User:Egm6322.s09/Report table/Best of report R2

 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 12:18, 7 February 2009 (UTC)

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


 * classnotes (including simple HW problems), graded over 100%


 * 2nd-order quasilinear PDEs
 * examples
 * verification of linearity


 * 2nd-order linear PDEs
 * matrix-operator form
 * constant coefficients
 * varying coefficients
 * equivalence between two forms: regular form and matrix form
 * HW: Condition for equality of mixed derivatives $$\displaystyle u_{xy} = u_{yx}$$. Best solution: Team Bit simpler to understand; Team Mafia the proof is a bit more complicated to read, but essentially the same. Note: Team Three good starting point, which coincides with the proofs in the other two reports, but need to use mean-value-theorem to conclude, and can use different step size along $$\displaystyle x$$ and $$\displaystyle y$$ to be more general as in the proofs in the other two reports; appears to do this proof on their own; good.
 * linearity of diffusion operator
 * linearity of derivative. Best solution: Team Mafia. Note: Team Bit Team Three gave a statement, but not a proof.
 * linearity of gradient operator
 * linearity of divergence operator
 * nonlinear transformation of coordinates
 * matrix-operator form in new coordinates


 * linearity, 2 definitions
 * definition 1 in class
 * definition 2 in Kolmogorov & Fomin, Selvadurai
 * additivity
 * homogeneity
 * examples of linear maps in higher dimensions, matrices, homogeneity
 * transformation of coordinates, rotation of coordinate system. Best solution: Team Bit see better explanation in class.  Note: Team Mafia only display the rotation matrix, and referred to a book, but not derived it.  Team Three did not do this problem.
 * affine mappings, not linear; example, rotation and translation
 * equivalence between two definitions, proof
 * sufficient condition
 * necessary condition