Math 21 a Math21a, Fall 2000
Course Head: Prof. Clifford H. Taubes
Dini surface: surface of constant negative curvature

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Answers to non-text book Physics section suggested problems

Section 1.3-1.4:
1) If the vertical vector, upward pointing unit vector is denoted by e and the unit vector in the direction of the horizontal projection of F is denoted by eŽ, then F = 12 2-1/2 (e + eŽ).
2) Let e denote the unit vector in the direction of the vertical projection of F and let eŽ denote the unit vector in that of the horizontal projection. Then, F = 5 (e + 31/2 eŽ).
Sections 1.6-1.7:
1) The work is 3 as measured in the implied units.
Sections 1.7-1.8:
1) The angular momentum vector is r x r = (-31/2/2, 0, 1) which is constant. This means implies that the motion is in the plane where -31/2 x/2 + z = 0.
Section 5.1:
1) The work is 5/3 in the implied units.
Section 2.7:
1) The minima is at p = 0 and = , the value there is ­1.
Section 3.4:
1) The total mass is 1000/3. The center of mass is (0, 0, 15/4).
Section 5.5
1) The total charge is 4.
2) The total charge is 4/3.

Last update, 9/20/2000, math21a@fas.harvard.edu