Differential equations for beginners
As the author himself points out, the book is accessible to a 12th grade high school student (Terminal, in the French system). It continues with Freshman and Sophomore (Bac+1 and Bac+2) up to a Junior (Bac+3) students (in sciences, engineering, economic and related fields). It is therefore this kind of (mainly Francophone, since it is written in French) readership which is targeted. The author has a clear vision of his goals. It is meant for ``beginners'' (as mentioned in the title of the book). As such, the author has managed to provide the right amount of details and explanation. The book is straightforward and self-contained. It is easy and pleasant to read. These facts support self-study. Therefore the book achieves its intended goals quite well. The book has seven chapters: 1. Scalar linear differential equations of first order with constant coefficients, of second order with constant coefficients. 2. Scalar linear differential equations of first order with continuous functions as coefficients. 3. Scalar linear differential equations of second order with continuous functions as coefficients. 4. First order linear systems with constant coefficients. 5. Classifications of differential systems \(X'=AX\) when \(A\) is a \(2\times 2\) matrix. 6. Nonlinear differential equations: A first visit. 7. First steps in the numerical approximation of solutions of differential equations: Euler's method. Clearly, these chapters may be divided into three parts: Linear case, nonlinear case and numerical approximation. In the first part the author provides different methods of resolutions of the homogeneous as well as the non-homogeneous linear first and second order differential equations. The basic and fundamental theorem of existence and uniqueness of solutions for nonlinear (first order) equations is stated and proved in the second part. By the way, the proofs of all the theorems are provided in this book. The method of separation of variables is discussed in this part for the special class of separable differential equations. The third part is devoted to Euler's method.NEWLINENEWLINEThis is, indeed, an interesting book. However, having in mind that it is intended for beginners, there are relatively few examples, although, sometimes, these few examples (one or two) are sufficient for the illustration of the notion, the concept, the idea or the theorem. When compared to other ``similar'' books, we notice that several ``traditional'' items are missing. In particular: -- There are no suggested problems at the end of each chapter. Instead, the author provides some annexes to complement the material and some necessary tools. -- Only 9 references are listed in the Bibliography. -- No index is provided. -- No lists of notation and symbols are given.
scientific article; zbMATH DE number 6204238