Free Delivery Over $100
|
|
|||
|
||||
OverviewDesigned for a rigorous first course in ordinary differential equations, Ordinary Differential Equations: Introduction and Qualitative Theory, Third Edition includes basic material such as the existence and properties of solutions, linear equations, autonomous equations, and stability as well as more advanced topics in periodic solutions of nonlinear equations. Requiring only a background in advanced calculus and linear algebra, the text is appropriate for advanced undergraduate and graduate students in mathematics, engineering, physics, chemistry, or biology. This third edition of a highly acclaimed textbook provides a detailed account of the Bendixson theory of solutions of two-dimensional nonlinear autonomous equations, which is a classical subject that has become more prominent in recent biological applications. By using the Poincaré method, it gives a unified treatment of the periodic solutions of perturbed equations. This includes the existence and stability of periodic solutions of perturbed nonautonomous and autonomous equations (bifurcation theory). The text shows how topological degree can be applied to extend the results. It also explains that using the averaging method to seek such periodic solutions is a special case of the use of the Poincaré method. Full Product DetailsAuthor: Jane Cronin (Highland Park, New Jersey, USA) , Zuhair Nashed (University of Central Florida, Orlando, USA) , Earl TaftPublisher: Taylor & Francis Ltd Imprint: CRC Press Edition: 3rd edition Weight: 0.544kg ISBN: 9780367387969ISBN 10: 0367387964 Pages: 408 Publication Date: 05 September 2019 Audience: College/higher education , Tertiary & Higher Education Format: Paperback Publisher's Status: Active Availability: In Print  This item will be ordered in for you from one of our suppliers. Upon receipt, we will promptly dispatch it out to you. For in store availability, please contact us. Table of ContentsPrefaces. Introduction. Existence Theorems. Linear Systems. Autonomous Systems. Stability. The Lyapunov Second Method. Periodic Solutions. Perturbation Theory: The Poincaré Method. Perturbation Theory: Autonomous Systems and Bifurcation Problems. Using the Averaging Method: An Introduction. Appendix. References. Index.Reviews... a classic treatment of many of the topics an instructor would want in such a course, with particular emphasis on those aspects of the qualitative theory that are important for applications to mathematical biology. ... A nice feature of this edition is an extended and unified treatment of the perturbation problem for periodic solutions. ... a solid graduate-level introduction to ordinary differential equations, especially for applications. ... -MAA Reviews, August 2010 … a classic treatment of many of the topics an instructor would want in such a course, with particular emphasis on those aspects of the qualitative theory that are important for applications to mathematical biology. … A nice feature of this edition is an extended and unified treatment of the perturbation problem for periodic solutions. … a solid graduate-level introduction to ordinary differential equations, especially for applications. … —MAA Reviews, August 2010 Author InformationCronin, Jane Tab Content 6Author Website:Countries AvailableAll regions |
||||
