Math 20E: Vector Calculus, Spring 2008

under construction!

Office hours: MW:5-6, F 1-2

Office: APM 5256, tel. (858) 534-2734

Teaching assistants: Daniel Budreau (email: Chris Tiee (email:

Computation of grade: The grade is computed from your scores in the final (50%), 2 midterms (20% each), and homework (10%). Passing grade for final required for passing the course!

Dates of exams:

Midterms: April 18 and May 19


  • J.E. Marsden & A.J. Tromba: Vector Calculus, 5th edition

    Tentative Syllabus (may change, i.e. we may go a bit faster or slower than indicated):

       Week 1: 1.1-5, 2.1(2): vectors, inner product, matrices, cross product, n-dimensional Euclidean space, geometry of real valued functions.
       Week 2: 2.3-6, 3.1-3.2 : differentiation, curves, gradients,
       Week 3: 4.2-4.4: arc length, vector fields, divergence and curl,
       Week 4: 5.1-5, 6.1(6.2): Double and triple integrals, change of order of integration, maps from R^2 to R^3.
       Week 5: 6.2, 7.1-3: change of variables theorem, path and line integrals, parametrized surfaces
       Week 6:
       Week 7:
       Week 8:
       Week 9:
       Week 10:

    Additional information: You can find additional information on the following website additional info. In particular, there are practice exams and their solutions, as well as lecture notes (in pdf format) in the section "Schedule and summary of lectures (tentative)" (click on the section numbers). These notes are from a course by another instructor, but might still be useful.

    Homework assignments

    Homeworks need to be turned in on or before the stated date, usually a Friday. No homework needs to be turned in on Fridays when a midterm is scheduled. However, some of the homework may also be part of the material being asked for the midterm. It is very important that you do the homework problems as most of the exam problems will be variations of homework problems.

    Disclaimer: I will try to get the homework assignment on the net in time. Due to time and other limitations, this may not always be possible. The fact that there is no assignment posted for a particular date does therefore NOT necessarily mean that no homework is due.

    for 4/4: Sec. 1.1: 16, Sec. 1.2: 8, 14, 22, Sec. 1.3: 6, 7, 12, 16a, Sec. 1.5: 4, 18

    for 4/11: Sec. 2.1: 6, 11 (level sets only), 21, 28, Sec. 2.3: 6a, 8cd, 12c, 18, 20, Sec. 2.4: 8, 18, Sec. 2.5: 4, 5c, 15, 8, 12,

    for 4/18: need not be turned in, but relevant for midterm: Sec. 2.6: 3c, 4a, 6a, 9, 12, 24b, Section 3.2: 2, 6. For further info about the midterm, see below.

    for 4/25: Sec. 4.2::2,10,12, Sec. 4.3: 3,4, 10, 14, 20, Sec. 4.4: 4,5,8,18,20,26,

    for 5/2: Sec. 5.1: 1a, Sec. 5.2: 2d,4, Sec. 5.3: 2f,6, Sec. 5.4: 2b,8, Sec. 5.5: 4,11, Sec. 6.1:3,4,10,

    for 5/9: Sec. 1.4: 4ab, Sec.6.2: 1,4a,8,9,19,25,29, Sec. 7.1:2a,4a Sec. 7.2: 1c, 2a, 3, 12, 15, 18

    for 5/16: Sec. 7.3:2,5,12,14, Sec. 7.4:1,4,6,11, Sec. 7.5:2,4,8,10,6,15,

    for 5/23: Sec. 7.6:2,3,5,7,10,18, no more homework this week, but start looking at the new one.

    for 5/30: Sec. 8.1:1,3d,4,9,12,13,14,20, Sec.8.2: 3,6,10,23,

    for 6/6: Sec. 8.3:4,7,10,12,13ac,20,24, Sec. 8.4:2,3,5a,8, NEED NOT BE TURNED IN.

    Information for final: The final will be cumulative, but will mostly deal with integrals over curves, surfaces and three-dimensional regions. You will get three pages of formulas. The first two are the ones you have already seen at the second midterm. The third one is as follows:

    Math 20E: Formulas 3

    Practice final

    Other practice exams

    Information for midterm The second midterm will be on Monday, May 19 in class. I will have an extra office hour Monday, 1-2. The material will go until the last homework assignment, i.e. until Section 7.5. You will get a sheet with formulas (see below). No other cheat sheet, books or calculators. Here are the formulas you will be given for your exam (you will not need to worry about the formulas for the flux).

    Math 20E: Formulas 1

    Math 20E: Formulas 2

    You can find practice exams on the webpage listed below. Look at the samples for second midterms. You need not worry about problems concerning the flux. On the other hand, there may also be problems about path and line integrals in the first midterms listed there. Possible problems may be

    Path and/or line integrals via parametrization, line integrals over gradient fields, how to detect gradient fields

    Double and triple integrals, change of variable formula

    parametrizations of curves and surfaces

    areas of surfaces, integrals of functions over surfaces

    Link to practice midterms

    The first midterm will be on Friday, April 18 in class. Unfortunately, I will be out of town on Friday, so no office hour on Friday. The material will go over the first three homework assignments, so basically chapters 1, 2 and 3.2. The problems will be similar to homework problems or to problems done in the lecture. You will be given a formula sheet, which will contain all the formulas on the following sheet which we have already used (you need not worry about formulas we have not covered yet, such as arc length, flow lines. divergence etc).

    Math 20E: Formulas

    There are practice midterms and solutions at the following webpage. As the midterms there were given later in the course, there are also problems involving vector fields, curl etc. You need not worry about these problems. Just look at the first midterms.

    Other midterms


    Office hours for finals week:

    Chris Tiee (APM 6444) Monday 2-4, (3-5(?)), Dan Budreau: (APM 6333), Tuesday 2-4, Instructor: Wednesday 12-2pm