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AuthorBetounes, David. author
TitleDifferential Equations: Theory and Applications [electronic resource] : with Mapleยฎ / by David Betounes
ImprintNew York, NY : Springer New York : Imprint: Springer, 2001
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Descript XIV, 680 p. 225 illus. online resource


This book was written as a comprehensive introduction to the theory of ordinary differential equations with a focus on mechanics and dynamical systems as time-honored and important applications of this theory. Hisยญ torically, these were the applications that spurred the development of the mathematical theory and in hindsight they are still the best applications for illustrating the concepts, ideas, and impact of the theory. While the book is intended for traditional graduate students in matheยญ matics, the material is organized so that the book can also be used in a wider setting within today's modern university and society (see "Ways to Use the Book" below). In particular, it is hoped that interdisciplinary programs with courses that combine students in mathematics, physics, engineering, and other sciences can benefit from using this text. Working professionals in any of these fields should be able to profit too by study of this text. An important, but optional component of the book (based on the inยญ structor's or reader's preferences) is its computer material. The book is one of the few graduate differential equations texts that use the computer to enhance the concepts and theory normally taught to first- and second-year graduate students in mathematics. I have made every attempt to blend toยญ gether the traditional theoretical material on differential equations and the new, exciting techniques afforded by computer algebra systems (CAS), like Maple, Mathematica, or Matlab


1 Introduction -- 2 Techniques, Concepts, and Examples -- 3 Existence and Uniqueness: The Flow Map -- 4 One-Dimensional Systems -- 5 Linear Systems -- 6 Linearization and Transformation -- 7 Stability Theory -- 8 Integrable Systems -- 9 Newtonian Mechanics -- 10 Motion on a Submanifold -- 11 Hamiltonian Systems -- A Elementary Analysis -- A.1 Multivariable Calculus -- A.2 The Chain Rule -- A.3 The Inverse and Implicit Function Theorems -- A.4 Taylorโ{128}{153}s Theorem and The Hessian -- A.5 The Change of Variables Formula -- B Lipschitz Maps and Linearization -- B.1 Norms -- B.2 Lipschitz Functions -- B.3 The Contraction Mapping Principle -- B.4 The Linearization Theorem -- C Linear Algebra -- C.1 Vector Spaces and Direct Sums -- C.2 Bilinear Forms -- C.3 Inner Product Spaces -- C.4 The Principal Axes Theorem -- C.5 Generalized Eigenspaces -- C.6 Matrix Analysis -- C.6.1 Power Series with Matrix Coefficients -- D CD-ROM Contents

Mathematics Mathematical analysis Analysis (Mathematics) Numerical analysis Mathematics Analysis Numerical Analysis


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