Ebook Ordinary differential equations and dynamical systems: Part 1

(BQ) Part 1 book "Ordinary differential equations and dynamical systems" has contents: Introduction, initial value problems, linear equations, differential equations in the complex domain, boundary value problems. | Ordinary Differential Equations and Dynamical Systems Gerald Teschl This is a preliminary version of the book Ordinary Differential Equations and Dynamical Systems published by the American Mathematical Society (AMS). This preliminary version is made available with the permission of the AMS and may not be changed, edited, or reposted at any other website without explicit written permission from the author and the AMS. Author's preliminary version made available with permission of the publisher, the American Mathematical Society To Susanne, Simon, and Jakob Author's preliminary version made available with permission of the publisher, the American Mathematical Society Author's preliminary version made available with permission of the publisher, the American Mathematical Society Contents Preface xi Part 1. Classical theory Chapter 1. Introduction 3 §. Newton’s equations 3 §. Classification of differential equations 6 §. First order autonomous equations 9 §. Finding explicit solutions 13 §. Qualitative analysis of first-order equations 20 §. Qualitative analysis of first-order periodic equations 28 Chapter 2. Initial value problems 33 §. Fixed point theorems 33 §. The basic existence and uniqueness result 36 §. Some extensions 39 §. Dependence on the initial condition 42 §. Regular perturbation theory 48 §. Extensibility of solutions 50 §. Euler’s method and the Peano theorem 54 Chapter 3. Linear equations 59 §. The matrix exponential 59 Linear autonomous first-order systems 66 §. Linear autonomous equations of order n 74 §. vii Author's preliminary version made available with permission of the publisher, the American Mathematical Society viii §. §. §. §. §. Contents General linear first-order systems Linear equations of order n Periodic linear systems Perturbed linear first order systems Appendix: Jordan canonical .