Mathematical Theorems: Boundary Value Problems and Approximations

The main content of this book is related to construction of analytical solutions of differential equations and systems of mathematical physics, to development of analytical methods for solving boundary value problems for such equations and the study of properties of their solutions. A wide class of equations (elliptic, parabolic, and hyperbolic) is considered here, on the basis of which complex wave processes in biological and physical media can be simulated. The method of generalized functions presented in the book for solving boundary value problems of mathematical physics is universal for constructing solutions of boundary value problems for systems of linear differential equations with constant coefficients of any type. In the last sections of the book, the issues of calculating functions based on Padé approximations, binomial expansions, and fractal representations are considered. The book is intended for specialists in the field of mathematical and theoretical physics, mechanics and biophysics, students of mechanics, mathematics, physics and biology departments of higher educational institutions.