Day 1, Mat225: Linear Algebra
Today:
- Welcome!
- Introductions (4x6 cards)
- Name
- Where are you from?
- Working? If so, where, and how many hours?
- Year (Sophomore, etc.)
- Major
- Why are you taking linear algebra?
- What is your height (feet/inches)?
- Something special about yourself.
- Welcome to David Freeman, especially....
- Some course details:
- The course website may be useful:
http://www.nku.edu/~longa/classes/mat225
- You should do the reading in advance of our discussion of
each section in class.
- Syllabus (logistics, etc.)
- The plan of attack
- I may use blackboard, but only in a limited way. You may certainly
find it useful for discussion. I will monitor it only loosely,
but please notify me if there is something that I should see or address.
- 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....
- 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 using.
- MATLAB will be available: I'll be working out the details....
- 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: Section 1.1 (First assignment:
pp. 11-13, #1, 4, 5, 10, 11, 16, 17, 22, 23, 24, 29, 33; due next Wednesday)
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