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| Introduction To Differential Equations | |
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| Basic Definitions and Terminology | |
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| Some Mathematical Models | |
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| Review | |
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| Exercises | |
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| First-Order Differential Equations | |
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| Preliminary Theory | |
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| Separable Variables | |
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| Homogeneous Equations | |
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| Exact Equations | |
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| Linear Equations | |
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| Equations of Bernoulli, Ricatti, and Clairaut | |
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| Substitutions | |
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| Picard's Method | |
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| Review | |
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| Exercises | |
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| Applications Of First-Order Differential Equations | |
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| Orthogonal Trajectories | |
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| Applications of Linear Equations | |
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| Applications of Nonlinear Equations | |
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| Review | |
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| Exercises | |
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| Essay: Population Dynamics | |
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| Linear Differential Equations Of Higher-Order | |
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| Preliminary Theory | |
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| Constructing a Second Solution from a Know Solution | |
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| Homogeneous Linear Equations with Constant Coefficients | |
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| Undetermined Coefficients: Superposition Approach | |
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| Differential Operators | |
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| Undetermined Coefficients: Annihilator Approach | |
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| Variation of Parameters | |
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| Review | |
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| Exercises | |
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| Essay: Chaos | |
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| Applications Of Second-Order Differential Equations: Vibrational Models | |
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| Simple Harmonic Motion | |
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| Damped Motion | |
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| Forced Motion | |
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| Electric Circuits and Other Analogous Systems | |
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| Review | |
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| Exercises | |
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| Essay: Tacoma Narrows Suspension Bridge Collapse | |
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| Differential Equations With Variable Coefficients | |
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| Cauchy-Euler Equation | |
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| Review of Power Series; Power Series Solutions | |
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| Solutions About Ordinary Points | |
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| Solutions About Singular Points | |
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| Two Special Equations | |
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| Review | |
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| Exercises | |
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| Laplace Transform | |
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| Laplace Transform | |
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| Inverse Transform | |
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| Translation Theorems and Derivatives of a Transform | |
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| Transforms of Derivatives, Integrals, and Periodic Functions | |
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| Applications | |
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| Dirac Delta Function | |
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| Review | |
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| Exercises | |
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| Systems Of Linear Differential Equations | |
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| Operator Method | |
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| Laplace Transform Method | |
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| Systems of Linear First-Order Equations | |
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| Introduction to Matrices | |
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| Matrices and Systems of Linear First-Order Equations | |
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| Homogeneous Linear Systems | |
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| Undetermined Coefficients | |
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| Variation of Parameters | |
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| Matrix Exponential | |
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| Review | |
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| Exercises | |
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| Numerical Methods For Ordinary Differential Equations | |
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| Direction Fields | |
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| The Euler Methods | |
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| The Three-Term Taylor Method | |
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| The Runge-Kutta Methods | |
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| Multistep Methods | |
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| Errors and Stability | |
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| Higher-Order Equations and Systems | |
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| Second-Order Boundary-Value Problems | |
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| Review | |
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| Exercises | |
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| Essay: Nerve Impulse Models | |
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| Gamma Function | |
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| Laplace Transforms | |
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| Review Of Determinants | |
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| Complex Numbers | |
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| Answers To Odd-Numbered Problems | |