, 9781643279176Essential Mathematics for the Physical Sciences, Volume 1: Homogenous Boundary Value Problems, Fourier Methods, and Special Functions is written by Brett Borden; James Luscombe and published by IOP Concise Physics. ISBNs for Essential Mathematics for the Physical Sciences, Volume 1 are 9781681744865, 1681744864 and the print ISBNs are 9781681744841, 1681744848. Additional ISBNs include 1681744848, 1643279173, 9781681744841, 9781643279176.