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| First-Order Differential Equations | |
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| Dynamical Systems: Modeling | |
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| Solutions and Direction Fields: Qualitative Analysis | |
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| Separation of Variables: Quantitative Analysis | |
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| Approximation Methods: Numerical Analysis | |
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| Picards Theorem: Theoretical Analysis | |
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| Linearity and Nonlinearity | |
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| Linear Equations: The Nature of Their Solutions | |
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| Solving the First-Order Linear Differential Equation | |
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| Growth and Decay Phenomena | |
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| Linear Models: Mixing and Cooling | |
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| Nonlinear Models: Logistic Equation | |
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| Systems of Differential Equations: A First Look | |
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| Linear Algebra | |
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| Matrices: Sums and Products | |
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| Systems of Linear Equations | |
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| The Inverse of a Matrix | |
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| Determinants and Cramers Rule | |
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| Vector Spaces and Subspaces | |
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| Basis and Dimension | |
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| Higher-Order Linear Differential Equations | |
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| The Harmonic Oscillator | |
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| Real Characteristic Roots | |
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| Complex Characteristic Roots | |
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| Undetermined Coefficients | |
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| Variation of Parameters | |
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| Forced Oscillations | |
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| Conservation and Conversion | |
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| Linear Transformations | |
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| Linear Transformations | |
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| Properties of Linear Transformations | |
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| Eigenvalues and Eigenvectors | |
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| Coordinates and Diagonalization | |
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| Linear Systems of Differential Equations | |
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| Theory of Linear DE Systems | |
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| Linear Systems with Real Eigenvalues | |
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| Linear Systems with Nonreal Eigenvalues | |
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| Stability and Linear Classification | |
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| Decoupling a Linear DE System | |
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| Matrix Exponential | |
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| Nonhomogeneous Linear Systems | |
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| Nonlinear Systems of Differential Equations | |
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| Nonlinear Systems | |
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| Linearization | |
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| Numerical Solutions | |
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| Chaos, Strange Attractors, and Period Doubling | |
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| Chaos in Forced Nonlinear Systems | |
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| Laplace Transforms | |
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| The Laplace Transform and Its Inverse | |
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| Solving DEs and IVPs with Laplace Transforms | |
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| The Step Function and the Delta Function | |
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| The Convolution Integral and the Transfer Function | |
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| Laplace Transform Solution of Linear Systems | |
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| Discrete Dynamical Systems | |
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| Iterative Equations | |
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| Linear Iterative Systems | |
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| Nonlinear Iterative Equations: Chaos Again | |
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| Control Theory | |
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| Feedback Controls | |
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| Introduction to Optimal Control | |
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| Pontryagin Maximum Principle | |