HMWK #4 (Due Thursday, Oct 15)
Section 9.6 (Take advantage of the command Plot3D in Mathematica to visualize the graph of a function of two variables. Click here)
Study this section carefully, reading it a few times. practice exercises. Solutions to the odd numbered ones are at the end of the book.
Submit 28, 30, 32
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Section 9.7
Study. Work on exercises. Submit problems 10, 16, 36
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Review Chapter 9. There is a good review of chapter 9 on page 688. Don't miss it.
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Section 10.1
Read it carefully. Take advantage of Mathematica's ParametricPlot3D to reproduce the figures in the text.
Work on many exercises. Don't miss 19-24, 29-35, 45, 46 (Learn about the command Tube).
Submit: 4, 6, 8, 10, 12, 14, 16, 26, 28, 36, 38, 44
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Section 10.2
Start reading this section. Work on exercises 21- 29
Submit 1, 2, 4, 6, 10, 11, 12, 14 (this one requires something on page 704), 16, 20, 22
HMWK #5 (Due Thursday, Oct 21)
Study Chapter 9 and what we have seen of chapter 10, we might have a surprise quiz coming up.
Section 10.2:
Work on ALL exercises.
Submit 17, 18, 19, 21, 24, 25, 26, 28 (use ParametricPlot3D), 30 (use ParametricPlot3D), 31, 32 (you may use ParametricPlot3D to visualize this, it's fun too!) , 33, 34, 40, 49, 50, 52.
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Section 10.3:
Study carefully only pages 707 - 709 (Stop right where the subsection "curvature" begins). Do the examples.
Submit 1, 2, 4, 6, 8, 10 For exercie10, use ParametricPlot3D[{Sin[t], Sin[2 t], Sin[3 t]}, {t, ......, .......}]
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Section 10.4:
Study carefully only pages 716 - 719. Do the examples. Work on exercises 1 - 32.
Submit: 4, 8, 10, 14, 17, 18, 22.
Not to submit, bring what you find to class: Explore the curve x(t) = t/(1 + t^2); y(t) = 2t/(1 + t^2); (You might want to use ParametricPlot[ ] with the option PlotRange -> All, which you have used before.)
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Take advantage of Mathematica, installed in our computers.
Here is code for problem 36, Section 9.7, about the distance between two cities.
HMWK #6 (Due Thursday, Nov 11)
11.5: Submit: 2, 4, 10, 14, 16, , 22, 24, 26, 30 (Not to submit: 47 - 52)
11.6: 40, 42, 50, 52
11.7: 3, 4, 6, 8, 12, 24, 36, 38 (Not to submit: many others, but don't miss 51)
11.8: (Not to submit 1-8, 45, 46) Submit: 8, 12, 14, 16, 40
Focus on Problem Solving (page 827): Submit 1, 2 , 3
Extra Credit (alone or in group 2, 3 or 4 people) (same page): 6
HMWK #7 (Due Thursday, Nov 18)
Read 12.1, 12.2 and 12.3 (This is your first reading of this material, we will review in class.)
12.2: Work on all exercises. Submit: 4, 8, 14, 16, 20, 24, 26, 30. Is 32 difficult?
12.3: Submit 2,4 and 8.
11.7: Not to submit, but IMPORTANT exercise to work on: 51
HMWK #8 (Due Thursday, Dec 2)
Read again. Study carefully every paragraph!
Use Integrate[ ] to help you out finding antiderivatives. Write complete answers, guide the reader!
12.2 (Do 33, 34 and 37, 38, 39) Submit: 34, 38
12.3 Submit: 2, 4, 14, 16, 26, 32, 33, 34, 40, 55, 56, 58
12.4 Submit: 8, 10, 18
Skip 12.5
12.6
Submit: 1, 2, 8 (To visualize: ParametricPlot3D[{u Cos[v], u Sin[v], v}, {u, 0, 1}, {v, 0, Pi}]),
15, 16 (To visualize: Plot3D[ x y + x^2 + y^2, {x, 0, 2}, {y, 0, 2}])
22, 26
Extra credit: 5-6 of page 903 (bring your attempt, we can talk about it outside class)
Manipulate[
ContourPlot3D[x^2 + y^2 - z^2, {x, -3, 3}, {y, -3, 3}, {z, -3, 3},
Contours -> {c, c + 4}, Boxed -> False, Axes -> False], {c, -5, 6}]
r[u_, v_] := {Cos[u] Sin[v], Sin[u] Sin[v], Cos[v]};
norm[x_] := Sqrt[x.x];
Integrate[norm[Cross[D[r[u, v], u], D[r[u, v], v]]], {u, 0, 2 Pi}, {v, 0, Pi}]
r[t_] := { Cos[t], Sin[t], .2 t};Manipulate[Show[ParametricPlot3D[r[t], {t, 0, 2 Pi}, PlotStyle -> {Red},
PlotRange -> {{-2, 2}, {-2, 2}, {0, 1}}],
Graphics3D[{Thick, Black, Arrow[{r[s], r[s] + r'[s]}]}]], {s, 0, 2 Pi}]