Multivariable Calculus, Fall 2014
Topics, Notes, and Homework

For each date, you will find the homework assignment that is due that day, any lecture notes for downloading, and the key topics that are covered that day.
This schedule is approximate and subject to change!

Sections 9.1–9.4 (3 classes)
Thursday, August 28
In class:
Tuesday, September 2
Before class:
• Email me at chanusa@qc.cuny.edu with the following five 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 using Wolfram Alpha or Mathematica. With this curve, include a sentence about why it is interesting.
• On Thursday, we used the following curves. Modify these curves or experiment with something completely new!
• ParametricPlot[{t + 2 Sin[2t], t + 2 Cos[5t]}, {t, -2 Pi, 2 Pi}]
• ParametricPlot[{1.5Cos[t] - Cos[30t], 1.5Sin[t] - Sin[30t]}, {t, -2Pi, 2Pi}]
• 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%.
• Visit the course forum. Become a member of the forum, and write a brief reply to the Topic "Post Here First". If the above link is not working, visit this link.
• Complete the book problems from Chapter 9.1.
• Read through the course notes.
• Read Sections 9.2 and 9.3.
In class:
• Homework Discussion
• Material from Sections 9.2 and 9.3  (Notes pages 9-13) '
• Tangent lines to parametric curves
• Polar coordinates
• Polar equations and their graphs
• Tangent lines to polar curves
Thursday, September 4
Before class:
• 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 ⟩.
• Complete book problems from Chapter 9.3 and the start of Chapter 9.2.
• Read Sections 9.2 and 9.4.
In class:
Sections 10.1–10.6 (4 classes)
Tuesday, September 9
Before class:
• Complete the book problems through Chapter 9.4.
• Make sure you feel comfortable with the definitions, theorems, and proofs from Sections 9.1 through 9.4.
• I suggest completing the Chapter 9 review.
In class:
Thursday, September 11
Before class:
• Complete the book problems for Sections 10.1 and 10.2.
• Start 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).
In class:
• Homework Discussion
• Forces in Equilibrium
• Material from Section 10.3 and 10.4  (Notes pages 25-31) '
• Dot products
• Cross products
Tuesday, September 16
Before class:
• 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).
• Complete the book problems for Sections 10.2 and 10.3.
In class:
• Homework Discussion
• Applications: Work, Torque
• Material from Section 10.5  (Notes pages 32-37) '
• Equations of Lines
• Equations of Planes
Thursday, September 18
Before class:
• Complete the book problems for Sections 10.4 and 10.5.
• Start the third homework assignment on Webwork about vectors, lines, planes, and surfaces.
In class:
Tuesday, September 30
Before class:
• Complete the book problems for Section 10.6.
• Complete the third homework assignment on Webwork about vector products and surfaces.
• Prepare for Exam 1 on Wednesday. (See below for details and advice.)
In class:
• Homework Discussion
Exam 1 Information
• The first exam of the semester will take place during the first half of class on Thursday, October 2. (After a short break, the second half of the class period will be new material in Chapter 10.)
• The exam covers Sections 9.1–9.4 and Sections 10.1–10.6.
• Here are more details about the first exam.
• My students often ask for an example of the style of exam that I am liable to give. I am including my exam from last semester. The topics covered by the exam are the same topics, but you should expect your exam to be very different because there are many ways for me to ask questions that test your knowledge on these topics.
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 last semester's exam.
Sections 10.7–10.9 (2 classes)
Thursday, October 2
In class:
• Exam 1
• New Material in the second half of class.
• Material from Section 10.7  (Notes pages 42-48) '
• Vector functions
• Parametrizations of curves
• Tangent vectors
• Derivatives of vector functions
Tuesday, October 7
Before class:
• Complete the book problems for Section 10.7.
• Start the fourth homework assignment on Webwork about vector functions, arc length, and curvature.
In class:
Sections 11.1–11.6 (6 classes)
Thursday, October 9
Before class:
• Complete the book problems through Section 10.9.
• Complete the fourth homework assignment on Webwork about vector functions, arc length, and curvature.
In class:
Tuesday, October 14
Before class:
• Complete the book problems through Section 11.1.
In class:
• Material from Sections 11.2 and 11.3  (Notes pages 58-63) '
• Limits of functions of several variables
• Partial derivatives
Thursday, October 16
Before class:
• Complete the book problems through Section 11.2.
• Start working on the fifth homework assignment on Webwork about functions of multiple variables, limits, and tangent planes.
In class:
• Material from Sections 11.3 and 11.4  (Notes pages 64-70) '
• Higher Partial derivatives
• Clairaut's Theorem
• Interpretation of partial derivatives
• Tangent Plane
• Differentiability
Tuesday, October 21
Before class:
• Complete the book problems through Section 11.3.
