Week 9: Wed 3/9

• IMPS 5: 1, 9, 10, 11, 12, 6

• On all questions you may use any method you like provided it is valid.

Week 8: due Wed 3/1

• DGC III : 17 ,
• Read IMPS Chapter 4
• IMPS 4: 6, 8, 9, 10

• DGC III: 17 Hint: consider the vector field curl E + dB/dt. Show that this must be expressible as curl A, for some vector field A. Then show that A must be conservative.

Week 7: due Wed 2/22

• DGC II : 11(b), 12, 13(b),
• Read IMPS Chapter 3
• IMPS 3: 7, 8, 10

• DGC 11.11-13: You can also use a potential function method if you prefer.

Week 6: due Wed 2/15

• Read Chapters 1 and 2 of DGC
• DGC II : 5, 8, 10 (a),(b), 23 (read comments below)
• Read IMPS Chapter 2
• IMPS 2: 21, 23, 24, 25(b)

• DGC sometimes needs to use cumbersome notation and formulas, because they do everything in terms of graphs rather than parametric surfaces X(u,v). Note that equations II-12 and II-13 are the graph forms of the versions given in lecture.
• Gauss's Law (II-1) is a physical interpretation of what we were doing at the end of Wed. (2/8). Do you see how?
• DGC II.5: Using the parametric forms (rather than II-13) would be preferable here.
• DGC II.23: For each part, compute both integrals by deciding which integral is easier and just computing that.

Week 5: due Wed 2/8

• Do the problems in the following pdf file: Homework 5
• Before Wednesday, attempt the practice midterm (appearing soon in the exams section).

• Don't hand in your practice midterm solutions.

Week 4: due Wed 2/1

• DGC III (p105-109): 5, 19
• DGC IV (p144): 8
• IMPS 2: Exercises 2, 4, 5, 6

• III-5: "nabla X F" is alternative notation for curl(F).
• IV-8: The current density of a fluid is given by J= (rho) v where v is the velocity. You might find it helpful to note curl(uF) = (grad u) x F + u curl F
• 2.6: The unit normal for the flux here will be constant and perpendicular to the plane containing S. The flux integral will now be a two dimensional integral rather than a line integral.

Week 3: due Wed 1/25

• DGC III (p104): 3 (a)-(d), 4 (a)-(b)
• DGC IV (p144): 1 (b) using function (iv) and curve (iii), 4 (b)(i)
• IMPS 1: Exercises 12, 16, 17

• IV-1: The question is asking you to compute the integral directly from definition. (i.e. you're not allowed to just quote a theorem)
• IV-4: The non-bold r stands for the vector norm of the bold r.
• 1.12: Recall the electric field is the force the charged object exerts on a charge value +1 at each point. The axis for the disk in this case is the z-axis. (A disk is rotationally symmetric about its axis).
• 1.16: Only compute one way, but you can choose which.

Week 2: due Wed 1/18

• IMPS 1: Read all of Chapter 1, Exercises 4, 5, 8, 9, 10, 11
• IMPS 6: Exercises 14, 17

• 1.4: just find the center of mass.
• 1.8: feel free to ignore the hint and use a change of variables if you prefer.
• 1.11: this should read, above the xy-plane.

Week 1: due Wed 1/11

• IMPS 6: Exercises 2, 3, 4, 6, 7, 10, 11, 15, 16
• IMPS 1: Exercises 2, 6 (pages 28, 38)

• 6.3: part 1 should be find G o F not F o G.
• 6.4: part 2 its ok to give your answer as a combination of x,y and r,s,t.
• 6.6: should read G(r,"theta") not G(r"theta").
• 6.16: the 3rd component of F should be Hv; here R and H are constants.
• 1.6: use standard x,y,z coordinates for this problem.