This is an excellent text for self-study or as a supplement to a classroom text. It is fairly wide ranging, covering a large portion of the mathematics needed during the first few years of an engineering, or physical science program. However, it is not quite comprehensive, lacking some areas that have gained significant importance in recent times, e.g, discrete transforms. Although some Fourier Series and transforms are covered in the companion volume "Advanced Engineering Mathematics".
The pretests and revision (more commonly called review in the US) sections are quite helpful. The book de-emphasizes formal definitions, as concepts and intuitive descriptions are provided in conjunction with examples. However, in some instances this can lead to problems, where the appropriate problem-solving approach is well-presented but the lack of a formal definition can lead to some "fuzziness". In these cases an inexpensive mathematics dictionary, or standard text, should provide the needed clarity.
Some sections or chapters are quite elementary and may not be needed by many readers. For example, the book starts with an approximately 70 page section on arithmetic which includes conversion between different number systems, e.g. octal, hex, decimal.
The book is well designed and laid out, avoiding the distracting overuse of color found in some competing texts. The authors are usually quite clear, and quickly get to the "meat" of a topic. Extra material is kept to a minimum. One section where this is not true is the Programme (sections) on Functions where unneeded, and arguably unhelpful, box graphics are introduced and used fairly extensively to visually denote the the ideas of function input and output. However, the boxes are not standard mathematical constructs for handling functions. In my opinion, these extraneous constructs are an unnecessary distraction, as the function notation carries with it all the structure needed for comprehension and the function notation is what students will see in later work. Hopefully, these boxes can be eliminated in later editions.
The book shows a much earlier publishing heritage as some mathematical terms no longer in common usage are still retained.
For a book this size, there are an unusually small number of errors or misstatements and these are usually obvious. One example where this is not true is when the authors use the terms "range" and "co-domain" incorrectly as synonyms.
This is an outstanding and well-written book. The book's presentation of desired learning outcomes, i.e., behavioral objectives, at the start of each Programme is excellent. Material is presented in easily digestible short sections that allow for breaks to be taken at almost any time, without the need to stop in the middle of an unfinished section. Pretest quizzes allow readers to determine what sections they can skip and what sections they need to work on. As there are very few required backward references, previously learned topics can be skipped without problem. A minor deficiency is the lack of more formal definitions. These are usually not needed. However, in a number of cases they would help aid understanding and reduce the chance of encountering unexpected problems in later work. However, the book's strong emphasis on carefully developing concepts needed to comfortably handle the mathematical manipulation and problem solving skills required for engineering is exceptional. I have no hesitation in giving it the highest recommendation.