Ordinary Differential Equations

Reviewed by Malgorzata Marciniak, Assistant Professor, LAGCC on 12/26/18

Comprehensiveness rating: 4 see less

Elegant and relatively short textbook is written on less than 150 pages but covers a 12-week course in 10 chapters and 6 appendices. The appendices take about a quarter of the book and could serve as review materials or lessons on their own.

Content Accuracy rating: 4

In the Preface the author claims that he uses this textbook for the first course of ordinary differential equations for mathematics students, but it seems that this material is suitable for the second course. The book does not furnish proofs of theorems, but each chapter contains problem sets and few examples. The book contains the list of contents, biography, list of figures, list of tables, and index. Additional comments are provided on the margins.

Relevance/Longevity rating: 4

For most US institutions the book appears to be an excellent complementary textbook for those who would like to gently introduce a little bit of mathematical theory but do not aim for too heavy load of theorems and definitions. Majority of the book is devoted to discussion about stability of two-dimensional autonomous systems. The emphasis is on the concept rather than calculations. The text is generously furnished with pictures.
The textbook will remain valuable regardless the flow of time.

Clarity rating: 5

The textbook is extremely well written but with some overuse of language. Majority of the material is devoted to analysis of the stability of autonomous systems in two variables. The word “manifolds” used in the titles of chapters does not reflect on the generality used in the text that limits examples to curves on the plane. The manifold that actually appears in the textbook is a plane curve.
The book contains the list of contents, biography, list of figures, list of tables, and index. It is easy to navigate through and the comments on the margins provide suggestions about the interconnections of topics.

Consistency rating: 5

All terms related to differential equations used in the textbook are introduced in a form of a definition. Many examples are assisted by pictures which significantly improve the clarity of the exposition. Notation, terminology and appearance are consistent throughout the book.

Modularity rating: 5

The book is conveniently divided into 10 chapters and 6 appendices with material carefully selected into a logical flow. Chapters do not carry additional subdivisions except steps of procedures, examples or sets of problems.

Organization/Structure/Flow rating: 5

The content of the book is organized into a logical flow and contains a significant amount of cross references provided by comments on the generous margins. Each chapter begins with definitions, followed by examples or steps of procedures and ends with sample problems.

Interface rating: 5

The interface is well organized according to TeX standards of books with broad margins left for comments. The author uses the margins skillfully providing cross references, footnotes, references and additional comments.

Grammatical Errors rating: 5

The text is grammatically excellent.

Cultural Relevance rating: 5

The book topic does not touch sensitive topics of race, culture, religion, background.

Comments

Suggestions for the textbook: few suggested reflexive problems for consideration may make a use of the vast margins.
For example: in chapter 1 the author defines autonomous equations. In chapter 2 he proves that they have the time-shift property. A sharp student may develop curiosity whether every ODE having the time-shift property must necessarily be autonomous and how the proof may be approached in an elementary way using methods presented in the book.