MATH 61
    (Both sessions in BK 126)
    Summer 2004

    Prof. Gu
    Olin 1279
    x18929
    gu@math.hmc.edu

Office Hours

Monday to Friday 5:00-6:00 pm and by appointment.

Tutors and Graders

Berg, Brenion, Hudson, Johnson

Quizzes and Exam

There are two quizzes and one final exam which have been scheduled on Tuesday May 25, Tuesday June 1 and Friday June 4 respectively.
Two quizzes which will account for 20% of the course grade. The final exam accounts for 40% of the course grade.

Homework Assignments

Here is some advice on how to set out your homework.
Homework is due at the start of class on Mondays, Tuesdays, Wednesdays, Thursdays and Fridays.
It is worth 40% of your grade.

The problems below are from the textbook Vector Calculus, 2nd Edition,
by Susan Colley.

Solution keys


HW #1       Due Tuesday, May 18

READ     Sections 4.1, 4.2

DO         Section 4.1 (Taylor's Theorem), p. 252:    5, 11, 14, 21(a).

HW #2       Due Wednesday, May 19

READ     Sections 4.3, 4.4

DO         Section 4.2 (Extrema of Functions), p. 266:    7, 10, 20, 22(a), 29, 32.
(Don't use Lagrange multipliers for these.)
For 32, parametrize the boundary by cos(t), sin(t), then optimize in t.

HW #3       Due Thursday, May 20 in class.

READ     Sections 4.4 pp.282-285 on Least Squares Approximation, 5.5

DO         Section 4.3 (Lagrange Multipliers), p. 279:    1, 2, 8, 19, 21, 23, 29.

DO         Section 4.4 (Applications of Extrema - Least Squares Approximation),
p. 292:    6(a), (c) (only the part referring to (a)).
For (a), it helps to tabulate the values of xi, yi, xi2, and xiyi first.

HW #4       Due Friday, May 21 in class.

READ     Section 5.5

DO         Section 5.5 (Change of Variables), p. 354:    1, 4, 6, 8, 10, 11, 16, 19.
Hint for 19: Sketch the cardioid and circle first - a computer algebra system such as Maple will help.

Start reviewing for the quiz I, which will be take place Tuesday, May 27, in class. The quiz I is on sections 4.1, 4.2, 4.3, 4.4, 5.5, 6.1, 6.2.
HW #5       Due Mon, May 24, in class.

READ     Sections 5.5, 6.2

DO         Section 5.5 (Change of Variables), p. 354:    5, 7, 24, 29. For problems 24 and 29, first use the Jacobian to DERIVE the formula for the volume element in spherical (24) and cylindrical (29) coordinates.

DO         Section 6.2 (Green's Theorem),
p. 398:    4, 13, 15, 17, 20.

Optional bonus problem: Sec 5.5 Q30. Start by using an apple corer
to cut a potato along the three orthogonal directions.
Look for a symmetry in the first octant.

Tuesday, May 25: No homework due, because of quiz I.
HW #6       Due Wed May 26, in class.

READ     Section 6.3

DO         Section 6.3 (Conservative Vector Fields), p. 409:    1, 8, 12, 13, 15, 19.

DO         Section 6.4 (Miscellaneous Exercises for Chapter 6 - cons. v. f.'s, and work), p. 410:    20, 22.
Hint for Q 20: Careful, F is not conservative!
Hint for Q 22: d/dt{x(t) DOT y(t)} = x'(t)y(t) + x(t)y'(t)

HW #7       Due Thursday, May 27, in class.

READ     Sections 7.1, 7.2

DO         Section 7.1 (Parametrized Surfaces), p. 427:    1, 7, 11, 19, 22.

DO         Section 7.2 (Surface Integrals), p. 448:    1, 6, 7, 17, 20.

HW #8       Due Friday, May 28, in class.

READ     Sections 7.2, 7.3

DO         Section 7.2 (Surface Integrals), p. 448:    9, 11, 13, 15, 21.
Note: A 'closed' cylinder is capped off by top and bottom discs.
You should parametrize each of the surfaces involved.
Try polar coords for the flat top and bottom.

Start reviewing for the quiz II, which will be take place Tuesday, June 1, in class. The quiz II is on sections taught after quiz I.
HW #9       Due Monday May 31, in class.

READ     Sections 7.3, 7.4

DO         Section 7.3 (Stokes' Theorem), p. 464:    1, 2, 5, 10.
Section 7.3 (Gauss' Divergence Theorem), p. 464:    9, 11, 12, 14.

DO        

Tuesday, June 1: No homework due, because of quiz II.
HW #10       Due Wednesday June 2, in class:
a summary of the materials covered so far,
a list of questions that you have for the course so far,
and one problem that you think it should be on the final exam.
HW #11       Due Thursday June 3, in class.

READ     Section 5.6

DO         Section 5.6 (Average value, moment of inertia), p. 369:    4, 11, 21.

DO         Section 6.4 (Average value, centre of mass, moment of inertia), p. 410:    1(b), (c).

DO         Section 7.5 (Centre of mass, moment of inertia), p. 484:    7(b), 8, 9.



Last modified May 16, 2003, by Weiqing Gu. gu@math.hmc.edu

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