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Ordinary Differential Equations with Applications to Mechanics

2007-06-04 Mathematics
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Release : 2007-06-04
Genre : Mathematics
Kind : eBook
Book Rating : 408/5 ( reviews)

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Book Synopsis Ordinary Differential Equations with Applications to Mechanics by : Mircea Soare

Download or read book Ordinary Differential Equations with Applications to Mechanics written by Mircea Soare. This book was released on 2007-06-04. Available in PDF, EPUB and Kindle. Book excerpt: This interdisciplinary work creates a bridge between the mathematical and the technical disciplines by providing a strong mathematical tool. The present book is a new, English edition of the volume published in 1999. It contains many improvements, as well as new topics, using enlarged and updated references. Only ordinary differential equations and their solutions in an analytical frame were considered, leaving aside their numerical approach.

Differential Equations, Mechanics, and Computation

2009-11-13 Mathematics
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Release : 2009-11-13
Genre : Mathematics
Kind : eBook
Book Rating : 385/5 ( reviews)

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Book Synopsis Differential Equations, Mechanics, and Computation by : Richard S. Palais

Download or read book Differential Equations, Mechanics, and Computation written by Richard S. Palais. This book was released on 2009-11-13. Available in PDF, EPUB and Kindle. Book excerpt: This book provides a conceptual introduction to the theory of ordinary differential equations, concentrating on the initial value problem for equations of evolution and with applications to the calculus of variations and classical mechanics, along with a discussion of chaos theory and ecological models. It has a unified and visual introduction to the theory of numerical methods and a novel approach to the analysis of errors and stability of various numerical solution algorithms based on carefully chosen model problems. While the book would be suitable as a textbook for an undergraduate or elementary graduate course in ordinary differential equations, the authors have designed the text also to be useful for motivated students wishing to learn the material on their own or desiring to supplement an ODE textbook being used in a course they are taking with a text offering a more conceptual approach to the subject.

Introduction to Partial Differential Equations with Applications

2012-04-20 Mathematics
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Release : 2012-04-20
Genre : Mathematics
Kind : eBook
Book Rating : 17X/5 ( reviews)

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Book Synopsis Introduction to Partial Differential Equations with Applications by : E. C. Zachmanoglou

Download or read book Introduction to Partial Differential Equations with Applications written by E. C. Zachmanoglou. This book was released on 2012-04-20. Available in PDF, EPUB and Kindle. Book excerpt: This text explores the essentials of partial differential equations as applied to engineering and the physical sciences. Discusses ordinary differential equations, integral curves and surfaces of vector fields, the Cauchy-Kovalevsky theory, more. Problems and answers.

Differential Equations: Theory and Applications

2013-06-29 Mathematics
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Release : 2013-06-29
Genre : Mathematics
Kind : eBook
Book Rating : 716/5 ( reviews)

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Book Synopsis Differential Equations: Theory and Applications by : David Betounes

Download or read book Differential Equations: Theory and Applications written by David Betounes. This book was released on 2013-06-29. Available in PDF, EPUB and Kindle. Book excerpt: This book provides a comprehensive introduction to the theory of ordinary differential equations with a focus on mechanics and dynamical systems as important applications of the theory. The text is written to be used in the traditional way or in a more applied way. The accompanying CD contains Maple worksheets for the exercises, and special Maple code for performing various tasks. In addition to its use in a traditional one or two semester graduate course in mathematics, the book is organized to be used for interdisciplinary courses in applied mathematics, physics, and engineering.

Ordinary Differential Equations and Dynamical Systems

2012-08-30 Mathematics
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Release : 2012-08-30
Genre : Mathematics
Kind : eBook
Book Rating : 283/5 ( reviews)

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Book Synopsis Ordinary Differential Equations and Dynamical Systems by : Gerald Teschl

Download or read book Ordinary Differential Equations and Dynamical Systems written by Gerald Teschl. This book was released on 2012-08-30. Available in PDF, EPUB and Kindle. Book excerpt: This book provides a self-contained introduction to ordinary differential equations and dynamical systems suitable for beginning graduate students. The first part begins with some simple examples of explicitly solvable equations and a first glance at qualitative methods. Then the fundamental results concerning the initial value problem are proved: existence, uniqueness, extensibility, dependence on initial conditions. Furthermore, linear equations are considered, including the Floquet theorem, and some perturbation results. As somewhat independent topics, the Frobenius method for linear equations in the complex domain is established and Sturm-Liouville boundary value problems, including oscillation theory, are investigated. The second part introduces the concept of a dynamical system. The Poincare-Bendixson theorem is proved, and several examples of planar systems from classical mechanics, ecology, and electrical engineering are investigated. Moreover, attractors, Hamiltonian systems, the KAM theorem, and periodic solutions are discussed. Finally, stability is studied, including the stable manifold and the Hartman-Grobman theorem for both continuous and discrete systems. The third part introduces chaos, beginning with the basics for iterated interval maps and ending with the Smale-Birkhoff theorem and the Melnikov method for homoclinic orbits. The text contains almost three hundred exercises. Additionally, the use of mathematical software systems is incorporated throughout, showing how they can help in the study of differential equations.

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