According to my experience, teaching numerical methods can be an ordeal: students typically do not like the related courses. The reason stems from the fact that the topic is difficult, that is, not easy to follow; additionally, the attendees sometimes cannot see much sense in studying it. The former is not easy to be overcome--there is no royal road to math, to traverse Euclid--and especially concerns numerical methods that are likely not to impress a young adept in the field. On the other hand, the potential usefulness is relatively easy to show, for instance, the inherent optimization methods embedded in neural networks are the basis of contemporary machine learning, known to all Google users. Therefore, each and every good textbook on numerical methods should address the first aforementioned problem, that is, provide a clear explanation of the problems and methods. Gupta’s book is really an example of how to do that efficiently.

The book deals with a typical numerical methods curriculum and can be read by any undergraduate student familiar with the fundamentals of calculus. The selection of topics provides a typical engineer with a full toolbox, and nicely includes many methods to attack the selected problems given.

The book (almost 800 pages) consists of 16 chapters, six concise appendices, and an index. The structure is well-thought-out; it is typically necessary to go through all the previous chapters in order to understand the next one (which works for a semester-long course). Here, I only enumerate the topics discussed: number systems and error analysis as preparatory material; solving nonlinear equations, polynomial equations, and systems of linear and nonlinear equations; eigenvalues and eigenvectors; interpolation and various types of approximation; dealing with finite operators; differentiation and integration; and ordinary differential equations (and their systems) and partial differential equations. One can see that the selection of topics is very broad and representative of a book that claims to start with the fundamentals.

For sure, the book is aimed at beginners. Everything is explained very clearly. Background knowledge necessary to understand the presented material is thoroughly covered, along with end-of-book appendices on using computers for numerical methods, the Taylor series, the notion of linearity in various contexts, basic functions with their plots, and the Greek alphabet.

A very valuable feature of the book is that it contains many numerical examples showing how each of the covered methods works. Therefore, there is a large potential for self-study, especially because each chapter includes a set of exercises with answers. Additionally, each part of the material is summarized with a clear table showing the basic aspects, formulas, and features of all the presented approaches. It is evident that the book is based on Gupta’s extensive teaching experience with the topic and aimed at helping students understand the toughest parts.

Overall, the mathematical side of the story is well described. Nevertheless, alternative options present the topic with some software examples [1]. Today, numerical methods should be taught with computer exercises, so this is a nice and desirable approach (although the roots of the field are in the pre-computer era, it is hard to imagine a current engineer who does not use this basic tool to support the applications). Gupta’s book does not follow this path, but focuses on a thorough explanation of the classical results related to the field.

One can argue that to fully understand the field, it will be necessary for the students to practice the methods on their own. Apparently, this was not the aim of the author. I understand this approach--software is in many cases a matter of fashion, and what is now popular (like Python) might be outdated in a few years. Contrary to that, the mathematical part will always be up to date. However, a teacher selecting textbooks for a course in numerical methods will have to remember that, while Gupta’s book is a perfect match for lectures or exercise classes, a separate text will be helpful for organizing laboratory or project classes.