Summer 2009 - MAT 203 (Calculus III w/ Applications)

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Class:			MAT 203 (Calculus III w/ Applications)
Instructor:			Brandon Williams
Grader:			Panagiotis Gianniotis
Class Time:			Monday, Wednesday, Thursday 10:00am - 12:35pm in Physics P118
Office Hours:			Wednesday 3:00 - 4:00pm MLC, or by appointment

Textbook:
I will not be following any textbook exactly, but a popular book for this course is James Stewart's Multivariable Calculus. You can get either the new version (see here) or the old version (see here).

Course Description:
This course is a continuation of the usual Calculus I and II sequence. Our goal is to extend all of the basic ideas of calculus (functions, limits, derivatives, integrals, etc.) in 2, 3 and possibly more dimensions. We will hopefully end with the vast generalization of the fundamental theorem of calculus known as Stoke's theorem.

Policy:
Problems will be posted below each week, but are not due at any time. We will go over these problems each Monday. There will be weekly quizzes given every Wednesday. The quizzes will be roughly 20-30 minutes, and will be based on the previous week's lectures. There are 5 quizzes in total, but the lowest quiz grade will be dropped. The final exam will be given on the last day of class. Each quiz will be worth 15 points and the final will be worth 40 points for a total of 100 possible points.

Final Information:
The final will take place July 9th, during class.

Extra References:
Calculus III Lectures by Michael Hutchings at Berkeley

Syllabus (Tentative):

Week	Class	Material	Problems
1	June 1	Introduction Vectors Dot Product Projections	PS 1 (12.1, 12.2, 12.3) PS 2 (12.4, 12.5) PS 3 (12.7)
	June 3	Cross Product Some Geometry - lines - planes
	June 4	Coordinate Systems - cylindrical - spherical Vector Valued Functions of Several Variables - surfaces
2	June 8	Calculus on Curves - continuity - derivative - integral	PS 4 (13.1, 13.2) PS 5 (13.3) PS 6 (14.1, 14.2)
	June 10	Quiz on last week's material! Calculus on Curves (continued) - arc length - curvature
	June 11	Limits & Continuity Partial Derivatives
3	June 15	Tangent Planes Matrix Multiplication Chain Rule	PS 7 (14.4, 14.5) PS 8 (14.6, 14.7)
	June 17	Quiz on last week's material! Directional Derivatives Maxima & Minima
	June 18	More on Maxima & Minima
4	June 22	Iterated Integrals of Scalar Functions Fubini's Theorem	PS 9 (15.2, 15.3, 15.7) PS 10 (15.4) PS 11 (15.5, 15.8)
	June 24	Quiz on last week's material! More integrals over regions Change of coordinates
	June 25	More change of coordinates Surface Area
5	June 29	Line Integrals	PS 12 (16.1, 16.2) PS 13 (16.3) PS 14 (16.4)
	July 1	Quiz on last week's material! FTC of Line Integrals
	July 2	Green's Theorem
6	July 6	Overview	Practice Final Exam
	July 8	Quiz on last week's material! Review
	July 9	Final Exam!

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