Schedule of Lectures for Mat214

Lecture 1. *Tues. Jan 23*

• 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.

Lecture 2. *Thrs. Jan 25*

• 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

Lecture 3. *Tues. Jan 30*

• 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.

Lecture 4 *Thrs. Feb. 1*

• 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.

Lecture 5 *Tues. February 6*

• Find the line of intersection of the planes: y - x - z = 1 x + y - z = -1
• Find the angle that v= 2 i + j makes with (-1,1,1), (1,0,1), (-2,2,1).
• 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});

Exam 1 *Thrs. February 8*

Lecture 6: *Tues. February 13*

Lecture 7: *Thrs. February 15*

Lecture 8: *Tues. February 20*

Lecture 9: *Thrs. February 22*

Lecture 10: *Tues. February 27*

Lecture 11: *Tues. March 12*

Lecture 12: *Thrs. March 14*

Lecture 13: *Tues. March 19*

Lecture 14: *Thrs. March 21*

Lecture 15: *Tues. March 26*

Lecture 16: *Thrs. March 28*

Lecture 17: *Tues. April 2*

Lecture 19: *Tues. April 9*

Lecture 20: *Thrs. April 11*

Lecture 21: *Tues. April 16*

Lecture 22: *Thrs. April 18*

Lecture 23: *Tues. April 23*

Lecture 24: *Thrs. April 25*

Lecture 25: *Tues. April 30*

Lecture 26: *Thrs. May 2*

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.