Differential Equations

1 MATHEMATICAL MODELS 1.1 Mathematical Models and Differential Equations 1.2 Classification of Differential Equations 1.3 Solutions to Differential Equations 1.4 Chapter Summary Problems

2 FIRST-ORDER DIFFERENTIAL EQUATIONS 2.1 Equations Directly Integrable 2.2 The Method of Integrating Factors 2.3 Separable Equations 2.4 Exact Equations 2.5 Computer Methods to Solve Differential Equations 2.6 Adomian's Decomposition Method (ADM) for Linear Equations 2.7 Adomian's Decomposition Method (ADM) for Nonlinear Equations 2.8 The Modified Decomposition Method (MDM) 2.9 Chapter Summary Problems

3 SECOND-ORDER DIFFERENTIAL EQUATIONS 3.1 Equations Directly Integrable 3.2 Equations with One Missing Variable 3.3 The General Second-Order Linear Differential Equation 3.4 Linear Homogeneous Equations with Constant Coefficients 3.5 Linear Nonhomogeneous Equations with Constant Coefficients 3.6 Applications of Linear Differential Equations with Constant Coefficients 3.7 The Method of Laplace Transforms 3.8 Adomian's Decomposition Method (ADM) for Linear Equations 3.9 Adomian's Decomposition Method (ADM) for Nonlinear Equations 3.10The Modified Decomposition Method (MDM) for Nonlinear Equations 3.11Other Methods to Solve Nonlinear Equations 3.12Chapter Summary Problems

4 SYSTEMS OF DIFFERENTIAL EQUATIONS 4.1 Linear Algebra and Systems of Differential Equations 4.2 Systems of First-Order Linear Differential Equations 4.3 Systems of Two First-Order Equations 4.4 The Eigenvalue Method of Finding Solutions to Systems of First-Order Linear Differential Equations 4.5 Fundamental Matrix Solution and the Matrix Exponential Function 4.6 The Nonhomogeneous Equation. The Method of Variation of Parameters 4.7 Adomian's Decomposition Method (ADM) for Linear Systems 4.8 Adomian's Decomposition Method (ADM) for Nonlinear Systems 4.9 The Modified Decomposition Method (MDM) for Nonlinear Systems 4.10Chapter Summary Problems

APPENDIX A: ANSWERS TO PROBLEMS

BIBLIOGRAPHY

INDEX