This 750-plus-page book on applied linear analysis is the culmination of the authors’ more than three decades of experience teaching graduate students in chemical engineering, as well as a continuation of their own mentors’ legacy. It is reminiscent of books with titles such as *Applied mathematics for engineers and scientists* that were very popular in the decades covering 1950 to 1980. The authors very carefully interweave theory with specific applications involving compartmental models and multi-scale analysis, and illustrate the use of the Mathematica software system. Their expertise and enthusiasm for the topics is very evident.

The book contains 30 chapters divided into six parts. Part 1, “Applied Matrix Algebra,” contains the first seven chapters. It lays the foundation for the rest of the book and contains extensive coverage of theory and methods for solving linear systems, eigen systems, generalized eigen systems and canonical forms, and the standard treatment of quadratic forms. Part 2 (four chapters) provides a succinct treatment of basic concepts from finite-dimensional linear spaces.

Parts 3 and 4 are devoted to the treatment of initial and boundary value problems for linear ordinary differential equations (ODEs), respectively. After a good introduction to the initial value problem and systems with periodic coefficients, Part 3 covers special topics related to functions of complex variables, series solutions, and a comprehensive introduction to the theory and applications of the Laplace transform methods for solving linear systems of ODEs. Part 4 contains a detailed treatment of two-point boundary value problems, the role of Green’s function, Strum-Liouville theory, and integral equations.

Part 5 contains detailed coverage of the theory and application of the classical Fourier transform theory for problems with varying geometries. In addition to the several examples illustrated throughout many parts, Part 6 (five chapters) is exclusively devoted to the analysis of problems that are germane to chemical engineering. This final part provides a nice pathway to understanding the various tools and techniques developed throughout the book. The bibliography includes a short list of books and papers, and the index is very useful.

The authors suggest a couple of different possible topics to develop and teach in a graduate-level course based on this book. Overall, an excellent book that belongs in every library.