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| Preface | |
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| Elements of Matrices, Determinants, and Calculus | |
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| Introduction | |
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| Problem-Solving Process | |
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| Problem analysis | |
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| Solutions (proof) strategies | |
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| Algebra of Matrices | |
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| Determinants | |
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| Matrix Calculus | |
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| Notes and Comments | |
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| First-Order Differential Equations | |
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| Introduction | |
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| Mathematical Modeling | |
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| Integrable Equations | |
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| General problem | |
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| Procedure for finding a general solution | |
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| Initial value problem | |
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| Procedure for solving the IVP | |
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| Linear Homogeneous Equations | |
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| General problem | |
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| Procedure for finding a general solution | |
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| Initial value problem | |
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| Procedure for solving the IVP | |
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| Linear Nonhomogeneous Equations | |
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| General problem | |
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| Procedure for finding a general solution | |
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| Initial value problem | |
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| Procedure for solving the IVP | |
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| Fundamental Conceptual Algorithms and Analysis | |
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| Notes and Comments | |
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| First-Order Nonlinear Differential Equations | |
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| Introduction | |
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| Mathematical Modeling | |
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| Energy Function Method | |
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| General problem | |
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| Procedure for finding a general solution representation | |
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| Integrable Reduced Equations | |
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| General problem | |
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| Procedure for finding a general solution representation | |
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| Linear Nonhomogeneous Reduced Equations | |
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| General problem | |
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| Procedures for finding a general solution representation | |
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| Variable Separable Equations | |
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| General problem | |
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| Procedure for finding a general solution | |
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| Homogeneous Equations | |
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| General problem | |
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| Procedure for finding a general solution | |
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| Bernoulli Equations | |
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| General problem | |
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| Procedure for finding a general solution | |
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| Essentially Time-Invariant Equations | |
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| General problem | |
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| Procedure for finding a general solution | |
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| Notes and Comments | |
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| First-Order Systems of Linear Differential Equations | |
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| Introduction | |
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| Mathematical Modeling | |
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| Linear Homogeneous Systems | |
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| General problem | |
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| Procedure for finding a general solution | |
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| Initial value problem | |
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| Procedure for the solving IVP | |
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| Procedure for Finding the Fundamental Matrix Solution | |
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| General Linear Homogeneous Systems | |
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| General problem | |
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| Procedure for finding a general solution | |
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| Initial value problem | |
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| Procedure for solving the IVP | |
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| Linear Nonhomogeneous Systems | |
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| General problem | |
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| Procedure for finding a general solution | |
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| Initial value problem | |
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| Procedure for solving the IVP | |
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| Fundamental Conceptual Algorithm Analysis | |
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| Notes and Comments | |
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| Higher-Order Linear Differential Equations | |
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| Introduction | |
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| Mathematical Modeling | |
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| Linear Homogeneous Equations | |
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| General problem | |
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| Procedure for finding a general solution | |
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| Initial value problem | |
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| Procedure for solving the IVP | |
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| Companion System | |
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| Higher-Order Linear Nonhomogeneous Equations | |
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| The Laplace Transform | |
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| Applications of the Laplace Transform | |
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| Notes and Comments | |
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| Topics in Differential Equations | |
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| Introduction | |
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| Fundamental Conceptual Algorithms and Analysis | |
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| Method of Variation of Parameters | |
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| Generalized Method of Variation of Parameters | |
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| Differential Inequalities and Comparison Theorems | |
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| Energy/Lyapunov Function and Comparison Theorems | |
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| Variational Comparison Method | |
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| Linear Hybrid Systems | |
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| General problem | |
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| Linear Hereditary Systems | |
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| General problem | |
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| Qualitative Properties of the Solution Process | |
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| Linear Stochastic Systems | |
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| Notes and Comments | |
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| Bibliography | |
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| Index | |