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Definitions and Examples. Second-Order Equations and Systems. Linear, Homogeneous Equations with Constant Coefficients.
Harmonic Motion. Inhomogeneous Equations; the Method of Undetermined Coefficients. Variation of Parameters. Forced Harmonic Motion. Project 4. The Definition of the Laplace Transform. Basic Properties of the Laplace Transform The Inverse Laplace Transform. Discontinuous Forcing Terms.
The Delta Function. Project 5. Runge-Kutta Methods. Numerical Error Comparisons. Practical Use of Solvers. A Cautionary Tale. Project 6. Vectors and Matrices.
Solving Systems of Equations. Homogeneous and Inhomogeneous Systems.
Bases of a subspace. Square Matrices.
Chapter 8: An Introduction to Systems. Geometric Interpretation of Solutions.
Qualitative Analysis. Linear Systems. Properties of Linear Systems. Project 8. Chapter 9: Linear Systems with Constant Coefficients. Overview of the Technique. Planar Systems. Phase Plane Portraits. The Trace-Determinant Plane. Higher Dimensional Systems. The Exponential of a Matrix. Qualitative Analysis of Linear Systems. Higher-Order Linear Equations. Inhomogeneous Linear Systems. Project 9. Chapter Nonlinear System s. The Linearization of a Nonlinear System. Long-Term Behavior of Solutions.
Invariant Sets and the Use of Nullclines. Conserved Quantities.
Nonlinear Mechanics. The Method of Lyapunov. Predator—Prey Systems. Project Series Solutions to Differential Equations.