This is a very interesting and useful book for any advanced undergraduate and beginning graduate student on mathematics, statistics, computational physics, chemistry, and engineering, with a focus on numerical analysis and computational science.

The main scope of this book is to provide students with the opportunity to apply numerical analysis and the well-known MATLAB to solve problems in their own specialties.

The book is unique in how its subjects are introduced. While the basic approach of most other books is to present (and extend) the theory of a subject and at the end to provide some exercises on this subject, the authors follow a different approach with this book. They propose investigating the subjects of the book via the solution of exercises. Many chapters of the book have the following structure: (1) review of the subject, (2) theoretical exercises, and finally (3) programming exercises. In some cases a combination of theoretical and programming exercises exists. This is an excellent approach: it combines theory and programming, and gives students the opportunity to understand the theory/programming of the exercises.

Specifically, the book consists of 13 chapters. Chapter 1 is an introduction to MATLAB, covering tables, vectors, matrices, and plotting. Chapter 2 gives details on matrices (computations) and linear systems. Chapter 3 investigates eigenvalues and eigenvectors. Chapter 4 investigates the most important vector and matrix norms and how one can use them; condition numbers are also presented. Chapter 5 studies several iterative methods for the solution of nonlinear equations of the form x = f(x). Chapter 6 investigates interpolation theory and chapter 7 gives an introduction to the development of Bézier curves and surfaces and Bernstein polynomials.

Chapter 8 provides more details on approximation. Chapter 9 is an introduction to approximating integrals (for example, the development of quadratures, composite rules, and extrapolation). Chapter 10 investigates least squares approximation, and chapter 11 looks at discrete and continuous approximations (polynomial approximation, Fourier series, and so on). Chapter 12 investigates the numerical solution of ordinary differential equations via Runge-Kutta and predictor-corrector methods. Finally, chapter 13 covers finite difference methods for partial differential equations.