Differential equations for beginners
type: Item
instance of: scholarly article
zbMATH Open document ID: 1332.34002
publication date: 2013-09-03T00:00:00Z
Mathematics Subject Classification ID: 34-01
Mathematics Subject Classification ID: 34A05
Mathematics Subject Classification ID: 34A30
Mathematics Subject Classification ID: 34A34
Mathematics Subject Classification ID: 65L05
zbMATH DE Number: 6204238
author: Jean-Baptiste Hiriart-Urruty
MaRDI profile type: Publication
title: Differential equations for beginners
review text: 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 th…
reviewed by: N.-E. Tatar
description: scientific article; zbMATH DE number 6204238