Oscillations in Nonlinear Systems (Dover Books on Mathematics), by Jack K. Hale
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Oscillations in Nonlinear Systems (Dover Books on Mathematics), by Jack K. Hale
Best Ebook PDF Oscillations in Nonlinear Systems (Dover Books on Mathematics), by Jack K. Hale
By focusing on ordinary differential equations that contain a small parameter, this concise graduate-level introduction to the theory of nonlinear oscillations provides a unified approach to obtaining periodic solutions to nonautonomous and autonomous differential equations. It also indicates key relationships with other related procedures and probes the consequences of the methods of averaging and integral manifolds.Part I of the text features introductory material, including discussions of matrices, linear systems of differential equations, and stability of solutions of nonlinear systems. Part II offers extensive treatment of periodic solutions, including the general theory for periodic solutions based on the work of Cesari-Halel-Gambill, with specific examples and applications of the theory. Part III covers various aspects of almost periodic solutions, including methods of averaging and the existence of integral manifolds. An indispensable resource for engineers and mathematicians with knowledge of elementary differential equations and matrices, this text is illuminated by numerous clear examples.
Oscillations in Nonlinear Systems (Dover Books on Mathematics), by Jack K. Hale- Amazon Sales Rank: #2013323 in eBooks
- Published on: 2015-03-24
- Released on: 2015-03-24
- Format: Kindle eBook
From the Back Cover
By focusing on ordinary differential equations that contain a small parameter, this concise graduate-level introduction to the theory of nonlinear oscillations provides a unified approach to obtaining periodic solutions to nonautonomous and autonomous differential equations. It also indicates key relationships with other related procedures and probes the consequences of the methods of averaging and integral manifolds.Part I of the text features introductory material, including discussions of matrices, linear systems of differential equations, and stability of solutions of nonlinear systems. Part II offers extensive treatment of periodic solutions, including the general theory for periodic solutions based on the work of Cesari-Halel-Gambill, with specific examples and applications of the theory. Part III covers various aspects of almost periodic solutions, including methods of averaging and the existence of integral manifolds. An indispensable resource for engineers and mathematicians with knowledge of elementary differential equations and matrices, this text is illuminated by numerous clear examples.Dover (2015) republication of the edition originally published by McGraw-Hill, New York, in 1963, and reprinted by Dover Publications, Inc., in 1992.See every Dover book in print atwww.doverpublications.com
About the Author A longtime professor at Brown University, Jack K. Hale is Regents Professor Emeritus at the Georgia Institute of Technology and the author of Dover's Ordinary Differential Equations.
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Most helpful customer reviews
5 of 5 people found the following review helpful. Chaos theory before it was... By Roger Bagula I suppose the best thing about this book is that it is cheap.It was written at a time before Henon and modern chaos theorybecame the rage.It is very good on van der Pol oscillatory theory.It doesn't mention economics, population, prey-predator dynamicsor Mandelbrot,but it deals with the equations, none the lessfrom what is at times an over generalized point of view.It is very good on systems of linear differential equationswith both periodic solutions and near-periodic solutions.It doesn't use the more modern Jacobian approach, but an earlier one.I found information in here that was useful to my own research.
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