1. DE Models: General outline
Notes/handouts: Models.pdf. Additional: models; chemical kinetics
2. Analytic solutions: method of separation
ii) Intro to Mathematica: Easy Mathematica (Wolfram alpha; Wolfram CDF-player )
Real Mathematica in 20 minutes. DE-solutions with Mathematica; Integrating separable DE,
iii) Applications of Linear DE: CR-circuits-Mixing.pdf. Discontinuous DE.nb
iv) Logistic US-population;.Data fit nb.
Extra : Sliding down a slope; Poisseuille flow and CR –circuit; Flight with friction.pdf
3. Qualitative methods: slope-field.
DEtools package for Mathematica 6/7 by Selwyn Hollins (follow installation instructions) Basic examples.nb
4. Numeric Methods (Euler): Excell ; Euler.nb. Uniqueness/existence: pdf
5. Phase-line, Equilibria, Bifurcations: notes; nb
Extra: Fisheries in decline (NYT; Wild Fisheries in 45 Years)
6. First order Linear equations and multipliers
i) LDE, Linear Superposition, Undetremined coefficients
ii) Applications of multipliers; Mixing.pdf
iii) Rocket science.
7. Other techniques:
Change of variables, Riccati eq-n(notes; nb). Extra: fastest slope ( tif; nb )
2.1-3. Modeling with differential systems
i) Notes on DS models Phase plane: nb (same with DifEqs package nb)
Extra: Kepler problem
2.4. Euler method for systems:nb, Excel
Nonlinear oscillators: Duffing and P-delta; nb (non linear oscillators). Equilibira types: nb
SIR model of epidemics: notes (section 2.6); nb
2.5. Lorenz 3D system: strange attractors and chaos (lorenz.nb)
Additional: notes on Rayleigh-Benard convection.Wikipedia: Edward J. Lorenz ; Lorenz attractor.
Weather patterns animations: 3D Lorenz; Higher-D truncated convective system (110 equations)
3.1. Linear DS- models: notes; DSolve for LDS.nb
3.2-3: Eigenvalue method: Examples; Eigenvalue demo.nb; Eigenvalues.nb
3.4: Complex eigenvalues (spirals and centers): Notes
3.5: Repeated and zero eigenvalues notes
Applications to LDS models: notes . Migration.pdf.
3.7: Equilibria and Bifurcations: Notes (trace-determinant plane), nb
3.8: 3D systems (Linearized Lorenz DS): notes; nb.
Extra topics: Matrix Exponential.pdf, and nb
Tracking moving target nb
Population dynamics tif, data table, UN link.
4.1- 3.6: Characteristic polynomial and Method of undetermined coefficients: notes, damped free-oscillations.nb
4.2-3: Forced oscillation: Modulation and Resonance (notes; additional pdf).
nb: Periodically forced oscillations; Qualitative analysis: modulation and resonance
Additional topics: i) LRC-circuits.
5.1-2: Nonlinear models. Phase plot nb
5.2: Equilibria, linearization, stability. Volterra-Lotka competition: Example. Analysis.
5.3-4: Hamiltonian and Conservative systems. Gradient and Dissipative systems: pdf; summary of Hamiltonian and Gradient DS
Notebooks: Hamiltonian and gradient; VL predator-prey cycles ; Linear and nonlinear oscillations
5.5: 3D systems.nb. Food chain and Lorenz system "chaotic weather "
5.6: Forced nonlinear oscillations and chaos nb
6.1. Basic Laplace transform (nb).
6.2. Forced oscillations via Laplace transform: nb. Square-wave
6.3. Delta-function (nb) and convolution (nb). Bumpy road nb. Fundamental solutions and variation of parameters pdf .
E-mail: dxg5@case.edu Phone: (216) 368-2857