Differential Geometry (and Relativity) - Summer 2000
Homework Assignments (with tentative due dates)

Chapter 1
Section Problems Due Date Points
1.1 2, 5, A, B Tuesday 6/6 15
1.1 6a, 9, 15a Wednesday 6/7 10
1.2 1c, 1d, 2, 4 Thursday 6/8 13
1.3 2c, 3, 7 Friday 6/9 13
1.4 1, 3d, 4, 12, C Monday 6/12 16
1.5 1, 3, 6 Tuesday 6/13 12
1.6 2a, 2b, 5a, 9b Wednesday 6/14 12
1.7 4b, 10b Thursday 6/15 6
1.7 1, 14c Friday 6/16 6
1.8 1a, 3, 5a Tuesday 6/20 9
1.9 2a, 6, D Wednesday 6/21 12
- - Subtotal 124

Chapter 2
Section Problems Due Date Points
2.1 1 Thursday 6/22 3
2.2 3, 6, 8 Friday 6/23 9
2.4 1, 4 Monday 6/26 6
2.5 2 Monday 6/26 3
2.6 3, 4, 5 Tuesday 6/27 9
2.7 3abc, 6, 7, 11 Wednesday 6/28 14
2.8 1, 2, 3, 8 Thursday 6/29 12
2.10 1 Thursday 6/29 2
- - Subtotal 58

Chapter 3
Section Problems Due Date Points
3.1 1 Monday 7/3 3
3.2 2 Monday 7/3 5
3.7 1, 3 Wednesday 7/5 6
3.8 4, 9 Thursday 7/6 12
3.9 3 Monday 7/10 3
3.10 2, E Tuesday 7/11 3
Black Holes E Tuesday 7/11 4
- - Subtotal 36
- - Grand Total 218

Problem A. Prove the curvature of a straight line is 0 (using the definition of k(s)).

Problem B. Find the equation of the plane through 3 noncolinear points (x1, y1, z1), (x2, y2, z2), and (x3, y3, z3). Don't just plug into a formula, but give a detailed geometric argument and derive the equation.

Problem C. Verify that

Problem C

Problem D. Verify equation (69a) on page 88 of the text.

Problem E. Calculate the Schwarzschild Solution in Eddington-Finkelstein coordinates.

Reading Assignments

The following reading assignments are from the supplemental Einstein book:

Sections Date to Discuss
Preface, 1.1 - 1.6 Thursday 6/15
1.7 - 1.12 Wednesday 6/21
Appendix I Monday 6/26
1.13 - 1.17 Wednesday 6/28
2.18 - 2.22, Appendix III Monday 7/3
2.23 - 2.29, Appendix IV Thursday 7/6
3.30 - 3.32, Appendix V Friday 7/7

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