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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 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.1 Review of the First Course . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.1.1 First Order Differential Equations . . . . . . . . . . . . . . . . . . . 1.1.2 Second Order Linear Differential Equations . . . . . . . . . . . 1.1.3 Constant Coefficient Equations . . . . . . . . . . . . . . . . . . . . . . 1.1.4 Method of Undetermined Coefficients . . . . . . . . . . . . . . . . 1.1.5 Cauchy-Euler Equations . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.2 Overview of the Course . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.3 Appendix: Reduction of Order and Complex Roots . . . . . . . . . . Problems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 2 2 7 8 10 13 16 17 19 2 Systems of Differential Equations . . . . . . . . . . . . . . . . . . . . . . . . . . 2.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.2 Equilibrium Solutions and Nearby Behaviors . . . . . . . . . . . . . . . . 2.2.1 Polar Representation of Spirals . . . . . . . . . . . . . . . . . . . . . . 2.3 Matrix Formulation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.4 Eigenvalue Problems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.5 Solving Constant Coefficient Systems in 2D . . . . . . . . . . . . . . . . . 2.6 Examples of the Matrix Method . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.6.1 Planar Systems - Summary . . . . . . . . . . . . . . . . . . . . . . . . . 2.7 Theory of Homogeneous Constant Coefficient Systems . . . . . . . . 2.8 Nonhomogeneous Systems . . . . . . . . . . . . . . . . . . . . . . . . . . . . .