Lecture 1. *Tues. Sept. 3*
Lecture 2. *Thrs. Sept. 5*
Cornell lectures available: Vectors, Vector Geometry, The Dot Product
Lecture 3. *Tues. Sep. 10*
Lecture 4. *Thrs. Sep. 12*
Lecture 4 *Tues. Sept. 17*
Cornell lectures available: The Cross Product, Applications of the cross product: planes, volumes
The plane through 3 points
The plane containing two lines
Two planes and one point
Two planes, angle, line..
Lecture 5 *Thrs. Sept. 19*The distance from a point to a line
The distance from a point to a plane
Lecture 6 *Tues. Sept. 24*Review exercises in preparation for Exam1 this Thrs.
Recall only Maple and Chap10 are included. Don't forget to bring a number 2 pencil and your SUNYA ID.
Exam 1: *Thrs. Sept 26 13*In class Exam on Maple and the Geometry and Algebra of 3D euclidean space.
Lecture 7: *Tues. Oct. 1*Vector functions:[Limits], [derivatives] and integrals of vector valued functions.
Cornell lectures available: Kinematics with vector Calculus.
Lecture 8: *Thrs. Oct. 3*[Unit Tangent, Unit Normal], [Arc length and curvature]. Tangential and Normal components of acceleration. [Formulas for plane curves].
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
Lecture 9: *Tues. Oct. 8*[Functions of several variables, Level Curves, plot3d in Maple], [Limits and Continuity.]
[Exercises of limits of functions of several variables]
Assignment set 3: p816/1,4,5,8,10,11,13,14,16,19,20,21,22,23.
Lecture 10: *Thrs. Oct. 10*Partial Derivatives
Examples with Maple
Examples with Maple
Assignment set 4: p762-4/31,42,48. p772-4/3,4,5,12,21,22,26,28,29,33,44.
Lecture 11: *Tues. Oct. 15*Differentiability
Examples of the Chain Rule with Maple
Using the Chain Rule to compute rates
Lecture 12: *Thrs. Oct. 17*Directional derivatives
Lecture 13: *Tues. Oct. 22*Review exercises for Exam2 this Thursday.
Exam2: *Thrs. Oct. 24*In class Exam.
Lecture 14: *Tues. Oct. 29*Maxs, Mins and Saddle points
Examples with maple.
More on Lagrange Multipliers.
Lecture 15: *Thrs. Oct. 31*Multipe Integrals. Definition of the double integral of f(x,y) over a rectangular domain D. Fubini's theorem. Volumes and Areas computed with double integrals. Integration over non-rectangular domains.
Lecture 16: *Tues. Nov. 5*Properties of double integrals. Changing the variables to polar coordinates. Polar rectangles. Element of area in polar coordinates.
Lecture 17: *Thrs. Nov. 7*Change of variables formula. Examples.
Lecture 18: *Tues. Nov. 12*Surface Integrals. Examples
Lecture 19: *Thrs. Nov. 14*EXAM 3 in class.
Lecture 20: *Tues. Nov. 19*Vector Fields. Definition. Divergence and Curl. Physical interpretation. Examples. Computations with maple (diverge and curl commands).
Lecture 21: *Thrs. Nov. 21*Line Integrals
Definition for scalar functions. Example of a computation from the definition. Formula for computing line integrals in terms of a parametrization for the curve. Line integrals of vector fields. The physical concept of Work. Formula involving the unit tangent vector.