Differential equations. An introduction to basic concepts, results and applications
type: Item
instance of: scholarly article
zbMATH Open document ID: 1356.34001
DOI: 10.1142/9941
author: Ioan I. Vrabie
publication date: 2016-06-14T00:00:00Z
Mathematics Subject Classification ID: 34-01
Mathematics Subject Classification ID: 34A05
Mathematics Subject Classification ID: 34A12
Mathematics Subject Classification ID: 34A36
Mathematics Subject Classification ID: 34D20
Mathematics Subject Classification ID: 45D05
Mathematics Subject Classification ID: 49-01
Mathematics Subject Classification ID: 34K99
zbMATH DE Number: 6593154
zbMATH Keywords: ordinary differential equation
zbMATH Keywords: integration techniques
zbMATH Keywords: existence
zbMATH Keywords: uniqueness
zbMATH Keywords: continuous dependence on initial data and parameters
zbMATH Keywords: saturated solutions
zbMATH Keywords: stability
zbMATH Keywords: differential equations with discontinuous right-hand sides
zbMATH Keywords: first integrals
zbMATH Keywords: Volterra equations
zbMATH Keywords: calculus of variations
zbMATH Keywords: global solutions
zbMATH Keywords: delay functional differential equations
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1142/9941
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title: Differential equations. An introduction to basic concepts, results and applications
review text: This is the 3rd edition of a remarkably comprehensive textbook in differential equations. Writing a textbook in this field is not an easy job. Since the 50ies of the previous century it has been pointed out that writing a book on ordinary differential equations is somehow a problem of personal taste. The author, an outstanding representative of the Iaşi (Romania) school of ordinary and partial differential equations, has focused in his book on those topics he knew better but also on those his teaching experience considered as representative. Consequently, taking into account the success of the first edition of 2004 [Zbl 1070.34001], the author augmented the book by new chapters -- relevant for both research and teaching. For instance, the 2nd edition was augmented by two chapters: Volterra equations (which nevertheless belongs to a standard course on ``Differential and integral equations'') -- viewed as a good starting point for Operator Theory/Functional Analysis -- and Calculus of variations (usually included in a course of Mathematical Physics) -- possibly in connection with Optimization Theory. An interesting feature of the 2nd edition was the introduction of the Laplace transform. Usually the Laplace transform is avoided in the curricula of Mathematics while being basic in Electrical/ Mechanical Engineering for studying transients (described by ordinary differential as well as by Volterra equations, sometimes even by partial differential equations of hyperbolic or parabolic type).NEWLINENEWLINEThe 3d edition is also augmented by two such new chapters: on Nonlocal problems and on Delay functional differential equations. The Chapter on nonlocal problems (Chapter 10) deals with ``nonlocal'' initial conditions e.g. \(x(0)=g(x(\cdot))\) with \(x(\cdot)\) some future state. For the solutions of such problems, existence, uniqueness and global stability are discussed. For the delay functional differential equations (Chapter 11) there are considered local and global exi…
reviewed by: Vladimir Răsvan
description: scientific article; zbMATH DE number 6593154