Here is a list of surprising things that students don't know: Engaged Student

  • basis vectors that go with curvilinear coordinates
  • matrices as transformations
  • power series as approximations
  • eigenvectors as the things that are “unchanged” by a transformation
  • a geometric conception of fields
  • how to add two functions pointwise
  • how to read equations as words
  • what is planar about plane waves?
  • geometric interpretations of dot and cross products
  • the meaning of the vertical axis on a graph
  • how to shift a graph left or right, up or down
  • how to expand a sum (see video from E&E 5/29/09 FIXME)
  • do not understand what “features” are when asked to describe the features of a physical situation

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