Notes and slides

• Introduction and preliminaries (PDF)
  • Slides
• Conservation principles and PDE models (PDF)
  • Slides
• Linearity and linear operators (PDF)
  • Slides: preliminaries
  • Slides: eigenvalue problems
• Separation of variables (PDF)
  • Slides: introduction
  • Slides: polar coordinates
  • Slides: inhomogeneous equations
• Higher dimension PDEs and eigenvalue problems (PDF)
  • Slides: multidimensional eigenvalue problems
  • Slides: rectangles and disks
  • Slides: some examples
  • Slides: spherical harmonics
• Green's functions and distributions (PDF)
  • Slides: Distributions
  • Slides: Green's functions in one dimension
  • Slides: Higher dimensional Green's functions
  • Slides: Method of images
  • Slides: Using Green's formulas
• Fourier transforms (PDF)
  
  • Slides: The Fourier transform
  • Slides: Differential equations and Fourier transforms
• First and second order wave equations (PDF)
  
  • Slides: Linear wave equations
• The method of characteristics (PDF)
  
  • Slides: Method of characteristics
• Quasilinear transport, shocks and rarefactions (PDF)
  • Slides: Shocks and rarefactions
• Dispersion relations, linearization and stability (PDF)
  
  • Slides: dispersion, stability, linearization
• Symmetry and similarity solutions (PDF)
  
  • Slides: Symmetry and similarity solutions