• Continue working on the fifth homework assignment on Webwork about functions of multiple variables, limits, and tangent planes.
In class:
• Material from Sections 11.4 and 11.5  (Notes pages 71-73) '
• Linear Approximations
• Differentials
• Chain Rule
• The Chain Rule simplifies implicit differentiation
Thursday, October 23
Before class:
• Complete the book problems through Section 11.4.
• Complete the fifth homework assignment on Webwork about functions of multiple variables, limits, and tangent planes.
In class:
Tuesday, October 28
Before class:
• Complete the book problems through Section 11.5.
• Start working on the sixth homework assignment on Webwork.
In class:
• Material from Section 11.6  (no new notes)
• Path of steepest ascent
• Tangent plane to a level surface
Thursday, October 30
Before class:
• Complete the book problems for Section 11.6.
• Complete the sixth homework assignment on Webwork.
• Prepare for Exam 2 on Monday.
In class:
• Homework Discussion
Exam 2 Information
• The second exam of the semester will take place during the first half of class on Tuesday, November 4. (After a short break, the second half of the class period will be new material in Chapter 11.)
• The exam covers Sections 10.7–10.9 and Sections 11.1–11.6.
• Again, I am including my exam from last semester. The topics covered by the exam are the same topics, but you should expect your exam to be very different because there are many ways for me to ask questions that test your knowledge on these topics.
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 last semester's exam.
Sections 11.7–11.8 (2.5 classes)
Tuesday, November 4
In class:
• Exam 2
• Material from Section 11.7 (Notes pages 81-86) '
• Local and Global Extrema
• Second derivative test
• Extreme Value Theorem
Thursday, November 6
Before class:
• Complete the book problems for Section 11.7.
In class:
• Material from Section 11.8 (Notes pages 87-90) '
• Optimization
• Method of Lagrange multipliers
• Examples
Sections 12.1–12.7 (5.5 classes)
Tuesday, November 11
Before class:
• Start the seventh homework assignment on Webwork.
• Complete the book problems for Section 11.8. (Ignore any questions involving multiple Lagrange multipliers (λ AND μ)
In class:
• Material from Sections 11.8 and 12.1 (Notes pages 91-95) '
• Riemann sums
• Double integrals
Thursday, November 13
Before class:
• Complete the book problems for Section 12.1.
In class:
• Material from Sections 12.2 and 12.4 (Notes pages 96-103) '
• Fubini's Theorem
• Properties of double integrals
• Double integrals over any domain
• Slicing in x vs. slicing in y
Tuesday, November 18
Before class:
• Complete the seventh homework assignment on Webwork.
• Complete the book problems for Section 12.2.
In class:
• Material from Sections 12.3 and 12.4 (Notes pages 104-109) '
• Changing order of integration
• Mass or charge of a lamina given a density function
• Double integrals in polar coordinates
• Pirate coordinates
• Mass or charge density in polar coordinates
Thursday, November 20
Before class:
• Start the eighth homework assignment on Webwork.
• Complete the book problems for Sections 12.3 and 12.4.
In class:
• Material from Section 12.5 (Notes pages 110-116) '
• Triple integrals
• Projecting solids onto coordinate planes
• Density and average value in three dimensions
Tuesday, November 25
Before class:
• Complete the eighth homework assignment on Webwork.
• Complete the book problems for Section 12.5.
In class:
• Material from Sections 12.6 and 12.7 (Notes pages 117-119) '
• Cylindrical and Spherical Coordinates
• Converting from Euclidean Coordinates w/ group work
Tuesday, December 2
Before class:
• Start the ninth homework assignment on Webwork.
• Complete the book problems for Section 12.6 and 12.7.
In class:
• More practice on Sections 12.6 and 12.7 (no new notes)
Please fill out the college-wide course evaluations, distinct from the course evaluations that will be given out in class. Thank you for your feedback!
Thursday, December 4
Before class:
• Complete the ninth homework assignment on Webwork.
• Prepare for Exam 3 on Tuesday.
In class:
• Homework Discussion
Exam 3 Information
• The third exam of the semester will take place during the first hour of class on Tuesday, December 9. The remainder of class will be spent quacking like a duck, or some other important activity.
• The exam covers Sections 11.7–11.8 and Sections 12.1–12.7.
• Again, I am including my exam from last semester. The topics covered by the exam are the same topics, but you should expect your exam to be very different because there are many ways for me to ask questions that test your knowledge on these topics.
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 last semester's exam.
Tuesday, December 9
In class:
• Exam 3
Thursday, December 11
• Final Exam Review
Please fill out the college-wide course evaluations, distinct from the course evaluations that will be given out in class. Thank you for your feedback!
Thursday, December 18
In class:
• Final Exam, 1:45–3:45