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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 | |