Mathematics - Partial Differential Equations (PDE) 2
Collected Lectures on Partial Differential Equations (PDE)
📝 Notes on Partial Differential Equations - John K. Hunter (University of California at Davis) 📝 Partial Differential Equations: Lecture Notes - Erich Miersemann (Leipzig University) 📝 Linear Methods of Applied Mathematics - E. Harrell, J. Herod (Georgia Tech)
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 $$ \begin{equation} u_t - \Delta u = 0. \end{equation} $$