tailieunhanh - Ebook A second course in ordinary differential equations: Dynamical systems and boundary value problems - Part 1

(BQ) Part 1 book "A second course in ordinary differential equations: Dynamical systems and boundary value problems" has contents: Introduction, systems of differential equations, nonlinear systems, boundary value problems. | Russell L. Herman A Second Course in Ordinary Differential Equations: Dynamical Systems and Boundary Value Problems Monograph December 2, 2008 Contents 1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Review of the First Course . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . First Order Differential Equations . . . . . . . . . . . . . . . . . . . Second Order Linear Differential Equations . . . . . . . . . . . Constant Coefficient Equations . . . . . . . . . . . . . . . . . . . . . . Method of Undetermined Coefficients . . . . . . . . . . . . . . . . Cauchy-Euler Equations . . . . . . . . . . . . . . . . . . . . . . . . . . . . Overview of the Course . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Appendix: Reduction of Order and Complex Roots . . . . . . . . . . Problems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 2 2 7 8 10 13 16 17 19 2 Systems of Differential Equations . . . . . . . . . . . . . . . . . . . . . . . . . . Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Equilibrium Solutions and Nearby Behaviors . . . . . . . . . . . . . . . . Polar Representation of Spirals . . . . . . . . . . . . . . . . . . . . . . Matrix Formulation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Eigenvalue Problems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Solving Constant Coefficient Systems in 2D . . . . . . . . . . . . . . . . . Examples of the Matrix Method . . . . . . . . . . . . . . . . . . . . . . . . . . . Planar Systems - Summary . . . . . . . . . . . . . . . . . . . . . . . . . Theory of Homogeneous Constant Coefficient Systems . . . . . . . . Nonhomogeneous Systems . . . . . . . . . . . . . . . . . . . . . . . . . . . . .