I'm not going to blame anyone except for the fact that I'm probably a slow learner. Can somebody explain some of the things I'm learning in layman terms? That way I can have some context when I'm reading about them. Right now, the things I'm reading have no meaning, so it's really hard to understand it. I would also really appreciate it if someone gave me a really loose proof too. You don't need to go into the math, I'm thinking something along the lines of "Well we take what is called a "blank" equation, and manipulate it until we get an inequality..this is useful because..etc" Here is what I do understand so far: Fourier series/transforms/integrals and why that is useful. Solving first order and quasi-linear PDE's via separation of variables and characteristic method. Ok here goes: 1. What is the "Energy Method" and what does it do? 2. What are "shocks"? and why is that a problem? 3. What does it mean what they say "Parabolic, Hyperbolic, Elliptical problem?" 4. What do they mean by "well-posedness and uniqueness?"