Differential Equations, Dynamical Systems, and an Introduction to Chaos

Hirsch, Devaney, and Smale’s classic Differential Equations, Dynamical Systems, and an Introduction to Chaos has been used by professors as the primary text for undergraduate and graduate level courses covering differential equations. It provides a theoretical approach to dynamical systems and chaos written for a diverse student population among the fields of mathematics, science, and engineering. Prominent experts provide everything students need to know about dynamical systems as students seek to develop sufficient mathematical skills to analyze the types of differential equations that arise in their area of study. The authors provide rigorous exercises and examples clearly and easily by slowly introducing linear systems of differential equations. Calculus is required as specialized advanced topics not usually found in elementary differential equations courses are included, such as exploring the world of discrete dynamical systems and describing chaotic systems. Classic text by three of the world’s most prominent mathematicians Continues the tradition of expository excellence Contains updated material and expanded applications for use in applied studies Hirsch, Devaney, and Smale's classic Differential Equations, Dynamical Systems, and an Introduction to Chaos has been used by professors as the primary text for undergraduate and graduate level courses covering differential equations. It provides a theoretical approach to dynamical systems and chaos written for a diverse student population among the fields of mathematics, science, and engineering. Prominent experts provide everything students need to know about dynamical systems as students seek to develop sufficient mathematical skills to analyze the types of differential equations that arise in their area of study. The authors provide rigorous exercises and examples clearly and easily by slowly introducing linear systems of differential equations. Calculus is required as specialized advanced topics not usually found in elementary differential equations courses are included, such as exploring the world of discrete dynamical systems and describing chaotic systems. Classic text by three of the world's most prominent mathematicians Continues the tradition of expository excellence Contains updated material and expanded applications for use in applied studies Content: Front Matter , Page i Copyright , Page ii Preface to Third Edition , Page ix Preface , Pages xi-xiv 1 - First-Order Equations , Pages 1-19 2 - Planar Linear Systems , Pages 21-38 3 - Phase Portraits for Planar Systems , Pages 39-59 4 - Classification of Planar Systems , Pages 61-72 5 - Higher-Dimensional Linear Algebra , Pages 73-105 6 - Higher-Dimensional Linear Systems , Pages 107-138 7 - Nonlinear Systems , Pages 139-157 8 - Equilibria in Nonlinear Systems , Pages 159-186 9 - Global Nonlinear Techniques , Pages 187-212 10 - Closed Orbits and Limit Sets , Pages 213-232 11 - Applications in Biology , Pages 233-255 12 - Applications in Circuit Theory , Pages 257-276 13 - Applications in Mechanics , Pages 277-303 14 - The Lorenz System , Pages 305-328 15 - Discrete Dynamical Systems , Pages 329-359 16 - Homoclinic Phenomena , Pages 361-384 17 - Existence and Uniqueness Revisited , Pages 385-409 Bibliography , Pages 411-413 Index , Pages 415-418 "Differential Equations, Dynamical Systems, and an Introduction to Chaos, now in its third edition, covers the dynamical aspects of ordinary differential equations. It explores the relations between dynamical systems and certain fields outside pure mathematics, and continues to be the standard textbook for advanced undergraduate and graduate courses in this area.""Written for students with a background in calculus and elementary linear algebra, the text is rigorous yet accessible and contains examples and explorations to reinforce learning."--Back cover