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Lecture 1. *Tues. Sept. 2*
- Distribution of the syllabus.
- VAX accounts are required by next week. The use of: help, mail or pine, maple
and lynx on the vax. Graphical web browsers are available in the library and
in terminal rooms around campus.
- A first quick over-all look at maple and the windows interface.
Using maple to find max, min and inflection points.
Lecture 2. *Thrs. Sept. 4*
- Introduction to the Algebra and Geometry of Euclidean Space.
- Vectors.
- Addition of vectors and scalar multiplication.
- Inner product and length.
- Orthonormal Coordinate Systems.
Working with vectors in Maple
Maple exercises
Cornell lectures available: Vectors,
Vector Geometry,
The Dot Product
Lecture 3. *Tues. Sep. 9*
- Right handed Coordinate systems
- Geometric properties of the cross product.
- Algebraic properties of the Cross Product: anticommutativity, not associativity, distributivity, multiplication by scalars.
Maple Proofs
Lecture 4. *Thrs. Sep. 11*
- More properties of Cross Products. Examples.
Maple proof that cross products are
not associative
- Lines in 3D: velocity vector, position vector, change of clocks. Parallel lines,
perpendicular lines, angle between lines, intersection of lines.
- Planes in 3D: normal vector, position vector, angle between planes.
Assignment1: p637-8/4,7,12,13,16,17,22,27,29,30,31,32,37,39,41,42,46,47,
49,50,51
p655-7/4,5,13,14,17,18,19,20,24,26,27,29,33,34,36,37,38,40,44,48,51,56,
57,58,59.
p663-5/5,6,7,11,12,16,18,22,23,26,28,29,30,31,39,40,41,43,44,48.
Lines with Maple
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