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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 1.1-1.2)
• 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: 1-forms (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.