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Schedule of Lectures for Mat214

Lecture 1. *Tues. Jan 23*

Lecture 2. *Thrs. Jan 25*

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

Lecture 3. *Tues. Jan 30*

Lecture 4 *Thrs. Feb. 1*

Maple exercises
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

Lecture 5 *Tues. February 6*

Review exercises in preparation for Exam1 this Thrs.
Recall only Maple and Chap10 are included. Don't forget to bring a calculator (able to handle sines and cosines) a number 2 pencil and your SUNYA ID.

Exam 1 *Thrs. February 8*

In class Exam on Maple and the Geometry and Algebra of 3D euclidean space.

Lecture 6: *Tues. February 13*

Vector functions: Limits, derivatives and integrals of vector valued functions.
Cornell lectures available: Kinematics with vector Calculus.

Lecture 7: *Thrs. February 15*

Unit Tangent, Unit Normal, curvature. Tangential and Normal components of acceleration.
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 8: *Tues. February 20*

Functions of several variables, Level Curves, plot3d in Maple, Limits and Continuity, partial derivatives.

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

Lecture 9: *Thrs. February 22*

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

Lecture 10: *Tues. February 27*

Partial derivatives and Chain rules.

Lecture 11: *Tues. March 12*

Directional derivatives and the Gradient.

Lecture 12: *Thrs. March 14*

Maxima and minima of functions of several variables. Lagrange Multipliers.
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)

Lecture 13: *Tues. March 19*

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.
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.

Lecture 14: *Thrs. March 21*

Properties of double integrals. Changing the variables to polar coordinates. Polar rectangles. Element of area in polar coordinates. Change of variables formula. Examples.

Lecture 15: *Tues. March 26*

Review exercises and preparation for Exam3. Sections included in the exam are: 12.6, 12.7, 12.8, 13.1, 13.2, 13.3.

Lecture 16: *Thrs. March 28*

Exam 3.

Lecture 17: *Tues. April 2*

Introduction to vector analysis. Definition of a vector field, divergence and curl
Link: Lab on Divergence

Lecture 19: *Tues. April 9*

Fundamental theorem for line integrals, Conservative vector fields, scalar potentials, conservation of energy, introduction to Green's theorem on the plane.

Lecture 20: *Thrs. April 11*

Positively oriented, closed, piecewise smooth, simple curves. Statement and proof of Green's Theorem, Extension to regions with wholes, Computation of area with line integrals, Other forms of Green's Theorem.
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.

Lecture 21: *Tues. April 16*

General parametric surfaces, Surface integrals, The element of surface area, Orientable surfaces, Stokes' theorem.

Lecture 22: *Thrs. April 18*

Introduction to geometric algebra, bivectors, the wedge product, differential forms, the exterior derivative, Statement of the General Fundamental Theorem of Calculus.

Lecture 23: *Tues. April 23*

Review problems from chapter 14. Preparation for Exam4 on Thursday April 25.

Lecture 24: *Thrs. April 25*


Lecture 25: *Tues. April 30*

Final Grades, Evaluations, Explanation of how the Make-up on Thrs May 2nd can change your final letter grade in the course.

Lecture 26: *Thrs. May 2*

Make-up Exam5. All is included.

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.