Linearization via the Lie Derivative
by Carmen Chicone, Richard Swanson
Publisher: American Mathematical Society 2000
Number of pages: 64
The standard proof of the Grobman--Hartman linearization theorem for a flow at a hyperbolic rest point proceeds by first establishing the analogous result for hyperbolic fixed points of local diffeomorphisms. In this exposition we present a simple direct proof that avoids the discrete case altogether.
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by Klaus Schmitt, Russell C. Thompson - University of Utah
The intent of this set of notes is to present several of the important existence theorems for solutions of various types of problems associated with differential equations and provide qualitative and quantitative descriptions of solutions.
by Marcel B. Finan - Arkansas Tech University
Contents: Basic Terminology; Qualitative Analysis: Direction Field of y'=f(t,y); Existence and Uniqueness of Solutions to First Order Linear IVP; Solving First Order Linear Homogeneous DE; Solving First Order Linear Non Homogeneous DE; etc.
by Leif Mejlbro - BookBoon
Some examples of simple differential equations. The book covers separation of variables, linear differential equation of first order, the existence and uniqueness theorem, the Bernoulli differential equation, and the setup of model equations.
by George A. Osborne - Boston, Ginn & Company
This work has been prepared to meet a want in a course on the subject, arranged for advanced students in Physics. It could be used in connection with lectures on the theory of Differential Equations and the derivation of the methods of solution.