Partial Differential Equations in Classical Mathematical Physics [Paperback]

The book's combination of mathematical comprehensiveness and natural scientific motivation represents a step forward in the presentation of the classical theory of PDEs.This text considers the theory of partial differential equations as the language of continuous processes in mathematical physics. Representing a step forward in the presentation of the classical theory of PDEs, it will be appreciated by mathematicians as well as physicists.This text considers the theory of partial differential equations as the language of continuous processes in mathematical physics. Representing a step forward in the presentation of the classical theory of PDEs, it will be appreciated by mathematicians as well as physicists.This book considers the theory of partial differential equations as the language of continuous processes in mathematical physics. This is an interdisciplinary area in which the mathematical phenomena are reflections of their physical counterparts. The authors trace the development of these mathematical phenomena in different natural sciences, with examples drawn from continuum mechanics, electrodynamics, transport phenomena, thermodynamics, and chemical kinetics. At the same time, the authors trace the interrelation between the different types of problems--elliptic, parabolic, and hyperbolic--as the mathematical counterparts of stationary and evolutionary processes. This combination of mathematical comprehensiveness and natural scientific motivation represents a step forward in the presentation of the classical theory of PDEs, one that will be appreciated by students and researchers in applied mathematics and mathematical physics.Preface; 1. Introduction; 2. Typical equations of mathematical physics. Boundary conditions; 3. Cauchy problem for first-order partial differential equations; 4. Classification of second-order partial differential equations with linear principal part. Elements of the theory of characteristics; 5. Cauchy and mixed problems for the wave elc%