This textbook provides an introduction to numerical methods, incorporating theory with specific computing exercises and programmed examples of presented techniques. Chapters 2-8 of the book describe 49 programs written in Fortran 95 covering a wide range of numerical applications. Many of the programs discussed use a sub-program library called nm \_ lib that contains 23 subroutines and functions. In addition, there is a precision module that controls the precision of calculations. Chapter 2 deals with numerical solutions of systems of linear algebraic equations, while chapter 3 considers the roots of a single nonlinear equation and systems of nonlinear equations. In chapter 4, eigenvalue equations are considered, while chapter 5 deals with interpolation and curve fitting. Chapter 6 is devoted to numerical quadrature and chapter 7 introduces the solving of ordinary differential equations by numerical tools. Chapter 8 shows how to solve partial differential equations using finite difference and finite element approaches.
In all chapters, mathematical ideas and definitions are introduced as they occur and most numerical aspects are illustrated with computer programs. The library routines are described and listed in appendices A and B, respectively. All software described in the text can be downloaded from the web site, www.mines.edu/~vgriffit/NM. The textbook shows many different contexts of numerical analysis and offers an excellent introduction to more comprehensive subroutine libraries such as the numerical algorithm group (NAG). The book may be of interest to graduate students and software developers in engineering and mathematics.