Multivariable Calculus Fall 2013
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Christopher Hanusa > Courses > Multivariable Calculus Fall 2013 > Homework
 
Homework
Multivariable Calculus – Fall 2013
Skip after Exam 1 Skip after Exam 2
Homework 1
Due Tuesday, September 3, 2013
  • Email me at chanusa@qc.cuny.edu with the following four things: (1) Your name, (2) Your class (Math 201) (3) the email address where you are best contacted, (4) your graduation year, and (5) the most interesting parametric curve you could make with Wolfram Alpha or Mathematica. With this curve, include a sentence about why it is interesting.
    • In class, we used the following curves. Modify these curves or experiment with something completely 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: (1st Edition)  1, 4, 9, 13, 15, 18, 21, 22, 24, 29, 39
    • Section 9.1: (2nd Edition)  1, 4, 9, 13, 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!
  • Work on all problems. Bold questions should be made higher priority. Italic questions are harder than average.
  • Last, think to contribute to the course blog with some interesting multivariable calculus links!
Homework 2
Due Tuesday, September 10, 2013
  • 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, Ed. 1 pp. 502-503 or Ed. 2 pp. 526-527) from the book and complete the following homework problems.
    • Section 9.2: (1st Edition)  2, 3, 6, 7, 11, 13, 16, 17, 21 (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 9.2: (2nd Edition)  2, 3, 6, 7, 11, 13, 16, 17, 21 (use your calculator), 27, 28, 29, 35 (And use your calculator to give the answer within 4 decimal places), 37, 38, 41, 44, 53, 54
    • Section 9.3: (1st Edition)  1, 3, 5, 8, 11, 14, 17
    • Section 9.3: (2nd Edition)  1, 3, 5, 9, 11, 14, 18
      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 3
Due Thursday, September 12, 2012
  • Read Sections 9.3 (ignore tangents in polar coordinates) and 9.4 (ignore arc length in polar coordinates) and complete the following homework problems.
    • Section 9.3 (1st Edition):  21, 26, 27, 28, 29, 34, 38, 39, 41, 46, 55, 57, 58, 61, 66
    • Section 9.3 (2nd Edition):  21, 23, 25, 29, 33, 34, 38, 39, 41, 46, 55, 57, 58, 61, 66
    • Section 9.4 (1st Edition):  1, 5, 6, 9, 10, 16, 17, 20, 21, 25, 29–32
    • Section 9.4 (2nd Edition):  1, 5, 6, 9, 11, 15, 17, 20, 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 4
Due Tuesday, September 17, 2013
  • 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). The official due date is Thursday but you should complete as much as possible for Tuesday so that we can discuss it in class.
  • Read Sections 10.1 and the beginning of Section 10.2 from the book. Then complete the following homework problems.
    • First, practice some of the questions from Section 9.4 because you did not them.
    • Section 10.1 (1st Edition):  4, 5, 10, 11, 13, 19, 21, 23, 25, 27, 29, 31, 33
    • Section 10.1 (2nd Edition):  4, 5, 10, 11, 13, 19, 21, 23, 25, 27, 29, 31, 33
    • Section 10.2 (1st Edition):  2, 4, 9, 11, 13, 15, 17, 19, 21, 25, 27,
    • Section 10.2 (2nd Edition):  2, 4, 9, 11, 13, 15, 17, 21, 24, 29, 35,
Homework 5
Due Thursday, September 19, 2013
  • 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 the end of Section 10.2, as well as Section 10.3. from the book and complete the following homework problems.
    • Complete the questions from Section 10.2.
    • Section 10.3 (1st Edition):  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 10.3 (2nd Edition):  1, 6, 7, 9, 11, 12, 14, 15, 18, 19, 21, 23, 24, 29, 32, 33, 37, 39, 45, Challenge Questions: 36, 42, 49
Homework 6
Due Tuesday, September 24, 2013
  • Read Sections 10.4 and 10.5 from the book and complete the following homework problems.
