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Math 567: Notes

Lecture Notes
  • I. Linear Waves and Dispersion
    • Jan. 5: linear `wave' equations and dispersion relations
    • Jan. 10: solution by Fourier transform
    • Jan. 12: dispersion and group velocity
    • Jan. 17: measuring dispersion: decay estimates
    • Jan. 19: measuring dispersion: space-time estimates

  • II. Nonlinear Dispersive PDE: Examples, Structure, Well-Posedness
    • Jan. 31: the water wave problem: shallow water, Boussinesq, and KdV
    • Feb. 2: origins of the nonlinear Schroedinger equation
    • Feb. 7: local existence theory (classical solutions)
    • Feb. 9: local existence theory (rougher solutions)
    • Feb. 14: Hamiltonian systems, symmetries, conservation laws: ODEs