Day 1, Mat234: Linear Algebra
Today:
- Welcome!
- Introductions (3x5 cards)
- Name
- Where are you from?
- Year (Sophomore, etc.)
- Major
- Something special about yourself.
- The name of your invisible friend.
- Some course details:
- The course website may be useful:
http://www.nku.edu/~longa/classes/mat234
- Syllabus (logistics, etc.)
- Our text is free, available as a pdf:
Note: save the two files in the same directory (without
changing file names), so that clicking on an exercise will
send you to its answer and clicking on an answer will send you
to its exercise.
- You should do the reading in advance of our discussion of
each section in class.
- Because the text is virtual, you will be allowed to use an
electronic reader in class. That includes a laptop, but I'm concerned
that it not be used for doing your emails, etc. We'll see how this
works, but please don't abuse the system. Ordinarily I forbid the use
of electronic devices in class (especially cell phones).
- The plan of attack (we're using
the author's suggestion on page v, first timetable - slightly
modified to include an additional test, as well as the padding that an extra
week provides).
- Questions?
- A brief overview:
- What is linear algebra?
- Fun and powerful
- almost universal
- well-behaved (by comparison with life in the non-linear
lane...)
- Linear equations:
- ax+by=c
no sweat, right? Geometrically, a line.
- Systems of linear equations:
- a1x+b1y = c1
- a2x+b2y = c2
More troublesome? Geometrically, the intersection
of two lines -- if it exists! Ah, an important
issue that arises immediately....
- Vectors - 2-d, 3-d, ..., n-d:
- Computer scientists, graphics, physicists, mathematicians:
manipulation and transformation (e.g. rotation, scaling,
projection)
- Physicists and chemists:
- Positions of points (say stars, or molecules)
-
- Matrices:
- Urban Planners (and everyone!): spreadsheets
- Computer Scientists: images, and image compression (for example)
- Applications
- e.g. averages (see image compression,
for example)
- Mathematicians, CS: encryption
- Everyone: Least Squares solutions to over-determined systems of equations
- decompositions:
- Software/technology:
- I'll be making (limited) use of the TI-92/89, but you'll
be able to use it on the exams, so it's worth practicing. You
may use any calculator, but the more powerful, the better.
- Other software will be used (e.g. Mathematica, Octave)
- I'll use my
octave interface, to access octave, a MATLAB clone. This is
useful in class, and for you (so that you can work at home).
- Next time: Read Section One.I.1
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