    • Section 10.4 (1st Edition):  3, 5, 6, 7, 8, 9, 10, 12, 14, 15, 16, 21, 23, 25, 27, 29, 33, 35, 36, 45, Challenge Questions: 38, 42
    • Section 10.4 (2nd Edition):  3, 4, 6, 7, 8, 13, 14, 16, 18, 19, 20, 25, 27, 29, 31, 33, 37, 39, 40, 53, Challenge Questions: 42, 50
    • Section 10.5 (1st Edition):  1, 4, 5, 10, 14, 15, 17, 18, 24, 25, 27, 29, 33, 34, 38, 41, 43. Challenge Question: 54
    • Section 10.5 (2nd Edition):  1, 4, 5, 10, 14, 15, 17, 18, 24, 25, 27, 29, 35, 36, 40, 43, 45. Challenge Question: 56
Homework 7
Due Thursday, September 26, 2013
  • Complete the third homework assignment on Webwork about vector functions and surfaces.
  • Complete Webwork 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 10.6 (1st Edition):  5, 6, 7, 9, 11, 13, 15, 17, 19, 21, 25, 29, 30, Challenge Questions: 31, 34
    • Section 10.6 (2nd Edition):  5, 7, 8, 9, 17, 13, 15, 16, 19, 24, 25, 29, 30, Challenge Questions: 31, 34
EXAM 1 on Tuesday, October 1, 2013 (unless fire drill scheduled)
  • The first exam of the semester will take place during the first half of class on Tuesday, October 1, 2013. (After a short break, the second half of the class period will be new material in Chapter 10.)
  • 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". (You have not seen the material from Questions 1, 5, and 7.)
  • There will be a Question and Answer session during the second half of class on Thursday, September 26, 2012.
  • 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 1 Ed / pp 526-527 2 Ed), 9.4 (except arc length in polar, p 509 1 Ed / p533 2 Ed)
    • Chapter 10, Sections 10.1-10.6
  • I highly suggest that you review the three 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, 1 Ed / p. 517, 2 Ed)
    • Intuitive explanation of area formula for polar coordinates (p. 507, 1 Ed / p. 531, 2 Ed)
  • 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 (up through TI-86) are allowed, but I come around and delete their memory before the exam.
Homework 8
Due Thursday, October 3, 2013
  • Read Section 10.7 from the book and complete the following homework problems.
    • Section 10.7 (1st Edition):  2, 3, 4, 5, 7, 11, (17-22), 23, 24, 28, 29, 33, 35, 37, 39, 41, 43, 45, 47, 48, 49, 51, 55, 56, 57, 58, 59, 61, 63, 65, 66, 73, 74, 75 Challenge Questions: 70, 71, 77
    • Section 10.7 (2nd Edition):  2, 3, 4, 5, 8, 11, (17-22), 23, 24, 28, 29, 33, 35, 37, 39, 41, 43, 45, 47, 48, 49, 51, 57, 58, 59, 60, 61, 63, 65, 67, 68, 77, 78, 79 Challenge Questions: 72, 74, 81
Homework 9
Due Tuesday, October 8, 2013
  • Start Homework Assignment 4 on Webwork about calculus of vector functions.
  • Read Sections 10.7 and 10.9 (not including components, pp 584-588 1st Ed/pp 2nd Ed 610-613) from the book and complete the following homework problems.
    • Complete the homework questions from Chapter 10.7.
    • Section 10.9 (1st Edition):  1, 3, 5, 7, 9, 11, 13, 15, 18, 25, Challenge Question: 27
    • Section 10.9 (2nd Edition):  1, 3, 5, 7, 9, 11, 13, 15, 18, 25, Challenge Question: 29
Homework 10
Due Thursday, October 10, 2013
  • Complete Homework Assignment 4 on Webwork about calculus of vector functions.
  • Read Sections 10.8 (not including curvature, normal, binormal vectors pp 574-578 1st Ed/pp 599-603 2nd Ed) and 11.1 from the book and complete the following homework problems.
