MATH 61
    Spring 2003 (second half)

    Prof. Ward
    Olin 1281
    x76019
    ward@math.hmc.edu

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Homework Assignments

Here is some advice on how to set out your homework.
Homework is due at the start of class on Mondays and Fridays.
It is worth 20% of your grade.

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


HW #1       Due Fri Mar 14

READ     Sections 4.1, 4.2

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

Mon Mar 24: Welcome back from break. No homework due.
HW #2       Due Fri Mar 28 by 3pm in the envelope outside my office, Olin 1281. (Special time and place because of Cesar Chavez holiday: no class on Friday Mar 28.)

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 Mon Mar 31, 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 Fri Apr 4, 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.

HW #5       Due Mon Apr 7, 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.

Start reviewing for the midterm, which will be handed out on Friday 11 April and due on Mon 14 April. The midterm is on sections 4.1, 4.2, 4.3, 4.4, 5.5, 6.1, 6.2, 6.3.
HW #6       Due Fri Apr 11, 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)

Mon April 14: No homework due, because of midterm.
HW #7       Due Fri Apr 18, 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 Mon Apr 21, in class.

READ     Sections 7.2, 7.3

DO         Section 7.2 (Surface Integrals), p. 448:    9, 11, 13, 15.
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.

DO         Section 7.3 (Stokes' Theorem), p. 464:    1, 2, 5, 10.

HW #9       Due Fri Apr 25, in class.

READ     Sections 7.3, 7.4

DO         Section 7.3 (Gauss' Divergence Theorem), p. 464:    9, 11, 12, 14.

DO         Section 7.5 (Miscellaneous Exercises: average value of a function, mass of a surface), p. 484:    7(b), 8.

HW #10       Due Mon Apr 28, in class.

READ     Section 5.6

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

DO         Section 6.4 (Average value, centre of mass, moment of inertia), p. 410:    1(b), (c), 2, 3.

DO         Section 7.5 (Centre of mass, moment of inertia), p. 484:    9, 11.

HW #11       Due Fri May 2, in class.

Last one!

READ     Section 3.2

DO         Section 3.2 (Arclength and Differential Geometry), p. 214:    3, 8, 12, 13, 17, 27.

Hint for 17(a): Think of the curve y = f(x) as being in R3, not just in R2.
Your parametrization of this curve should look like x(t) = ( ... , ... , 0).



Last modified April 28, 2003, by Lesley Ward. ward@math.hmc.edu

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