ORDINARY DIFFERENTIAL EQUATIONS: A DYNAMICAL POINT OF VIEW

Ordinary differential equations is a standard course in the undergraduate mathematics curriculum that usually comes after the first university calculus and linear algebra courses taken by a mathematics major. Such courses may also typically be attended by undergraduates from other areas of physical and social sciences, and engineering. The content of such a course has remained fairly static over time, despite the expansion of the topic into other disciplines as a result of the dynamical systems point of view.

This core undergraduate course updated from the dynamical systems perspective can easily be covered in one semester, with room for projects or more advanced topics tailored to the interests of the students.

Contents:
PrefaceList of FiguresList of TablesGetting Started: The Language of ODEsSpecial Structure and Solutions of ODEsBehavior Near Trajectories and Invariant Sets: StabilityBehavior Near Trajectories: LinearizationBehavior Near Equilibria: LinearizationStable and Unstable Manifolds of Hyperbolic EquilibriaLyapunov's Method and the LaSalle Invariance PrincipleBifurcation of Equilibria, IBifurcation of Equilibria, IICenter Manifold TheoryJacobians, Inverses of Matrices, and EigenvaluesIntegration of Some Basic Linear ODEsSolutions of Some Second Order ODEs Arising in Applications: Newton's EquationsFinding Lyapunov FunctionsCenter Manifolds Depending on ParametersDynamics of Hamilton's EquationsA Brief Introduction to the Characteristics of ChaosBibliographyIndex
Readership: Undergraduate students in mathematics, physical science, social science, and engineering that use ordinary differential equations.

Key Features: Develops an undergraduate course in ordinary differential equations within the framework of dynamical systems theory Enables the student to understand the nature and significance of research in areas of science and engineering that use this point of view Provides students with the mathematical tools and an entry point for research in these areas