부산대학교 도서관

This is a well presented and helpful textbook at the advanced undergraduate or perhaps graduate level. \par In Chapter 1, the boundary value problems of mathematical physics are presented. \par In Chapter 2 the author introduces generalized functions and their Fourier transforms. Chapter 3 is devoted to the Cauchy problem; the retarded potential, the wave equation and the heat equation are treated in succession. Chapter 4 deals with integral equations. The Fredholm and Hilbert-Schmidt theorems are studied. This chapter is, in the reviewer's opinion, a welcome addition to the contents of many similar textbooks. Chapter 5 is devoted to boundary value problems for elliptic equations. This includes the study of eigenvalue problems, the Sturm-Liouville theory, harmonic functions, the Newtonian potential, the Laplace and Poisson equations in space, Green's functions and the Dirichlet problem, spherical functions, the two-dimensional Laplace equation and the Helmholtz equation. \par Finally, in Chapter 6 the author examines mixed problems of hyperbolic and parabolic types.