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Elementary differential equations and boundary value problems. 10th edition. International student version. (English) Zbl 1275.34001

New York, NY: Wiley (ISBN 978-1-118-32361-8/pbk). xix, 809 p. (2013).
The book combines “a sound and accurate (but not abstract) exposition of the elementary theory of differential equations with considerable material on methods of solution, analysis, and approximation that have proved useful in a wide variety of applications” (a quotation from the preface). As it is suggested by the number of its editions, it is invaluable as a textbook for undergraduate students of mathematics, science or engineering. Moreover, it is an extensive source of examples of mathematical modelling via differential equations.
From the instructor’s perspective, the contents provides enough flexibility to choose particular topics from the individual chapters which are independent of each other as far as it is possible and, above all, from a wide variety and range of problems for homework assignments, student projects and examinations.
Most of the book deals with ordinary differential equations except for one chapter concerning partial differential equations. More precisely, the contents is described as follows. The introductory Chapter 1 presents some first insights into mathematical modelling. A detailed exposition of methods for solving first-order differential equations is given in Chapter 2. The theory of the linear ordinary differential equations is considered in Chapters 3 (second order) and 4 (higher order). Then, the method of series solutions for second-order linear equations is presented (Chapter 5) followed by the the Laplace transform (Chapter 6). Next, the material is considered in Chapter 7 from the general perspective of the systems of linear first-order equations. In Chapter 8, the exposition is shifted from analytical techniques to numerical methods. Chapter 9 contains basic knowledge on the qualitative theory of nonlinear differential equations and chaos illustrated with numerous examples, graphical representations and discussions. The classical partial differential equations of mathematical physics are presented in Chapter 10, where special attention is paid to preliminary topics from the theory of Fourier series. The last chapter deals with boundary value problems and Sturm-Liouville theory.
The major revisions made in the present edition are the following (as indicated in the preface): Sections 8.5 and 8.6 have been interchanged; derivations and proofs in several chapters have been expanded or rewritten to provide more details; the fact that the real and imaginary parts of a complex solutions of a real problem are also solutions is already formulated as a theorem in Sections 3.2 and 7.4; the treatment of generalized eigenvectors in Section 7.8 has been expanded both in the text and in the problems; there are twenty new or revised problems; there are new examples in Sections 2.1, 3.8 and 7.5; about a dozen figures have been modified to make essential features more prominent; there are several new historical footnotes, and some others have been expanded.
For reviews of previous editions, see [5th ed. (1992; Zbl 0807.34002); 4th ed. (1986; Zbl 0652.34001); 3rd ed. (1977; Zbl 0353.34001); 2nd ed. (1969; Zbl 0182.11401); MĂ©xico: Editorial Limusa-Wiley, S.A. (1967; Zbl 0178.09001); 1st ed. (1965; Zbl 0128.30601)].

MSC:

34-01 Introductory exposition (textbooks, tutorial papers, etc.) pertaining to ordinary differential equations
34A45 Theoretical approximation of solutions to ordinary differential equations
34B05 Linear boundary value problems for ordinary differential equations
34B15 Nonlinear boundary value problems for ordinary differential equations
65L05 Numerical methods for initial value problems involving ordinary differential equations
35-01 Introductory exposition (textbooks, tutorial papers, etc.) pertaining to partial differential equations
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