This book is written for students in engineering and applied mathematics. The emphasis is on description of the numerical methods rather than on the proofs or analysis. The authors present some elements of continuum mechanics, partial differential equations, and numerical analysis in this text which they use as a year-long graduate course. There are six chapters and an appendix. Each chapter ends with exercises and references. Chapter 1 deals with basic equations of continuum mechanics. Chapter 2 deals with numerical methods. Finite differences and variants of the projection method (such as Galerkin’s method, collocation method, finite-element method) are discussed. Ch. 3,4,5 deal respectively with elliptic, parabolic, and hyperbolic equations. Ch. 6 treats higher order equations, nonlinear equations (such as nonlinear diffusion), and discusses some problems in oil reservoir modeling. In the appendix some standard auxiliary material in vector and tensor analysis is given. The scope of the presentation in this text is rather broad and the text can be used by students with different interests.
(On pp. 307 and 412 the authors write Gudonov where Godunov should be.)