Math 4530-1
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Professor Korevaar
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Homework is due at the start of class, on Fridays, unless otherwise noted. Homework solutions will be posted by the following Monday, I hope.
Homework assignments (most recent first):
Circled or underlined problems are to be handed in, others are only recommended.
Due Monday, April 18:
Class exercises 1, 2, 3 (April 6 class notes), 4 (April 11).
4.8.10, 4.8.11, 4.8.15, 4.8.21, 4.8.25.
Due Friday, April 8:
4.3.5, 4.3.6, 4.4.3.
Due Friday, April 1:
Class exercise from Friday March 25: show that for a graph z=f(x,y) the mean curvature is (1/2)*div((1/sqrt(1+|grad(f)|^2))*grad(f)).
4.2.3, 4.2.8. For 4.2.8, you might want to use the files shape.mws, shape.pdf
Solutions:
sols7a.pdf
4.2.8.pdf 4.2.8.mws
Grading: 17 points, distributed as follows:
Class I = 2 points, 4.2.3 = 3 points, 4.2.8 a-f = 2 points each.
Due Friday, March 25:
Chapter 3 problems:
3.3.13, 3.4.5, 3.4.6,
Class exercises:
Ia) Verify that the formula for inverse stereographic projection is given by X(u,v) = (1/(1+u^2+v^2))*<2u, 2v, u^2+v^2-1>.
Ib) Show that X(u,v) above is conformal (See March 9 notes)
II) Use the general formula in March 21 notes to rederive the Christoffel formulas for the Xuu expression.
Solutions:
sols6.pdf
Grading: 16 points, distributed as follows:
3.3.13 = 2 points, 3.4.5 = 3 points, 3.4.6 = 2 points.
Ia, Ib, II = 3 points each.
Due Monday, February 28: (Exam Friday!)
Chapter 2 problems:
2.15
3.4, 3.9, 3.10, 3.11
4.4, 4.6, 4.7
Chapter 3 problems:
3.1.5, 3.1.6, 3.1.10, 3.1.11
3.2.4, 3.2.6, 3.2.26, 3.2.13, 3.2.14, 3.2.15
3.3.6, 3.3.8.
Solutions:
sols5.pdf
Grading: 37 points, distributed as follows:
Chapter 2: 2.15 = 2 points, 3.4a = 1 point, 3.4b = 2 points; 3.9, 3.10, 3.11, 4.6, 4.7 = 2 points each.
Chapter 3: 1.5, 1.6 = 2 points each; 1.10, 1.11 = 1 point each; 2.4 = 3 points, 2.26ab = 1 point each; 2.26c = 2 points; 2.13, 2.14 = 2 points each; 2.15 = 3 points; 3.8 = 2 points.
Due Friday, February 11:
I and II from page 7 of feb4.pdf notes
Chapter 2 problems:
1.12, 1.13, 1.15, 1.20, 1.21, 1.22;
2.5, 2.6, 2.7, 2.8, 2.9;
5.6, 5.7, 5.8 (Maple)
Solutions:
sols4a.pdf hand-written portion
sols4b.pdf Maple portion
sols4.mws Maple code
Grading: 29 points, distributed as follows:
I, II = 3 points each;
1.12, 1.20, 1.21 = 2 points, 1.22 = 4 points;
2.7, 2.9 = 2 points each;
5.6 = 3 points, 5.7 = 2 points, 5.8 = 4 points.
Due Friday, February 4: Mostly Maple problems:
hwset3.pdf for looking
hwset3.mws for opening from Maple. You probably also want the procedures on our lecture page.
Solutions: sols3.pdf sols3.mws.
Grading: 23 points, distributed as follows:
1: procedures and computations = 5 points, picture = 2 points; 2 = 2 points each for two pictures; 3 = 2 points for picture, 3 points to show graph is catenary; 4 = 3 points; 5 = 4 points.
Due Friday, January 28: Chapter 1 problems:
3.19, 3.22, 3.27, 3.28;
4.4, 4.6, 4.7;
5.3, 5.4, 5.6, 5.7.
Class exercise I from jan24.pdf, the "uniqueness up to rigid motion" part of curves with given curvature and torsion functions.
Solutions: sols2.pdf
Grading: 15 points, distributed as follows:
3.19, 3.22, 3.28, 4.6, 4.7 = 3 points each.
Due Friday, January 21:
See pages 5-6 of Jan 12 notes: (Do all of these problems) jan12.pdf
On Jan 14 I added three additional problems 1.1.24, 1.1.25, 1.3.5
Solutions: sols1.pdf
Grading: 25 points, distributed as follows:
Part I: 2 points per part, total = 10 points.
Chapter 1: 1.13 = 2 points, 1.22 = 3 points, 1.25, 2.2, 2.7b, 2.8, 3.5 = 2 points each.