Author Kamyar M. Davoudi About This Book A First Course in Differential Equations With Applications in Engineering(Coming Soon) Table of Contents 1. Introduction to Differential Equations 1.1 Initial Value Problems Vs 1.2 Family Of Curves 1.3 What Is A Differential Equation 1.4 1 2. First-Order Differential Equations 2.1 Bernoullis Equation 2.2 2 2.3 Separable Equations 2.4 Linear Differential Equations Of The First Order 2.5 Exact First Order Equations 2.6 Riccatis Equation 2.7 Introduction 1 2.8 Integrating Factor 3. Modeling With First-Order Differential Equations 3.1 Test section 4. Higher-Order Differential Equations 4.1 The Use Of One Known Solution To Find Another 4.2 Particular Solutions By The Method Of Undetermined Coefficients 4.3 The Cauchyeuler Equation 4.4 Variation Of Parameters 4.5 Homogeneous Linear Differential Equations With Constant Coefficients 5. Modeling With Higher-Order Differential Equations 6. Systems of Linear Differential Equations 6.1 Constant Coefficient Systems 6.2 Nonhomogeneous Linear Systems 7. Laplace Transform 7.1 Definition of Laplace Transform 8. Series Solutions of Differential Equations 8.1 Power Series 8.2 The Method Of Frobenius 9. Numerical Solutions of Differential Equations 10. Prerequisite Math 10.1 Review Of Complex Numbers