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Modeling and Differential Equations | |
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The Modeling Approach | |
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A Modeling Adventure | |
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Models and Initial Value Problems | |
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The Modeling Process: Differential Systems | |
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Spotlight on Modeling: Radiocarbon Dating | |
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Spotlight on Modeling: Cold Medication I | |
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First-Order Differential Equations | |
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Linear Differential Equations | |
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Linear Differential Equations: Qualitative Analysis | |
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Existence and Uniqueness of Solutions | |
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Visualizing Solution Curves: Slope Fields | |
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Separable Differential Equations: Planar Systems | |
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A Predator-Prey Model: the Lotka-Volterra System | |
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Extension of Solutions: Long-Term Behavior | |
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Qualitative Analysis: State Lines, Sign Analysis | |
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Bifucations: A Harvested Logistic Model | |
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Snapshot on Solution Formula Techniques | |
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Spotlight on approximate numerical solutions | |
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Spotlight on computer implementation | |
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Spotlight on steady states: linear odes | |
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Spotlight on modeling: cold medication II | |
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Spotlight on change of variables: pursuit models | |
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Spotlight on continuity in the data | |
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Second-Order Differential Equations | |
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Models of Springs | |
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Undriven Constant-Coefficient Linear Differential Equations | |
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Visualizing Graphs of Solutions: Direction Fields | |
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Periodic Solutions: Simple Harmonic Motion | |
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Driven Linear ODEs: Undetermined Coefficients I | |
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Driven Linear ODEs: Undetermined Coefficients II | |
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Theory of Second-Order Linear Differential Equations | |
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Nonlinear Second-Order Differential Equations | |
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A Snapshot Look at Constant-Coefficient Polynomial Operators | |
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Spotlight on modeling: vertical motion | |
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Spotlight on modeling: shock absorbers | |
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Spotlight on einstein's field equations | |
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Applications of Second-Order Differential Equations | |
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Snapshot on Mechanical and Electrical Models | |
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Spotlight on modeling: tuning a circuit | |
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The Laplace Transform | |
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The Laplace Transform: Solving IVPs | |
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Working with the Transform | |
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Transforms of Periodic Functions | |
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Convolution | |
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Spotlight on the Delta Function | |
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Spotlight on Modeling: Time Delays And Collisions | |
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Linear Systems of Differential Equations | |
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Compartment Models: Tracking Lead | |
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Eigenvalues, Eigenvectors and Eigenspaces of Matrices | |
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Undriven Linear Differential Systems: Real Eigenvalues | |
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Undriven Linear Systems: Complex Eigenvalues | |
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Orbital Portraits for Planar Systems | |
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Driven Systems: The Matrix Exponential | |
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Steady States | |
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The Theory of General Linear Systems | |
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Spotlight on vectors, matrices, independence | |
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Spotlight on linear algebraic equations | |
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Spotlight on bifurcations: sensitivity | |
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Nonlinear Differential Systems | |
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Spotlight On Modeling: Destructive Competition | |
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Spotlight on Modeling: Bifurcation And Sensitivity | |
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Stability | |
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Stability and Linear Autonomous Systems | |
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Stability and Nonlinear Autonomous Systems | |
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Stability of PlanarNonlinear Systems | |
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Conservative Systems | |
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Spotlight on Lyapunov Functions | |
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Spotlight on Rotating Bodies | |
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Nonlinear Systems: Cycles and Chaos | |
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Cycles | |
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Solution Behavior in Planar Autonomous Systems | |
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Bifucations | |
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Chaos | |
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Spotlight On Chaotic Systems | |
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Fourier Series and Partial Differential Equations | |
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Vibrations of a Guitar String | |
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Fourier Trigonometric Series | |
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Half-Range and Exponential Fourier Series | |
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Temperature in a Thin Rod | |
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Sturm-Liouville Problems | |
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The Method of Eigenfunction E | |