Mathematics - Partial Differential Equations (PDE) 2
Collected Lectures on Partial Differential Equations (PDE)
A compact study list, grouped by level and type, with freely accessible material for studying Partial Differential Equations (PDE).
Some popular partial differential equations (PDEs)
Single PDEs # Linear equations # Laplace’s equation $$ \begin{equation} \Delta u = \sum_{i=1}^{n} u_{x_i x_i} = 0. \end{equation} $$ Helmholtz’s (or eigenvalue) equation $$ \begin{equation} -\Delta u = \lambda u. \end{equation} $$ Linear transport equation $$ \begin{equation} u_t + \sum_{i=1}^{n} b^i u_{x_i} = 0. \end{equation} $$ Liouville’s equation $$ \begin{equation} u_t + \sum_{i=1}^{n} (b^i u)_{x_i} = 0. \end{equation} $$ Heat (or diffusion) equation $$ \begin{equation} u_t - \Delta u = 0. \end{equation} $$