Lecture 14, 18.300, Tue Mar 29, 2022. Summary % -------------------------------------------------------------------------- #043.5 Dimensional analysis, similarity solutions, etc. This point is relevant after the prior problem set [#4]. % % -------------------------------------------------------------------------- Continue with diffusion effects in Traffic Flow: #044, #045, #046, #047, #048, #049 % Note that #042 [information loss at shocks] is intimately related to the topic here: When diffusion is small, we can neglect it EXCEPT at at shocks. This diffusion causes the dissipation/loss of info. there --- as shown in #049. % USEFUL FOR #047 [this is a recap of something done earlier]. REVIEW "graphical theory" for \dot{y} = f(y). Phase line, and qualitative plot of solutions y = y(t). Behavior near critical points by linearization. Inflection points. Etc. Exact solution by separation is useless, unless f(y) is pretty simple [e.g.: 1st/2nd order polynomial]. % % ========================================================================== NOTE: Here #nnn are references to the Lecture Points file. [PSQ] means Problem Set Question. The "lecture summaries and points" are NOT intended as study materials. The points purpose is explained in the "lecture points" file. The summaries are brief descriptions each lecture, used by the instructor to keep track of the material covered. They ARE *NOT* "lecture notes" to be used to study and/or replace attending the lectures, etc. They are provided for your convenience, as a help to organize your own notes. % ========================================================================== % EOF