Green's Functions: Construction and Applications (de Gruyter Studies in Mathematics): 42

“[…] the book is a useful source for everyone who is studying or working in fields of science, finance, or engineering that involve practical solutions of partial differential equations.”
L’Enseignement Mathématique 2/2012

“The monograph is a valuable source to any researcher or postgraduate student working in applied sciences or engineering that concern practical solutions of partial or ordinary differential equations.”
Marius Ghergu, Zentralblatt für Mathematik

Green’s functions represent one of the classical, intensively explored, and widely implemented concepts in the area of differential equations. This monograph is looking at applied elliptic and parabolic type partial differential equations primarily in two variables. The elliptic type includes the Laplace, static Klein-Gordon, biharmonic equation, and systems simulating the static equilibrium of thin shells. The parabolic type is represented by the classical heat equation and the Black-Scholes equation which has recently emerged as a mathematical model in financial mathematics.

The intention of this book is not only to familiarize the reader with a review of classical approaches that are traditionally used for the construction of Green’s functions. In addition to that, the reader will also be introduced to some nontrivial construction techniques and will be invited to a challenging research in this productive area of applied mathematics. Therefore the book is a useful source for everyone who is studying or working in fields of science, finance, or engineering that involve practical solutions of partial differential equations.