Why write yet another book on numerical methods? Having taught this course for a combined 10 years, we have continuously struggled to find a single textbook that works for chemical engineering students. There are outstanding books on the mathematical underpinnings of numerical methods, but the level of sophistication (theory–lemma) is often a turnoff for chemical engineering students and overkill at the introductory stage. There are also excellent generic books on numerical methods that include some engineering applications. We used one such book as a reference for the course, since many students do better with supplemental reading. The challenge with general books is that they do not incorporate sufficient chemical engineering examples, which leads to students wondering exactly how the textbook (which is often expensive) connects to the class. Moreover, with the explosion of online resources, it is quite easy to find explanations of standard numerical methods with the click of a mouse. (Whether those explanations are good or even correct is another issue entirely!) At the other end of the spectrum are chemical engineering textbooks solely devoted to applications with little discussion of the underlying numerical methods. These books provide a wealth of example problems, but they are not suitable for teaching students how to actually solve the problems.

Our goal in writing this texbook is to take a “Goldilocks” approach: not too rigorous, not too applied! At the same time, we want to firmly embed our discussion of numerical methods in the context of chemical engineering applications. The material presented in the book is based on the content of a course in numerical methods developed in our department more than 20 years ago. The book is intended for an undergraduate course in numerical methods, primarily for chemical engineering students. At Minnesota, this is a core course taught in the spring semester of the junior year. The students are taking this course concurrently with (i) Reaction Kinetics and Reactor Design and (ii) Mass Transfer and Separations. This location in the curriculum offers many opportunities to motivate the methods covered in the book and use them to solve realistic chemical engineering problems. For example, we have timed the numerical methods course and the reactors course so that, when we cover systems of ordinary differential equations in numerical methods, the reactors course covers systems of chemical reactions.