Ordinary differential equations : introduction and qualitative theory
著者
書誌事項
Ordinary differential equations : introduction and qualitative theory
（Monographs and textbooks in pure and applied mathematics, 292）
Chapman & Hall/CRC, c2008
3rd ed
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注記
Rev. of ed.: Differential equations. 2nd ed., rev. and expanded. c1994
Includes bibliographical references (p. [369]-376) and index
内容説明・目次
内容説明
Designed 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 Poincare 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 Poincare method.
目次
Prefaces. Introduction. Existence Theorems. Linear Systems. Autonomous Systems. Stability. The Lyapunov Second Method. Periodic Solutions. Perturbation Theory: The Poincare Method. Perturbation Theory: Autonomous Systems and Bifurcation Problems. Using the Averaging Method: An Introduction. Appendix. References. Index.
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