Modelling with ordinary differential equations : a comprehensive approach Cover Half Title Series Page Title Page Copyright Page Dedication Contents Preface Author 1. Introduction 1.1 Ordinary differential equations 1.2 The modelling process 2. Elementary solution methods for simple ODEs 2.1 Simple ODEs 2.1.1 Simple ODE of 1. type y = f(x) 2.1.2 Simple ODE of 2. type y = f(y) 2.1.3 Simple ODE of 3. type y = f(x) g(y) 2.1.4 Simple ODE of 4. type y = f(ax + by + d) 2.1.5 Simple ODE of 5. type y = f(y x) 2.2 Linear ODEs 2.3 Method of variation of the constants 2.4 Bernoullis differential equation 2.5 Riccatis differential equation 2.6 Exact differential equations 3. Theory of ordinary differential equations 3.1 The Cauchy problem and existence of solutions 3.2 Eulers method 3.3 Uniqueness of solutions 3.4 The Carathéodory theorem 4. Systems of ordinary differential equations 4.1 Systems of first order ODEs 4.2 Dependence of solutions on the initial conditions 4.3 Systems of linear ODEs 4.4 Systems of linear homogeneous ODEs 4.5 The dAlembert reduction method 4.6 Nonhomogeneous linear systems 4.7 Linear systems with constant coefficients 4.8 The exponential matrix 4.9 Linear systems with periodic coefficients 5. Ordinary differential equations of order n 5.1 Ordinary differential equations of order n in normal form 5.2 Linear differential equations of order n 5.3 The reduction method of dAlembert 5.4 Linear ODEs of order n with constant coefficients 5.5 Nonhomogeneous ODEs of order n 5.6 Oscillatory solutions 6. Stability of ODE systems 6.1 Local stability of ODE systems 6.2 Stability of linear ODE systems 6.3 Stability of nonlinear ODE systems 6.4 Remarks on the stability of periodic ODE problems 6.5 Autonomous systems in the plane.