User:Egm6322.s09/Report table/Best of report R1

 Under construction; not final (but close to being stable after a couple of weeks). The intention here is to document the best features in any report for the readers (including you); if you see any excellent features in any of the reports (including your team's) that I may have missed noticing, don't hesitate to let me know. I don't have time to read all reports in detail. Due to time constraint, I would only selectively looked at a few important features. I also added some annotations (e.g., related to errors, improvements, etc.) where I looked through for the benefit of everyone. Egm6322.s09 13:16, 27 January 2009 (UTC)

Latest archived version (possibly with comments): Team Bit Team Mafia Team Three


 * classnotes (including simple HW problems), graded over 100%
 * course overview, syllabus, course topics, wiki reports, software tools (for writing wiki articles, latex equation editor, drawing)
 * wikiversity, opening accounts, writing wiki articles (shortcuts, links, wiki text, math latex equations, etc.), team formation
 * introduction
 * independent variables, examples
 * dependent variables, examples
 * partial derivatives
 * nonlinear PDEs, general definition
 * $$\displaystyle n$$ independent variables
 * number of arguments (independent variables, 1st-order partial derivatives, 2nd-order)
 * Hessian
 * symbols for "equal by definition"
 * symmetric symbols $$\displaystyle \overset{\Delta}{=}$$, $$\displaystyle \overset{\rm def}{=}$$
 * asymmetric symbols $$\displaystyle =:$$, $$\displaystyle :=$$; advantages
 * $$\displaystyle 2$$ independent variables
 * examples: linear, diffusion operator, nonlinear
 * HW: more examples, 2 linear, 2 nonlinear
 * "We must welcome the future, because soon it will be the past. We must respect the past, because it was once all that was humanly possible."  George Santayana
 * linearity
 * definition in lecture
 * notation on maps (functions), domain, boundary, range, set of real numbers $$\displaystyle \mathbb R$$
 * additivity and homogeneity, definition of linear mapping from Kolmogorov & Fomin, p.123. HW: Show equivalence between definition in lecture and definition in K&F. Note: Team Mafia Better proof in class; Team Three Error (examples, not proof); Team Bit did not do this HW.
 * linear PDEs, examples. HW.
 * affine mappings, definition. Best contribution: Team Mafia
 * order
 * definition
 * 1st-order PDEs
 * linear
 * nonlinear
 * 2nd-order PDEs
 * heat equation, diffusion operator, coordinate-free notation. HW: Expand diffusion operator into a sum of several terms (summation convention).
 * tensors, tensor order, tensor product, gradient, divergence, component form, summation convention
 * contant coefficients
 * varying coefficients, functions of $$\displaystyle (x,y)$$. HW: Show that the diffusion operator with varying coefficients is linear. Note: Team Mafia Error; Team Bit Team Three did not do this HW.
 * quasilinear 2nd-order PDEs, examples
 * nonlinear PDEs


 * project or longer HW problems, graded over 100%

EGM 6322 Report Table