- Classification of linear Partial Differential Equations of order 2, canonical form.
- Fourier series (definition, Fourier theorem, odd and even periodic extensions, derivative, uniform convergence).
- Examples: Heat equation (Dirichlet’s and Newman’s problems), Wave equation (mixed type problem), Potential equation on a rectangle.
- Superposition of solutions, non-homogeneous equation.
- Infinite and semi-infinite Heat equation: Fourier integral, Green’s function. Duhamel’s principle.
- Infinite and semi-infinite Wave equation: D’Alembert’s solution.
- Potential equation on the disc: Poisson’s formula and solution as series.