In Section 3 the modifications of a classical wave equation are described, in Section 4--the corresponding evolution equation is presented.
The classical wave equation (1) has a closed solution (see ) for given initial conditions
For the classical wave equation such a replacement gives no advantage but for modified wave equations the evolution equations are widely used.
The classical wave equation (1) (or as derived for solid mechanics--Eq.
The classical wave equation has solution in terms of variables [xi] = x + [c.
Omitting the details [5,10,11], the classical wave equation (1) in new variables (23) is simply
Chapters cover differentiation, integration, series and limits, functions defined by integrals, complex numbers, ordinary differential equations, power series solutions of differential equations, orthogonal polynomials, Fourier series, Fourier transforms, operators, functions of several variables, vectors, plane polar coordinates and spherical coordinates, the classical wave equation
, the Schrodinger equation, determinants, matrices, matrix eigenvalue problems, vector spaces, probability, statistical regression and correlation, and numerical methods.