Day 20 in
Mat430
Last time
: Harmonic functions and PDEs
Next time
: More "old friends" among functions
Today
:
Announcements
Return of homework p. 60
Factoring takes energy, and tidies up: don't undo it!
Do it! Factor, if possible.
Reminder: you have three assignments due in the next three class periods -- try to keep up!
Today's activity, and new assignment:
Mon
3/1
28-30
Read 31-33 (chapter 3)
problems: pp. 89--, #1, 4, 5, 8, 13 (due Mon, 3/15)
Last time: we were working on Section 25: Harmonic functions
Definition
Theorem and big picture
An example PDE
Harmonic conjugates
Examples
This time: Exponentials and Logs
Section 28: the function
Definition -- the extension of
into the complex plane
The old familiar properties hold:
There are some new things under the sun:
f
can be negative
f
is periodic (with imaginary period)
Examples
Section 29: the "inverse",
Definition -- a multi-valued function (no surprise, really)
Branches
Even so, many of the old familiar properties hold.
Section 30: Branches of Log
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. Comments appreciated.