Differential Equations and Dynamical Systems - (Texts in Applied Mathematics) 3rd Edition by Lawrence Perko (Paperback)
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<p/><br></br><p><b> About the Book </b></p></br></br><p>This textbook, ideal for students and lecturers alike, is a systematic study of the qualitative and geometric theory of nonlinear differential equations and dynamical systems. It includes a thorough treatment of linear systems.</p><p/><br></br><p><b> Book Synopsis </b></p></br></br>Mathematics is playing an ever more important role in the physical and biological sciences, provoking a blurring of boundaries between scientific disciplines and a resurgence of interest in the modern as well as the clas- sical techniques of applied mathematics. This renewal of interest, both in research and teaching, has led to the establishment of the series: Texts in Applied Mathematics (TAM). The development of new courses is a natural consequence of a high level of excitement on the research frontier as newer techniques, such as numerical and symbolic computer systems, dynamical systems, and chaos, mix with and reinforce the traditional methods of applied mathematics. Thus, the purpose of this textbook series is to meet the current and future needs of these advances and encourage the teaching of new courses. TAM will publish textbooks suitable for use in advanced undergraduate and beginning graduate courses, and will complement the Applied Math- ematical Sciences (AMS) series, which will focus on advanced textbooks and research level monographs.<p/><br></br><p><b> From the Back Cover </b></p></br></br><p> </p> <p>This textbook presents a systematic study of the qualitative and geometric theory of nonlinear differential equations and dynamical systems.</p> <p>Although the main topic of the book is the local and global behavior of nonlinear systems and their bifurcations, a thorough treatment of linear systems is given at the beginning of the text. All the material necessary for a clear understanding of the qualitative behavior of dynamical systems is contained in this textbook, including an outline of the proof and examples illustrating the proof of the Hartman-Grobman theorem, the use of the Poincare map in the theory of limit cycles, the theory of rotated vector fields and its use in the study of limit cycles and homoclinic loops, and a description of the behavior and termination of one-parameter families of limit cycles.</p> <p>In addition to minor corrections and updates throughout, this new edition contains materials on higher order Melnikov functions and the bifurcation of limit cycles for planar systems of differential equations, including new sections on Francoise's algorithm for higher order Melnikov functions and on the finite codimension bifurcations that occur in the class of bounded quadratic systems.</p> <p></p><p/><br></br><p><b> Review Quotes </b></p></br></br><br><p>Reviews from the first edition: </p> <p>"...The text succeeds admiraby ... Examples abound, figures are used to advantage, and a reasonable balance is maintained between what is proved in detail and what is asserted with supporting references ... Each section closes with a set of problems, many of which are quite interesting and round out the text material ... this book is to be highly recommended both for use as a text, and for professionals in other fields wanting to gain insight into modern aspects of the geometric theory of continuous (i.e., not discrete) dynamical systems." MATHEMATICAL REVIEWS</p><br>
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