- Distribution of the syllabus.
- VAX accounts are required by next week. The use of: help, mail or pine, maple and lynx on the vax.
- A first quick over-all look at maple and the windows interface.

- Introduction to the Algebra and Geometry of Euclidean Space.
- Right handed 3D coordinate systems.
- Addition of vectors and scalar multiplication.
- Inner product and length.
- Distance between two points and angle between two vectors.
- Orthogonal Projections

Cornell lectures available: Vectors, Vector Geometry, The Dot Product

- Algebraic definition of the Cross Product: 1-2-3 rule, determinant, cross products for the basis vectors i,j,k.
- Simple properties: Distributivity, anticommutativity, linearity under scalar multiplication.
- Geometric property of the cross product.
- The triple scalar product: cross and dot = volume of the parallelepiped.
- Equations of lines in 3D.

- Equations of planes in 3D.
- A plane through the origin perpendicular to a given vector N.
- A plane through an arbitrary point perpendicular to N.
- A plane through 3 points.

- Intersections of lines and planes.
- Intersection of two lines.
- Intersection of two planes.
- Intersection of a line and a plane.

- Plotting lines and planes with Maple.

Cornell lectures available: The Cross Product, Applications of the cross product: planes, volumes

Assignment set 1: p655/5,10,13,18,21,24,29,32,37,49,56

p663-665/9,14,19,24,27,28,29,30,31,34,39,47,50,60

p673-674/4,7,12,14,16,19,21,24,31,36,45,52,63,64,65,66

- Find the line of intersection of the planes:
y - x - z = 1 x + y - z = -1 - Find the angle that
makes with (-1,1,1), (1,0,1), (-2,2,1).**v**= 2 i + j - Do the vectors:
i + 2k -j, i + j - k, 3i + j lie on a plane? - Compute the area of the triangle PQR where:
P(0,1,0), Q(2,1,0), R(1,0,1) - Find the symmetric equations of the line through the origin
perpendicular to the plane:
z - x - y = 5 - Consider the line:
x = -3t - 1 y = 2t - 2 z = t - 1 and the plane: x + y + z = 3. Do the line and the plane intersect? You may be able to look at both the line and the plane with maple:`> line:=plot3d([-3*t-1,2*t-2,t-1], t=-5..5,s=0..1,grid=[2,2]):``> plane:=plot3d(3-x-y,x=-3..3, y=-3..3,orientation=[103,110]):``> with(plots): display3d({line,plane});`

Cornell lectures available: Kinematics with vector Calculus.

Cornell Lectures available: [Tangent vector and curvature],[Normal, Twist and Binormal],[Tangential and Normal components of acceleration]

Assignment set 2: p700-1/2,5,8,10,12,15,20,25,45,48

p708-10/10,17,20,26,32,33.

Assignment set 3: p816/1,4,5,8,10,11,13,14,16,19,20,21,22,23.

Assignment set 4: p762-4/31,42,48. p772-4/3,4,5,12,21,22,26,28,29,33,44.

Assignment set 5: p779-80/4,7,8,11,12,15,18,19,31,32. p791-2/10,14,18,32,38,52,53. p802-5/35,37,47,48,50. p813-14/13,14,20,23,40.

Available: maxs and mins.. (under construction)

Assignment set 6: p829-30/9,24,29,36(use maple),38,41. p836-8/3,4,14,15,18,30, 37, 44,50,53.

Link: geom.umn.edu Lab on Divergence

Assignment set 7: p914-916/4,5,7,13,16,21,26,36,39,40,44,47,48. p922-24/4,6,7,9,13,21,26,29,30,36,37,39. p931-33/1,4,6,9,10,13,20,30,31,34.

**HINT:** Equations of planes, cross product,
tangent plane to a surface, total differentials,
length of a parametric curve, double integrals,
double int in polar coordinates, Lagrange Multipliers,
Green's theorem, line integrals, curl and div.