An interesting read, this book is composed of 13 chapters spread over two parts.

Chapter 1 covers MATLAB basics, including floating-point numbers, problems and conditioning, and algorithm stability. Chapter 2 explores matrices (including various vector norms, computations, and structures) and linear systems (that is, conditioning). The authors further extend their explanation of linear systems by introducing normal equations and QR factorization in chapter 3. Chapter 4 introduces the rootfinding problem and methods such as fixed-point iteration, Newton for nonlinear systems, and so on. In chapter 5, the authors discuss the interpolation problem, piecewise interpolation, cubic splines, finite differences and convergence, and numerical and adaptive integration. Chapter 6 describes initial-value problems, Euler’s method, differential equations, Runge-Kutta methods, and multistep methods (including implementation and zero-stability).

Part 2 starts with chapter 7. In it, the authors brief readers about matrix analysis, highlighting details regarding eigenvalue and singular value decomposition, symmetry and definiteness, and dimension reduction. Chapter 8 presents power, inverse, and matrix-free iterations, generalized minimum residual (GMRES), an analog of GMRES called MINRES, Krylov subspaces, and preconditioning. Chapter 9, “Global Function Approximation,” covers the barycentric formula, orthogonal polynomials, spectrally accurate integration, improper integrals, and trigonometric and polynomial interpolations. Chapter 10 includes sections on “Shooting,” “Differentiation Matrices,” “Collocation for Linear Problems,” “Nonlinearity and Boundary Conditions,” and “The Galerkin Method.” Chapter 11, “Diffusion Equations,” covers the Black-Scholes equation, absolute stability, stiffness, and so on. Chapters 12 and 13 cover “Advection Equations” and “Two-Dimensional Problems,” respectively.

Highlights listed under “key ideas in this chapter” make the book fitting for both beginning and advanced MATLAB learners. Furthermore, the authors include lists of technical terms and MATLAB commands used, as well as a prologue (“Two Imperfect Ideas”). Brief notes on linear algebra, a short bibliography, and index terms are also included. The authors’ extensive coverage with examples and exercises make for a more practical book, like a technically oriented manual for students, academics, and professionals working with MATLAB implementations.