Back to MATH 3010 Home Page
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 (2sided).
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 2forms or their surface integrals.
You are NOT responsible for flux integrals in the plane, or the Divergence
theorem in the plane.
Tests
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 36.

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 16r^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.