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| Introduction to Differential Equations | |
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| Definitions and Terminology | |
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| Initial-Value Problems | |
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| Differential Equations as Mathematical Models | |
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| Chapter 1 in Review | |
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| First-Order Differential Equations | |
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| Solution Curves Without a Solution | |
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| Separable Variables | |
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| Linear Equations | |
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| Exact Equations and Integrating Factors | |
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| Solutions by Substitutions | |
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| A Numerical Method | |
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| Chapter 2 in Review | |
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| Modeling with First-Order Differential Equations | |
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| Linear Models | |
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| Nonlinear Models | |
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| Modeling with Systems of First-Order Differential Equations | |
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| Chapter 3 in Review | |
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| Higher-Order Differential Equations | |
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| Preliminary Theory- Linear Equations | |
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| Reduction of Order | |
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| Homogeneous Linear Equations with Constant Coefficients | |
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| Undetermined Coefficients- Superposition Approach | |
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| Undetermined Coefficients- Annihilator Approach | |
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| Variation of Parameters | |
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| Cauchy-Euler Equation | |
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| Solving Systems of Linear Differential Equations by Elimination | |
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| Nonlinear Differential Equations | |
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| Chapter 4 in Review | |
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| Modeling with Higher-Order Differential Equations | |
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| Linear Models: Initial-Value Problems | |
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| Linear Models: Boundary-Value Problems | |
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| Nonlinear Models | |
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| Chapter 5 in Review | |
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| Series Solutions of Linear Equations | |
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| Solutions About Ordinary Points | |
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| Solutions About Singular Points | |
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| Special Functions | |
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| Chapter 6 in Review | |
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| Laplace Transform | |
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| Definition of the Laplace Transform | |
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| Inverse Transform and Transforms of Derivatives | |
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| Operational Properties I | |
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| Operational Properties II | |
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| Dirac Delta Function | |
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| Systems of Linear Differential Equations | |
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| Chapter 7 in Review | |
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| Systems of Linear First-Order Differential Equations | |
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| Preliminary Theory | |
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| Homogeneous Linear Systems | |
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| Nonhomogeneous Linear Systems | |
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| Matrix Exponential | |
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| Chapter 8 in Review | |
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| Numerical Solutions of Ordinary Differential Equations | |
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| Euler Methods | |
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| Runge-Kutta Methods | |
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| Multistep Methods | |
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| Higher-Order Equations and Systems | |
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| Second-Order Boundary-Value Problems | |
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| Chapter 9 in Review | |
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| Gamma Function | |
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| Matrices | |
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| Laplace Transforms | |
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| Answers for Selected Odd-Numbered Problems | |