Comprehensiveness rating: 3 read less
The book covers many of the material that is usually covered on an undergraduate engineering course on Differential Equations. It also was an extensive index. However, the book does not cover some important topics (e.g., more applications of the theory of ODEs, study of non-diagonalizable systems of DE). Overall, the material main material is there but it sometimes lacks depth in the presentation.
Accuracy rating: 4
This are lecture notes, not exactly a book. As lecture notes they do emphasize on the most important parts of the material. However there are some explanations that required revision (e.g., discussion on antiderivatives, hypothesis on some theorems). I think this lecture notes will benefit of a proper definition of concepts and a careful statement of theorems. I would not recommend this lectures for self study since they lack of some precision for the careful reader.
Relevance/Longevity rating: 5
This is a classic material and will hardly get obsolete
Clarity rating: 4
While most of the books is written in a lucid and accessible way. Some parts of the book are written in an informal way (e.g., “Do note that the definite integral and the indefinite integral (antidifferentiation) are completely different beast” or “Here is a good way to make fun of your friends taking second semester calculus. Tell them to find the closed form solution. Ha ha ha (bad math joke). It is not possible (in closed form)”). Also, there are some explanations that need further improvement.
Consistency rating: 4
I could not find inconsistencies in terminology while doing a fast read of the book. There are however many typos in the text and theorems.
Modularity rating: 5
As lecture notes (not book) the modularity of the are very good. There is a natural flow of the material.
Organization/Structure/Flow rating: 3
Overall, the organization of the material is standard. However, I found that the books goes back and forth in the topic of partial differential equations (PDEs). I prefer the more classical approach where the theory of PDEs are presented after covering ordinary differential equations (e.g., Boyce-Di Prima’s book). But this might be a matter of taste.
Interface rating: 4
The images on the book are good. I think the book could benefit of a more interactive interface with back and forth interlinks. Also, it will be nice to have reference to the web material produce by the author (see additional comments at the end)
Grammatical Errors rating: 4
I could find some minor grammatical errors.
Cultural Relevance rating: 3
Is hard to attest cultural relevance on mathematics notes like this ones. I could not find relevant culturally plural examples.
There are two very useful and important highlights about this book that I did not mentioned before. First, the LATEX code of the notes are provided by the author on his website. That in itself, makes the book a great contribution since it will allow improvements and extensions in a very smooth fashion. Actually, as mentioned on the author’s website there are already Portuguese notes that are a partial translation of this ones. Second, the author provides with many SAGE demos to illustrate some parts of the theory (e.g., Euler’s method, mechanical vibrations, resonances, etc). I would be nice if the additional material is mentioned when relevant during the text.