Multivariable Calculus Fall 2012
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Homework
Multivariable Calculus – Fall 2012
FINAL EXAM on Thursday, December 20, 2012 from 1:45-3:45 in Powdermaker Hall Room 104.
Homework 23
Due Thursday, December 13, 2012
  • Complete Webwork assignment 10.
  • Read Section 13.3. Then complete the following homework problems.
    • Section 13.3:  1-16 odd, 19-22
  • Class will be held at the normal time and place on Thursday, December 13. After the discussion of this homework set, we will have a review / Q&A day for the final.
  • We will hold a review session on Monday 12/17 from 11:30-1pm to make up for the second day of classes we missed.
EXAM 3 on Tuesday, December 11, 2012
  • The third exam of the semester will take place during the first half of class on Tuesday, December 11, 2012. (After a short break, we will discuss one final topic in Chapter 13 that will be on the final exam.)
  • The exam covers Sections 12.1-12.7 (not including moments or center of mass), 13.1, and 13.2 (pp 740-742).
  • I highly suggest that you review the recent Webwork assignments. You can return to an assignment and you are now able to see the correct answers. I especially recommend the Chapter Review on pages 724-726.
  • There will be questions that ask you to understand concepts from the course, possibly including, and not limited to:
    • The assumptions involved in Fubini's theorem, and the consequences of Fubini's theorem.
    • Definition of double integral on a rectangular region (pp 665-667)
    • Definition of vector field, gradient field
    • Computation of average value. (For example, Exercises 12.1.37 and 12.5.45)
  • The exam will be 60 minutes long. Graphing calculators (up through TI-85, not including TI-89) are useless for this exam but they are allowed; I will come around and delete their memory before the exam.
  • Here is a practice third exam.
Homework 22
Due Thursday, December 6, 2012
  • Read Section 13.1 and 13.2 (pp 740-742). Then complete the following homework problems.
    • Section 13.1:  11-18, 21-26, 29, 31
    • Section 13.2:  15-20, 23a, 24a, 26a, 33-36 Challenge Question: 39
Homework 21
Due Tuesday, December 4, 2012
  • Complete Webwork assignment 9.
  • Read Sections 12.6 and 12.7. Then complete the following homework problems.
    • Section 12.6:  13, 15, 16, 17-22, 26-28
    • Section 12.7:  15-20, 21-26, 31, 32, 35, 36Challenge Questions: 37, 40
Homework 20
Due Thursday, November 29, 2012
  • Read Sections 12.5-12.7. Then complete the following homework problems.
    • Complete the remaining groupwork questions from the class period.
    • Section 12.5:  7-16, 25-32, 45 Challenge Question: 47
Homework 19
Due Tuesday, November 20, 2012
  • Complete Webwork assignment 8.
  • Read Section 12.3 and pages 690-691 about Density and Mass. Then complete the following homework problems.
    • Section 12.3:  7-19 odd, 23-26, 29 Challenge Question: 20
    • Section 12.4:  In problems 7-10, only find the mass of the lamina.
Homework 18
Due Thursday, November 15, 2012
  • Read Section 12.2 and pages 690-691 about Density and Mass. Then complete the following homework problems.
    • Section 12.2:  7-19 odd, 25, 31-41 odd, 45, Challenge Questions: 23 48, 49
    • Section 12.4:  1. In problems 3-6, only find the mass of the lamina.
Homework 17
Due Tuesday, November 13, 2012
  • Read Section 12.1 from the book (ignoring the "Midpoint rule") and complete the following homework problems.
    • Section 12.1:  1, 3, 9, 10, 11-33 odd, 37, Challenge Question: 40
  • Queens College has decided upon the plan to make up the days of class that we missed.
    • Class will be held on Thursday, December 13 and will be a review / Q&A day for the final.
    • We'll have a review session sometime between Thursday 12/13 and Monday 12/17 to make up for the second day we missed.
    • Exam 3 will be moved to Tuesday 12/11.
    • The final exam will occur as scheduled on Thursday, 12/20 from 1:45-3:45.
EXAM 2 on Thursday, November 1, 2012 Now Scheduled for Thursday, November 8, 2012
  • The second exam of the semester will take place during the first half of class on Thursday, November 1, 2012 Tuesday, November 6, 2012. (After a short break, the second half of the class period will be new material in Chapter 12.)
