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MATH 3010 3.00AF (Fall 2015)
Vector Integral Calculus
Topics and notes
I'll do many examples and proofs at the blackboard, but I will use the data
camera in class to summarize the topics we cover. I will post those
summaries below, as a guide for anyone who misses a particular class, or
who wants a summary of topics covered.
 Week 1

Sep 11: Review of vectors and dot products (Sections 1.11.2)
 Week 2

Sep 14: Review of cross products and volume (Section 1.5)

Sep 16: Vector functions (Chapter 2), differentiability (Section 3.2)

Sep 18: Partial derivatives (Section 3.1) and the Jacobian matrix
(Section 3.2)
 Week 3

Sep 21: Examples, properties of the derivative (Section 3.2)
 Sep 23: More examples and properties

Sep 25: Chain rule (Section 3.3)
 Week 4

Sep 28: Tangents to level sets (Sections 3.4 and 4.5)

Sep 30: Implicit function theorem (Section 6.2)

Oct 2: Smoothness of level sets (Section 6.3)
Assignment 1 posted
 Week 5

Oct 5: Manifolds, inverse function theorem (Sections 6.2, 6.3, 4.5)

Oct 7: Examples, sketch of proof.

Oct 9: Outline of maxima and minima (Sections 3.6, 5.1, 5.2, 5.3).
Assignment 1 due
 Week 6
 Oct 12: No class (Thanksgiving)
 Oct 14: First Midterm
 Oct 16: Proof and examples for the second derivative test.
 Week 7

Oct 19: Lagrange multipliers (Section 5.4)
 Oct 21: Examples.

Oct 23: Integration (Sections 7.1 and 7.2)
Assignment 2 posted
 Week 8
 Oct 26: Change of variables (Section 7.6)

Oct 28: Polar coordinates (Section 7.3)
Midterm 1 returned, Assignment 3 posted
 Oct 30: Study break  no class
 Week 9

Nov 2: Spherical coordinates (Section 7.3)
Assignment 2 due, Assignment 1 returned

Nov 4: Examples, orientations.

Nov 6: Arc length (Section 3.5),
Line integrals (Section 8.3 introduction)
Assignment 3 due
 Week 10
 Nov 9: Second Midterm (drop date)

Nov 11: 1forms (The book gives a very general version in
Section 8.2, which I may come back to at the end of the course, if there
is time)
Assignment 2 returned

Nov 13: Exact forms (Sections 3.1 and 3.2)
Midterm 2 returned
 Week 11

Nov 16: Conservative vector fields, Green's theorem
(Sections 8.3.1 and 8.3.3)

Nov 18: Conservative vector fields and Green's theorem, continued.
Assignment 3 returned, Assignment 4 posted

Nov 20: Surface area (Section 8.4)
 Week 12

Nov 23: Surface area integrals (Section 8.4)

Nov 25: Surface integrals and flux (Section 8.4)

Nov 27: Surface integrals, Stokes' theorem (Section 8.5)
You may refer to the following, but are not responsible for them:
Explanation of the books' notation for surface integrals.
Proof of Stokes' theorem.
Assignment 4 due,
Assignment 5 posted
 Week 13

Nov 30: Stokes' theorem (Section 8.5)

Dec 2: Divergence theorem (3d) (Section 8.6)
You may refer to the following
Proof of the Divergence theorem, but are not responsible for it.

Dec 4: Divergence theorem (2d) (given by Prof. Madras, and not on exam)
Assignment 5 due
 Week 14
 Dec 7: Review session (given by Prof. Madras)  come with questions.