Preface - 2nd Edition

The second edition of this text continues with the emphasis given in the first edition and is targeted to both senior level undergraduate and first year graduate students without comprehensive numerical background. Motivation for the text has grown from the authors need to provide a text which covers both advanced features of numerical methods and specific applications in the process engineering field.

The computational tools available for numerical computation range from paper and pencil, to desktop computers up to super-computers. In this text, MATLAB is used as the computing environment due to its widespread availability to students and engineers. Computational methods presented in MATLAB are easy to read and understand and its graphical capabilities provide convenient method to present engineering results.

In writing the second edition, the authors have had the opportunity to improve both content and presentation of material, covering additional examples and end-of-chapter problems as well as additional coded examples. The text takes a broader view of presentation under the following chapters:

• Chapter 1 sets the groundwork for the rest of the book with introductory examples and model development steps. Introduction to computation and programming with MATLAB is achieved, coupled with appendix A and B. Taylor series approximation as well as fundamental theorems for number representation and basic definitions are presented.
• Chapter 2 deals with finding the roots of non-linear equations for functions of single variables as well as numerical acceleration. Both bracketing and open methods are explored.
• Chapter 3 deals extensively with topics from linear algebra. Direct elimination methods, including LU factorization of matrices are explored. Numerical methods for finding eigenvalues and eigen vectors, as well as iterative methods of Jacobi, Gauss Seidel as well as succesive relaxation techniques are extensively explored.
• Chapter 4 deals with nonlinear functions of several variables. The multi-dimensional Newton method is emphasized.
• Chapter 5 covers numerical methods for functional approximations. Part I of the chapter covers polynomial as well as piecewise interpolation. Least-squares approximation of data is investigated and the development of difference equations using difference operators is presented. Part II of the chapter deals with methods for numerical differentiation and integration. Several Newton-Cotes integration formula (based on evenly spaced nodes) and the Gaussian quadrature rules (based on optimally selected points) are explored.
• Chapter 6 treats the numerical methods for solving ordinary differential equations, beginning with basic techniques such as Euler, Runge Kutta and multistep methods. The methods are then extended to cover the solution of system of first order ODE’s and the concepts of stiffness and stability are introduced.
• Chapter 7 presents finite difference methods and shooting methods for the solution of linear and nonlinear boundary value problems. A number of practical examples from fluid mechanics and heat transfer are solved.
• Chapter 8 introduces finite-difference methods for solving elliptic, parabilic and hyperbolic equations. The method of lines is also introduced with examples.