  • The exam covers Sections 11.1-11.8 (except multiple constraints, pp.658–659).
  • I highly suggest that you review the three recent Webwork assignments. You can return to an assignment and you are now able to see the correct answers. I especially recommend the Chapter Review on pages 661–664.
  • There will be questions that ask you to understand concepts from the course, possibly including, and not limited to:
    • Show non-existence of limits by checking paths.
    • Definition of continuity (p. 607) and directional derivative (p. 636) for functions of two or more variables
    • If f is differentiable at P0, then ∇f(P0) points in the direction in which f increases the most rapidly (p. 640)
    • Using Extreme value theorem to prove existence of absolute extrema. (p. 651)
    • Geometric explanation of Lagrange multipliers (p. 654 and Exercise 11.8.19)
  • The exam will be 50 minutes long. Graphing calculators (up through TI-85, not including TI-89) are allowed, but I come around and delete their memory before the exam.
  • I have created a practice second exam. I suggest saving this for practice once you are completely prepared for the exam. As before, no guarantees of similarity are assured. All material in Chapter 11 is fair game for the exam; study everything. Click here for the "practice exam".
Homework 16
Due Thursday, November 1, 2012
Homework 15
Due Tuesday, October 30, 2012
  • Read Section 11.8 from the book (excluding two constraint Lagrange multipliers) and complete the following homework problems.
    • Section 11.8:  1, 3, 5, 7, 9, 15, 17, 19, 27, 33, 39
  • Reminder: Exam 2 is on Thursday, November 1, 2012 and will cover Sections 11.1–11.8. Class on Tuesday will consist of homework discussion from 11.8 and then a Question and Answer session covering all topics since the first exam.
Homework 14
Due Thursday, October 25, 2012
  • Read Section 11.7 from the book and complete the following homework problems.
    • Section 11.7:  2, 3, 5, 7, 9, 10, 11, 13, 23, 25, 27, 28, 29, 33, 35, 37, 42, 45, 46 Challenge Question: 48
  • Reminder: Exam 2 is on Thursday, November 1, 2012 and will cover Sections 11.1–11.8. Class on Tuesday will consist of homework discussion from 11.8 and then a Question and Answer session covering all topics since the first exam.
Homework 13
Due Tuesday, October 23, 2012
  • Complete Webwork assignment 6.
  • Read Section 11.6 from the book and complete the following homework problems.
    • Section 11.6:  3, 5, 7, 10, 11, 12, 15, 17, 19, 22, 23, 27, 28, 30, 31, 33, 37, 44 Challenge Questions: 41, 42, 43, 47
Homework 12
Due Thursday, October 18, 2012
  • Read Section 11.5 from the book and complete the following homework problems.
    • Section 11.5:  5, 7, 8, 11, 17-28, 31, 33, 37 Challenge Questions: 41, 45
Homework 11
Due Tuesday, October 16, 2012
  • Complete Webwork assignment 5.
  • Read Sections 11.3 and 11.4 from the book and complete the following homework problems.
    • Section 11.3:  37, 39, 43, 45, 47, 54, 55, 58, 66, 67, 71 Challenge Questions: 62, 70
    • Section 11.4:  1-6, 13, 15, 17, 19, 23, 28, 32
Homework 10
Due Thursday, October 11, 2012
  • Read Sections 11.2 and 11.3 from the book and complete the following homework problems.
    • Section 11.2:  2, 5, 7, 11, 19, 20, 21, 23, 25, 27 Challenge Questions: 15, 31, 32
    • Section 11.3:  2, 3, 4, 6, 7-32
  • The next Webwork assignment will be due on Tuesday, October 16.
Homework 9
Due Tuesday, October 9, 2012
  • Read Section 11.1 from the book and complete the following homework problems.
    • Section 11.1:  1, 3, 7, 9, 10, 13, 17, 20, 21, 22, 25, 27, 31, 34, 35, 41–46, 47, 51 Challenge Questions: 39, 53, 54
EXAM 1 on Thursday, October 4, 2012
  • The first exam of the semester will take place during the first half of class on Thursday, October 4, 2012. (After a short break, the second half of the class period will be new material in Chapter 11.)
