# Schedule of Lectures for Mat214 Fall 1997

### 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.

Carlos Rodriguez <carlos@math.albany.edu>