Differential Equations with YouTube Examples
by Jeffrey R. Chasnov
Publisher: BookBoon 2014
Number of pages: 57
This book, together with the linked YouTube videos, reviews a first course on differential equations. The main purpose is to help students prepare for their university exams. Theory is summarized, and the solutions of typical exam questions are demonstrated in YouTube videos. Additional practice questions are given and their solutions are presented in the Appendix.
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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 Robert M. Brooks, Klaus Schmitt - American Mathematical Society
These notes contain various versions of the contraction mapping principle. Several applications to existence theorems in differential and integral equations and variational inequalities are given. Also discussed are Hilbert's projective metric.
by Yulij Ilyashenko, Sergei Yakovenko - American Mathematical Society
A graduate-level textbook and survey of the recent results on analysis and geometry of differential equations in the real and complex domain. The book includes self-contained demonstrations of several fundamental results.
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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.