  • You have asked for an example of the style of exam that I am liable to give. I have created one. I suggest saving this for practice once you are completely prepared for the exam.
    Disclaimer: By clicking on the link provided, you agree to the following terms. This exam is given for informational purposes only. No guarantees of similarity are assured. All material discussed below is fair game for the exam; study everything. If you agree to these terms, click here for the "practice exam".
  • As mentioned above, there will be a Question and Answer session during the second half of class on Tuesday, October 2, 2012 and an additional Question and Answer session from 11:30 to 1:00 on Wednesday, October 3, 2012 in Kiely Hall 508 (unless there is a conflict).
  • The exam covers all material covered this semester so far, including:
    • Chapter 9, Sections 9.1, 9.2, 9.3 (except tangents, pp 502-503), 9.4 (except arc length in polar, p 509)
    • Chapter 10, Sections 10.1-10.7, 10.8 (except curvature, normal, binormal, pp 574-578), and 10.9 (except components, pp 584-588)
  • I highly suggest that you review the four Webwork assignments. You can return to an assignment and you are now able to see the correct answers. There are also Review Sections on pages 517-518 and 589-592. Try out the concept checks.
  • There will be questions that ask you to understand concepts from the course, possibly including, and not limited to:
    • Intuitive explanation of arc length formula for parametric equations (p. 494)
    • Intuitive explanation of area formula for polar coordinates (p. 507)
    • Definition of derivative of a vector valued function and geometrical interpretation (p. 565)
    • Prove that if ||r(t)|| is constant, then r(t) and r'(t) are orthogonal (p. 568, Ex. 12)
  • You should understand how to use your graphing calculator to:
    • Graph parametric and polar equations using appropriate plotting modes.
    • Choose suitable window to enhance the graph.
    • Use fnInt from the MATH menu to approximate integrals.
  • The exam will be 50 minutes long. Graphing calculators are allowed, but I come around and delete their memory before the exam.
Homework 8
Due Tuesday, October 2, 2012
  • Complete Homework Assignment 4 on Webwork about calculus of vector functions.
  • Read Sections 10.8 (not including curvature, normal, binormal vectors pp 574-578) and 10.9 (not including components, pp 584-588) from the book and complete the following homework problems.
    • Section 10.8:  1, 3, 6, 7 Challenge Question: 10
    • Section 10.9:  1, 3, 5, 7, 9, 11, 13, 15, 18, 25, Challenge Question: 27
    • I highly suggest reviewing old homework assignments and trying out homework questions and the concept checks from the Review Sections on pages 517-518 and 589-592.
  • In Preparation for Exam 2 on Thursday, October 4, 2012, Class on Tuesday will consist of homework discussion from 10.8 and 10.9 and then a Question and Answer session covering all topics from the semester so far.
  • In order to accommodate the Jewish holiday on October 2, there will be an additional (alternative?) Question and Answer session frmo 11:30-1pm on Wednesday, October 3, 2012. We will try to meet in Kiely Hall 508, unless there is a conflict in that room.
Homework 7
Due Thursday, September 27, 2012
  • Read Section 10.7 from the book and complete the following homework problems.
    • Section 10.7:  2, 3, 4, 5, 7, 11, (17-22), 23, 24, 28, 29, 33, 35, 37, 39, 41, 43, 45, 47, 48, 49, 51, 53, 55, 56, 57, 58, 59, 61, 63, 65, 66, 73, 74, 75 Challenge Questions: 70, 71, 77
  • There is no class on Tuesday, September 25, 2012.
Homework 6
Due Thursday, September 20, 2012
  • Complete Homework Assignment 3 on Webwork about vector operations and functions of 3-D surfaces.
  • Read Sections 10.5 and 10.6 from the book and complete the following homework problems.
    • Section 10.5:  4, 5, 10, 14, 15, 17, 18, 24, 25, 27, 29, 33, 34, 38, 41, 43. Challenge Question: 54
    • Section 10.6:  5, 6, 7, 9, 11, 13, 15, 17, 19, 21, 25, 29, 30, Challenge Questions: 31, 34
  • There is no class on Tuesday, September 18, 2012.
Homework 5
Due Thursday, September 13, 2012
  • Read Sections 10.3 and 10.4 from the book and complete the following homework problems.