    • Section 10.8 (1st Edition):  1, 3, 6, 7 Challenge Question: 10
    • Section 10.8 (2nd Edition):  1, 3, 8, 9 Challenge Question: 12
    • Section 11.1 (1st Edition):  1, 3, 7, 9, 10, 13, 17, 20, 21, 22, 25, 29, 31, 34, 35, 41–46, 47, 51 Challenge Questions: 39, 53, 54
    • Section 11.1 (2nd Edition):  1, 3, 7, 9, 10, 13, 18, 19, 21, 22, 25, 29, 31, 34, 35, 41–46, 47, 51 Challenge Questions: 37, 55, 56
Homework 11
Due Thursday, October 17, 2013
  • Read Sections 11.2 and 11.3 from the book and complete the following homework problems.
    • Start Homework Assignment 5 on Webwork.
    • Section 11.2 (1st Edition):  2, 5, 7, 11, 19, 20, 21, 23, 25, 27 Challenge Questions: 15, 31, 32
    • Section 11.2 (2nd Edition):  2, 5, 7, 11, 19, 20, 21, 23, 25, 27 Challenge Questions: 15, 33, 34
  • Reminder: there is no class on October 15.
Homework 12
Due Tuesday, October 22, 2013
  • Complete Webwork assignment 5.
  • Read Sections 11.2 and 11.3 from the book and complete the following homework problems.
    • Section 11.3 (1st Edition):  2, 3, 4, 6, 7-32
    • Section 11.3 (2nd Edition):  2, 3, 4, 6, 7-34
    • Section 11.3 (1st Edition):  37, 39, 43, 45, 47, 54, 55, 58, 66, 67, 71 Challenge Questions: 62, 70
    • Section 11.3 (2nd Edition):  39, 41, 45, 47, 50, 56, 55, 62, 70, 75 Challenge Questions: 66, 74
Homework 13
Due Thursday, October 24, 2013
  • Read Sections 11.4 and 11.5 from the book and complete the following homework problems.
    • Section 11.4 (1st Edition):  1-6, 13, 15, 17, 19, 23, 28, 32
    • Section 11.4 (2nd Edition):  1-6, 13, 17, 19, 21, 23, 28, 34
Homework 14
Due Tuesday, October 29, 2013
  • Start Webwork assignment 6.
  • Read Section 11.6 from the book and complete the following homework problems.
    • Section 11.5 (1st Ed):  5, 7, 8, 11, 17-28, 31, 33, 37 Challenge Questions: 41, 45
    • Section 11.5 (2nd Ed):  5, 7, 8, 11, 17-28, 31, 33, 37 Challenge Questions: 41, 45
    • Section 11.6 (1st Ed):  3, 5, 7, 10, 11, 12, 15, 17, 19,
    • Section 11.6 (2nd Ed):  3, 6, 7, 8, 11, 12, 15, 18, 19,
Homework 15
Due Thursday, October 31, 2013
  • Complete Webwork assignment 6.
  • Read Section 11.6 from the book and complete the following homework problems.
    • Section 11.6 (1st Ed):  22, 23, 27, 28, 30, 31, 33, 37, 44 Challenge Questions: 41, 42, 43, 47
    • Section 11.6 (2nd Ed):  22, 23, 27, 28, 30, 31, 33, 39, 48 Challenge Questions: 42, 43, 47, 51
  • Reminder: Exam 2 is on Tuesday, November 5, 2013 and will cover Sections 10.7-10.9 and 11.1–11.6. Class on Thursday will consist of homework discussion from 11.6 and then a Question and Answer session covering all topics since the first exam.
EXAM 2 will be held on Tuesday, November 5, 2013
  • The second exam of the semester will take place during the first half of class on Tuesday, November 5, 2013 IN KIELY 258. (After a short break, the second half of the class period will be new material from Section 11.7.)
  • Once again, I am providing last year's exam. 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". (On this practice exam, you are not responsible for the material from Questions 5 & 6. You might wish to revisit Questions 1, 5, and 7 from the practice exam from Exam 1.)
  • Here are more details about the second exam.
Homework 16
Due Thursday, November 7, 2013
  • Read Section 11.7 from the book and complete the following homework problems.
