The Contraction Mapping Principle and Some Applications
by Robert M. Brooks, Klaus Schmitt
Publisher: American Mathematical Society 2009
Number of pages: 90
These notes contain various versions of the contraction mapping principle. Several applications to existence theorems in the theories of differential and integral equations and variational inequalities are given. Also discussed are Hilbert's projective metric and iterated function systems.
Download or read it online for free here:
by Dmitry Panchenko - University of Toronto
Contents: First order differential equations; Existence and uniqueness of solutions for first order differential equations; Systems of first order equations and higher order linear equations; Solving higher order linear differential equations; etc.
by William F. Trench - Brooks Cole
This text has been written in clear and accurate language that students can read and comprehend. The author has minimized the number of explicitly state theorems and definitions, in favor of dealing with concepts in a more conversational manner.
by Norbert Euler - Bookboon
The book consists of lecture notes intended for engineering and science students who are reading a first course in ordinary differential equations and who have already read a course on linear algebra, general vector spaces and integral calculus.
by Carmen Chicone, Richard Swanson - American Mathematical Society
The proof of the Grobman-Hartman linearization theorem for a flow at a hyperbolic rest point proceeds by establishing the analogous result for hyperbolic fixed points of local diffeomorphisms. We present a proof that avoids the discrete case.