Reviewed by Andrew Zimmer, Assistant Professor, William and Mary, on 2/2/2018.

The text is not a reference book, but an introduction to differential equations. It contains the topics commonly covered in a standard sophomore … read more

Comprehensiveness rating: 5 read less

The text is not a reference book, but an introduction to differential equations. It contains the topics commonly covered in a standard sophomore level undergraduate course. The index appears to be effective. Further, at the start of each section the author references corresponding chapters in two of the commonly used books: Boyce and DiPrima’s "Elementary Differential Equations and Boundary Value Problems" and Edwards and Penney's "Differential Equations and Boundary Value Problems: Computing and Modeling."

Accuracy rating: 5

On a high level the book appears to be mostly error free - the main theorems are stated correctly, mathematical notation is used in the standard way, and historical attribution is accurate.
I have not read every section closely, but the in sections that I have the calculations and examples appear to be error free.

Relevance/Longevity rating: 5

This is standard material for an undergraduate course in Ordinary Differential Equations. I don't think the text will become obsolete in the near future.

Clarity rating: 3

As the word "notes" in the title suggests the book is fairly terse when compared to other textbooks. When used in a classroom setting I think this is fine. However, for self study a text with longer explanations may be preferable.

Consistency rating: 5

The notation seems consistent.

Modularity rating: 3

The nature of mathematics restricts the ability for the book to be completely modular. However, the author describes the interdependency between the chapters in the introduction.

Organization/Structure/Flow rating: 5

There are no issues with the book's organization/structure/flow.

Interface rating: 5

I saw no "interface" issues.

Grammatical Errors rating: 5

I noticed no grammatical errors that significantly impacted the readability of the text.

Cultural Relevance rating: 3

not applicable.

Comments

I have not used this text as an instructor. The last time I taught an differential equations course I used Boyce and DiPrima’s "Elementary Differential Equations and Boundary Value Problems" (which is the standard text at the institution I was teaching at). Through out the quarter, I also read through Jirí Lebl's text to see if it would appropriate to use the next time I taught the course. Overall I think Lebl's book compares well to Boyce and DiPrima’s text and the next time I teach I will probably use Lebl's book.
The book has several attractive features. First, there are many problems given in each section. Second, each section contains a reference to the corresponding material in two of the standard textbooks in ordinary differential equations. As an instructor this makes it easy to update lectures if one switches from one of these text. For students, this gives them as easy to find reference for an alternative approach or more detailed discussion. Perhaps the most attractive feature is that the book will never go out of print and there will be no pressure to update to a new edition.

Reviewed by Carlos Montalto Cruz, Postdoctoral Researcher, University of Washington, on 8/22/2016.

The book covers many of the material that is usually covered on an undergraduate engineering course on Differential Equations. It also was an … read more

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.

Comments

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.