    • Section 11.7 (1st or 2nd Ed):  2, 3, 5, 7, 9, 10, 11, 13, 23, 25, 27, 28, 29,
Homework 17
Due Tuesday, November 12, 2013
  • Read Section 11.8 from the book (excluding two-constraint Lagrange multipliers) and complete the following homework problems.
    • Section 11.7 (1st or 2nd Ed):  29, 33, 35, 39, 42, 45, 46 Challenge Question: 48
    • Section 11.8 (1st Ed):  1, 3, 5, 7, 9, 17, 19, 27, 33, 39
    • Section 11.8 (2nd Ed):  1, 3, 5, 7, 9, 19, 21, 27, 37, 43
Homework 18
Due Thursday, November 14, 2013
  • Complete Webwork assignment 7.
  • Read Section 12.1 from the book (ignoring the "Midpoint rule") and complete the following homework problems.
    • Section 12.1 (1st Ed):  1, 3, 9, 10, 11-33 odd, 37, Challenge Question: 40
    • Section 12.1 (2nd Ed):  1, 3, 9, 10, 11-33 odd, 39
Homework 20
Due Tuesday, November 19, 2013
  • Read Section 12.2 and pages 690-691 about Density and Mass. Then complete the following homework problems.
    • Section 12.2 (1st Ed):  7-19 odd, 25, 31-41 odd, 45, Challenge Questions: 23 48, 49
    • Section 12.2 (2nd Ed):  7-23 odd, 29, 37-47 odd, 51, Challenge Questions: 27 54, 58
    • Section 12.4 (both):  1. In problems 3-6, only find the mass of the lamina.
Homework 21
Due Thursday, November 21, 2013
  • 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 (both):  7-19 odd, 23-26, 29 Challenge Question: 20
    • Section 12.4 (both):  In problems 7-10, only find the mass of the lamina.
Homework 22
Due Tuesday, November 26, 2013
  • Read Section 12.5. Then complete the following homework problems.
    • Complete the remaining groupwork questions from the class period.
    • Section 12.5 (1st Ed):  7-16, 25-32, 45 Challenge Question: 47
    • Section 12.5 (2nd Ed):  7-16, 25-32, 49 Challenge Question: 51
Homework 23
Due Tuesday, December 3, 2013
  • Start Webwork assignment 9.
  • Read Sections 12.6 and 12.7. Then complete the following homework problems.
    • Section 12.6 (1st Ed):  11-13, 15, 16, 17-22, 26-28
    • Section 12.6 (2nd Ed):  11-13, 15, 16, 17-22, 28-30
    • Section 12.7 (1st Ed):  9-14 (odd), 15-20, 21-26, 31, 32, 35, 36, Challenge Questions: 37, 40
    • Section 12.7 (2nd Ed):  9-14 (odd), 15-20, 21-25, 28, 33, 34, 37, 38, Challenge Questions: 41, 44
••••••  Please fill out the college-wide course evaluations, distinct from the department course evaluations that will be given out in class. Thank you for your feedback! ••••••
Homework 24
Due Thursday, December 5, 2013
  • Complete Webwork assignment 9.
  • Complete any leftover questions from Sections 12.6 and 12.7 and Tuesday's worksheet.
  • Prepare questions for the Question and Answer session that will occur during the second half of the class period.
EXAM 3 on Tuesday, December 10, 2013
  • The third exam of the semester will take place during the first half of class on Tuesday, December 10, 2013 in KIELY HALL 258.
  • The exam covers Sections 11.7, 11.8 (excluding two-constraint Lagrange multipliers), and 12.1-12.7 (not including moments or center of mass).
  • Once again, I am providing last year's exam. 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". (On this practice exam, you are not responsible for the material from Question 4. You might wish to revisit Questions 5 and 6 from the practice exam from Exam 2.)
  • Here are more details about the third exam.
••••••  Please fill out the college-wide course evaluations, distinct from the department course evaluations that will be given out in class. Thank you for your feedback! ••••••
FINAL EXAM on Thursday, December 19, 2013 from 1:45-3:45 in Kiely Hall Room 258.
Back to the Multivariable Calculus Home Page
Christopher Hanusa – Queens College – Mathematics Department.