    • Section 10.3:  1, 3, 6, 7, 9, 10, 12, 13, 16, 17, 19, 21, 22, 23, 26, 27, 31, 33, 39, Challenge Questions: 30, 36, 43
    • Section 10.4:  3, 5, 6, 7, 8, 9, 10, 12, 14, 15, 16, 21, 23, 25, 27, 29, 33, 35, 36, 45, Challenge Questions: 38, 42
Homework 4
Due Tuesday, September 11, 2012
  • Complete the second homework assignment on Webwork about polar and parametric equations and an introduction to vectors. (Feel free to use your calculator or Wolfram Alpha).
  • Read Sections 10.1 and 10.2 from the book and complete the following homework problems.
    • Section 10.1:  4, 5, 10, 11, 13, 19, 21, 23, 25, 27, 29, 31, 33
    • Section 10.2:  2, 4, 9, 11, 13, 15, 17, 19, 21, 25, 27,
Homework 3
Due Thursday, September 6, 2012
  • Read Sections 9.3 (ignore tangents in polar coordinates, pp. 502-503) and 9.4 (ignore arc length in polar coordinates) from the book and complete the following homework problems.
    • Section 9.3:  21, 23, 24, 28, 29, 34, 37, 38, 39, 41, 46, 55, 57, 58, 61, 66
    • Section 9.4:  1, 5, 6, 9, 10, 15, 17, 19, 21, 25, 29–32
    • Also, practice your double angle identities (Sin(2x) & Cos(2x)). For example, give two expressions that are equivalent to sin2(2θ)-cos2(2θ). Give it in terms of (a) sin(4θ) and/or cos(4θ) AND (b) sin(θ) and/or cos(θ).
Homework 2
Due Tuesday, September 4, 2012
  • Log onto Webwork. Complete the first homework assignment there on parametric equations. Recall that your user name is your CAMS ID and your initial password is your CUNYFirst ID. Also, your solution to Problem 6 should be a vector solution. Write something like <x(t),y(t)>, using the angle brackets < and >.
  • Read Sections 9.2 and 9.3 (ignore tangents, pp. 502-503) from the book and complete the following homework problems.
    • Section 9.2:  2, 3, 6, 7, 11, 13, 16, 17, 22 (use your calculator), 27, 28, 29, 35 (And use your calculator to give the answer within 4 decimal places), 37, 40, 41, 44, 53, 54
    • Section 9.3:  1, 3, 5, 8, 11, 14, 17
      If you are shaky on polar coordinates, I suggest doing all of questions 1-20 (and more!)
  • Work on all problems. Bold questions should be made higher priority. Italic questions are harder than average.
Homework 1
Due Thursday, August 30, 2012
  • Email me at chanusa@qc.cuny.edu with the following four things: (1) Your name, (2) the email address where you are best contacted, (3) your graduation year, and (4) the most interesting parametric curve you could make with Wolfram Alpha or Mathematica (and a sentence about why it is interesting).
    • In class, we used the following curves. Try these or something new!
      ParametricPlot[{t + 2 Sin[2 t], t + 2 Cos[5 t]}, {t, -2 Pi, 2 Pi}]
      ParametricPlot[{1.5 Cos[t] - Cos[30 t], 1.5 Sin[t] - Sin[30 t]}, {t, -2 Pi, 2 Pi}]
      ParametricPlot[{Sin[t + Cos[100 t]], Cos[t + Sin[100 t]]}, {t, -2 Pi, 2 Pi}]
  • Thoroughly read the class web page including the syllabus and schedule. This should answer all the questions that you may have about the class. Next, take the syllabus quiz on Blackboard. Retake the quiz as necessary to earn a score of 100%.
  • Read Section 9.1 from the book and complete the following homework problems.
    • Section 9.1:  1, 4, 9, 14, 15, 18, 21, 22, 24, 29, 39
    • Practice your trig values:  sin, cos, tan, cot, sec, csc of 0, Pi/6, Pi/4, Pi/3, Pi/2 and multiples thereof.
      You should be able to give me the answer to sec(Pi/6) (or something similar) in less than 15 seconds!
Back to the Multivariable Calculus Home Page
Christopher Hanusa – Queens College – Mathematics Department.