Introduction to Partial Differential Equations      Peter J. Olver

1. What are Partial Differential Equations      [Exercises101]
2. Linear and Nonlinear Waves 
   2.2 Transport and Traveling Waves  2.3 Nonlinear Transport and Shocks  2.4 d'Alembert's formula
   [Exercises201]
3. Fourier Series
   [Exercises301]
4. Separation of Variables
   4.1The Diffusion and Heat Equations  4.2 The Wave Equation  4.3 The Planar Laplace and Poinsson Equations 4.4 Calssification of PDE
   [Exercise401]
5. Finite Differences
   5.1 Finite Difference Approximations  5.2 Numerical Algorithms for the Heat Equation  (3) 1-order PDE (4)the Wave Equation
   [Exercise501]
6. Generalized Functions and Green Functions
   The Fourier Series of the Delta Function  The method of Images
   [Exercise601]
7. Fourier Transforms                                             [Exercise701]
8. Linear and Nonlinear Evolution Equations
   8.1The Heat Equation   8.3 The Maximum Principle  8.4 Nonlinear Diffusion  8.5 Dispersion and Solitons  The KdV Equation  
   [Exercise801]
9. A General Framework for Linear Partial Differential Equations
   9.1 Adjoints   9.2 Self-Adjoint  9.3 Minimization Principle  THe Dirichlet Principle  9.4 Eigenvalues and Eigenfunctions
   [Exercise901]
10. Finite Element and Week Solutions                    [Exercise1001]
11. Dynamics of planar Media
    11.1 Diffusion in Planar Media  11.2 Explicit Solutions of the Heat Equation  11.3 Series Solutions of ODE  The Gamma Function  The Airy Equation  Bessel's Equation
    The Planar Wave Equation                                [Exercise1101]
12. Partial Differential Equations in Space
    12.1 The 3-dim Laplace and Poisson Equations   12.3 Green's Functions for the Poisson Equation  12.4 Heat Equation  12.5 Wave Equation  
    2.6 Spherical Waves and Huygens' Principle   12.7 The Hydrogen Atom      [Exercise1201]