Partial Differential Equations
- How does a PDE differ from an ODE?
- How is the order of a PDE defined?
- How is a linear PDE defined?
- Write down the PDEs for the Laplace, Poisson, Diffusion, and first order wave equations.
- What do $f_t$, $f_{xx}$, and $f_{xy}$ mean in the context of PDEs?
- Write out the gradient, divergence, and Laplacian operators in terms of their components in two dimensions:
- $\vec{\nabla}f$
- $\vec{\nabla}\cdot f$
- $\nabla^2 f$
- Classify the following problems as elliptic, parabolic, or hyperbolic
- Steady diffusion
- Unsteady diffusion
- Unsteady advection
- Steady advection and diffusion
- Unsteady advection and diffusion
- What order derivatives are associated with diffusive phenomena?
- What order derivatives are associated with advective phenomena?
- Review and understand the domain of dependence figures.
- (Note, the physical characteristics of advection and diffusion will significantly impact our numerical treatment of such terms.)