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# MATH 3010 3.00AF (Fall 2015) Vector Integral Calculus

Information about Assignments and Exams will be posted here, as it becomes available.

## Final Exam

I've put information about final exam scores and final grades into a table.

#### Exam instructions:

You may bring a calculator to the final exam, as well as an 8.5x11 formula sheet (2-sided).

You are responsible for what we covered in class, not for what is in the textbook. You are not responsible for repeating proofs that I gave in class, but you should understand those results (including the hypotheses, when they were stated explicitly). The exam will cover the whole semester's topics, but it will put a bit more weight on material that hasn't been tested yet (ie since the midterms). Here are some of the major topics we covered (see the Topics page for section references).

• Differentiability, Jacobian derivatives, gradients
• Chain rule
• Tangents, linear approximation
• Manifolds, level sets, Implicit function theorem, Inverse function theorem
• Maxima and minima, Hessians and the 2nd derivative test
• Lagrange multipliers
• Multiple integrals
• Jacobian determinants and change of variables
• Polar, cylindrical, and spherical coordinates
• Integrals of scalar functions along curves, with respect to arc length.
• Line integrals along curves, both in the form X dot ds and f dx + g dy
• Conservative vector fields
• Green's theorem in the plane
• Integrals of scalar functions on surfaces, with respect to surface area.
• Surface integrals (ie flux integrals over surfaces), in the form X dot n dA
• Stokes' theorem
• Divergence theorem in R^3
In particular, you are NOT responsible for 2-forms or their surface integrals. You are NOT responsible for flux integrals in the plane, or the Divergence theorem in the plane.

## Assignments

• Assignment 1 (corrected). Due Friday Oct 9, in class, or in the assignment box (by the 5th floor elevators, in the North wing of Ross) by noon. Solutions.
Graded problems were numbers 3-6.
• Assignment 2. Due Monday Nov 2, in class, or in the assignment box by noon. Solutions.
All problems were graded.
• Assignment 3. Due Friday Nov 6, in class, or in the assignment box by noon. Solutions.
All problems were graded.
• Assignment 4. Due Friday Nov 27, in class, or in the assignment box by noon. Solutions. [Note: there is a typo in the solution to 1b: the integral over C_2 should be of 0 dt, so the answer should be 1/2; There is also a typo in the solution to 4b: On the top, -y^3 is -8 giving an integral of 24.]
• Assignment 5 (last assignment). Due Friday Dec 4, in class, or in the assignment box by noon. Solutions (corrected).

## Practice problems

(Not to be handed in)
• Problem set 1: Review of vectors
• Section 1.1 problem 8
• Section 1.2 problems 1g, 5, 11
• Section 1.5 problems 5b, 6b, 7b, 12
After you do the problems, you may check your work against the solutions
• Problem set 2:
• Section 2.1 problem 4
• Section 2.2 problem 1 (open parts)
• Section 2.3 problems 8fg
• Section 3.2 problems 1c, 2b, 3d, 7, 12
• Section 3.3 problems 1, 2
After you do the problems, you may check your work against the solutions
• Problem set 3:
• Section 4.5 problems 2, 11
• Section 6.2 problems 1d, 3d
After you do the problems, you may check your work against the solutions (corrected).
• Problem set 4:
• Section 5.2 problems 1bhjl, 8, 13
• Section 5.3 problems 1bhjl, 2, 4
After you do the problems, you may check your work against the solutions.
• Problem set 5:
• Section Section 3.6 problem 1
• Section Section 5.4 problems 4, 7, 11, 12
After you do the problems, you may check your work against the solutions.
• Problem set 6:
• Section 7.1 problem 2
• Section 7.2 problems 1, 3, 12bc, 14
• Section 7.3 problems 1, 3, 7, 9
• Section 7.6 problems 4b, 8 [try x=r cos(theta), y=r/2 sin(theta)]
After you do the problems, you may check your work against the solutions. [Note: There is a typo in the solution to Section 7.6 problem 8. In the last line, r^2 should be 16-r^2. The final answer of 64 pi is still correct.
• Problem set 7. After you do the problems, you may check your work against the solutions
• Problem set 8:
• Section 8.3 problems 1b, 2e, 3ab, 5, 6. In problem 6, find ALL possible potentials.
After you do the problems, you may check your work against the solutions
• Problem set 9:
• Section 8.3 problems 8, 10ab, 14, 16
After you do the problems, you may check your work against the solutions (corrected).
• Problem set 10. Section 8.4, problems:
• 2, 6a - that is, find the surface area integral f dA of the function f(x,y,z)=x^2
• 7, 15bd, 16ab, 17
• 19 - that is, find the surface integral X dot n dA, where
• X = (0,0,1)
• X = (x/z, y/z, -1)
After you do the problems, you may check your work against the solutions.
• Problem set 11. After you do the problems, you may check your work against the solutions.
• Problem set 12. After you do the problems, you may check your work against the solutions.