Day 9 in Mat430

Today:

• Announcements
  • Return of your assignment, pp. 22--. Graded 1b, 6, 17.
    For #18, p. 22,
    • a couple of additional trig identities would be useful:
      • 

      • 

    • It often helps to work backwards: for example

      

  • Hand in homework, p. 25
  • Today's activity, and new assignment:

    Mon

    2/1

    12-13

    Read sections 14, 15 pp. 42, #1, 3, 4, 6, 8a (due Mon, 2/8)

• Section 12: Mappings
  • Visualizing functions of a complex variable generally requires 4-D glasses!;)
    • Plotting Moduli of the image cuts it to three-D
    • Alternatively, consider plotting
      • The Principal Argument of the image
      • The real part of the image
      • The imaginary part of the image
  • Rotations, translations, scalings,....
    • Mathematica demo
  • Mapping special curves, and straight lines (review of conic sections)
  • Mapping regions
  • Mapping boundaries

• Section 13: Example: the exponential function
  • In this example, we map lines in the domain space to regions in the image space.
  • The example shows a periodicity that our previous example didn't.