Classification of differential equations (orders, single eqs vs systems, linear vs nonlinear): Slides.
Direction fields: Maple.
Separable equations: dy/dt=f(t)g(y). Slides. Exercises. Maple.
First order linear differential equations: method of integrating factor. Slides. Exercises.
Solution structures: homog linear, nonhomog linear, & nonlinear diff eqs. Exercises. Maple.
A falling ball: Maple. Another Maple. More Maple.
Expoenetial growth/decay: Slides.
Solution structures: autonomous vs nonautonomous diff eqs. Maple.
Stability, asymptotic stability, and instability: Slides. A scholarpedia article. Exercises.
Linear Approximating Equations near Equilibria: Slides. Maple.
Bifurcations: Saddle-node bifurcations. Maple.
Homogenous 2-D linear systems with constant coefficients (distinct real & nonzero eigenvalues): Solution method and phase portraits. Slides. Exercises.
Homog 2-D linear systems with const coefficients (complex eigenvalues): Solution method and phase portraits. Slides.
Homog 2-D linear systems with const coefficients (zero eigenvalue): Solution method and phase portraits. Slides. Exercises.
Homog 2-D linear systems with const coefficients (repeated real eigenvalues): Solution method and phase portraits. Slides.
Homog 2-D linear systems with const coefficients: A catalogue of phase portraits. Slides. Slides in Maple. Another Maple file. More examples in Maple. Phase portraits with direction fields in Maple. Animations in Maple.
Shifted systems of the form: x'=A(x-a) and x'=Ax+b. Exercises. Maple.
Applications: electric circuits. Slides.
Nonlinear 2-D systems: Local phase portraits near critical points. Linear approximating systems. Stability/Instability. Slides. Exercises. Maple. Slides in Maple.
Applications: predator-prey systems. Maple.
Higher dimensional systems: fundamental matrices and matrix exponential. Slides. Lecture notes and exercises. Evaluate matrix exponential using the Laplace transform.
Higher dimensional homogeneous linear systems with const coefficients: Solution method. Exercises. Diagonalizable examples in Maple. Complex eigenvalues in Maple. More examples with complex eigenvalues in Maple.
Higher dimensional homogeneous linear systems with const coefficients: repeated eigenvalues. Slides. Maple.
Higher dimensional nonhomogeneous linear systems: variation of parameters. Slides. Notes with Examples and Exercises.
Three-D phase portraits: Maple.
Higher dimensional homogeneous linear systems with const coefficients: Stability, asymptotic stability, and instability. Slides.
Higher dimensional linear approximating systems: stability/instability of equilibria. Exericses. Maple.
Center manifolds: Examples in Maple. More examples in Maple.
Chaos in the Lorenz attractor: Maple. "Chaos Theory" on Wikipedia. Youtube videos on electric circuits and the Lorenz chaos, by Joshua Johnson.
Chaos in Duffing equation: Maple.
Solution structures of 2nd ord diff eqs: linear & nonlinear eqs. Exercises.
Second order linear homogeneous eqs with const coefficients: ay''+by'+cy=0. Slides. Maple.
Nonhomogeneous linear eqs (method of undetermined coefficients): Slides.
Higher order linear eqs with constant coefficients: Notes with Examples and Exercises. Homog eqs in Maple. Nonhomog eqs: undetermined coefficients in Maple. More undetermined coefficients in Maple.
Nonhomogeneous linear eqs (variation of parameters): Slides: 2D systems and 2nd order eqs. Slides: High-D systems and higher order eqs. Maple. One more example in Maple.
Fourier series and ODEs: Periodic solutions in Maple. Boundary value problems in Maple.
Spring-mass systems: Unforced vibration in Maple. Forced vibration in Maple. Animations in Maple. Resonance in Maple.
Introduction to the Laplace transform: Maple.
The inverse Laplace transform: Maple.
ODEs solved by the Laplace transform: Examples. Slides.
Systems of diff eqs solved by the Laplace transform: Maple.
Matrix exponential by the Laplace transform: Notes.
Piecewisely defined functions and periodic functions: Notes with Examples. Maple.
Spring-mass systems solved by the Laplace transform: Maple.
Impulse function. Delta function. Maple.
The convolution: Notes.
