Math 2233: Multivariable Calculus
Section 11
Fall 2021

Daily Assignments

Tuesday Dec 14, 12:40–2:40 PM: Final Exam

• Solutions to Mastery Quiz 10
• Practice Final
• Solutions to practice final

December 9: Divergence Theorem

• Due in class: Mastery Quiz 10
  • Topics 11, 12, 13, 14
  • I cut topic 15, which makes me sad but I don’t see a better choice
  • Submit up to 3
• Read the solutions to quiz 9
• Read sections 9.2-3 of the online notes
  • See also section 6.8 of Gilbert and Strang
• Feel free to read section 9.4 too if you want a peek at what we’d do with anothe day

December 2: Divergence

• Mastery Quiz 9
  • Topics 10, 11, 12, 13, 14
  • Do up to 4
• Read section 9.1 of the online notes
  • Read objective 6.5.1 of section 6.5 of Gilbert and Strang

November 30: Stokes’s Theorem

• Read section 8.3 of the online notes
  • Read section 6.7 of Gilbert and Strang

November 23: Flux Integrals

• Read the solutions to Mastery Quiz 8
• Read section 8.2 of the online notes
  • Read objectives 6.6.4-6.6.6 of section 6.4 of Gilbert and Strang

November 18: Surface Integrals

• Due in Class: Mastery Quiz 8
• Finish section 7.5 and read section 8.1 of the online notes
  • See also learning objectives 6.6.2 and 6.6.3 section 6.4 of Gilbert and Strang
  • I’d like to get through all of 6.6 today but I don’t expect to.

November 16: Curl and Green’s Theorem

• Read the Solutions to midterm 2
• Read section 7.4-5 of the online notes
  • Gilbert and Strang handle this material in a slightly different order. We are covering:
    • The “Curl” section of section 6.5
    • All of section 6.4

November 11: Midterm

• Practice Midterm 2
  • Solutions to practice midterm 2

November 9: Conservative Vector Fields

• Read Solutions to quiz 7
• Read sections 7.2-7.3 of the online notes
  • See also section 6.3 of Gilbert and Strang

November 4: Line Integrals

• Due in Class:Mastery Quiz 7
  • Topics: 7, 8, 9, 10
  • Do at most 3
• Read sections 7.1-7.2 of the online notes
  • See also section 6.2 of Gilbert and Strang

November 2: More on Vector Fields

• Read the solutions to mastery quiz 6
• Finish section 6.4 of the online notes
  • See also section 6.1 of Gilbert and Strang

October 28: Change of Variables and Vector Fields

• Due in class: Mastery Quiz 6
  • Topics 5, 6, 7, 8, 9
  • Do up to 4 topics
• Finish section 6.3 and start section 6.4 of the online notes
  • See also section 6.1 of Gilbert and Strang

October 26: Parametrized Surfaces

• Read the solutions to mastery quiz 5
• Read sections 6.2-3 of the online notes
  • See also objective 6.6.1 of section 6.6 and all of section 5.7 of Gilbert and Strang
  • Watch this video on changing coordinates in integrals.

October 21: Calculus of Curves

• Due in class: * Mastery Quiz 5
  • Topics 4, 5, 6, 7
  • Submit only three
  • Check Blackboard before submitting; your mastery scores have been updated from the midterm
  • If you absolutely cannot get it done for class, you can submit online later on Thursday, but please try to get it in in class
• Read section 6.1 of the online notes
  • See also section 3.1 and section 3.2 of Gilbert and Strang
• Some videos:
  • Animation of parametrized curves
  • A quieter curve animation

October 19: Polar and Cylindrical Coordinates

• Read the solutions
• Read Sections 5.3-4 of the online notes
  • See also section 5.3 and section 5.5 of Gilbert and Strang
• Watch a few videos to help you visualize integrals in other coordinate systems:
  • Cylindrical coordinates
  • Visualizing spherical coordinates
  • Illustrating the spherical wedge and explaining why the “Jacobian” factor in spherical integrals is $\rho^2 \sin (\phi)$. Especially relevant starting at about 7 minutes in.

October 14: Multivariable Integration

• Due in class: Mastery Quiz 4
  • Topics 2, 3, 4, 5, 6
  • Submit only three
  • Check Blackboard before submitting; your mastery scores have been updated from the midterm
  • If you absolutely cannot get it done for class, you can submit online later on Thursday, but please try to get it in in class
• Read Section 5.2 of the online notes
  • See also section 5.2 and section 5.4 of Gilbert and Strang

October 12: Riemann Sums and Integration

• Read the Solutions to the midterm
• Read Section 5.1 of the online notes
  • See also section 5.1 of Gilbert and Strang

October 7: Constrained Optimization

• Read Section 4.3 of the online notes
  • See also section 4.8 of Gilbert and Strang

October 5: Midterm 1!

• Read the solutions to quiz 3.

• Practice Midterm 1

  • Solutions to practice midterm 1

September 30: Global Extrema

• Due in Class: Mastery Quiz 3
  • Topics 1, 2, 3, 4
  • Last chance for topic 1
• Read Section 4.2 of the online notes
  • See also the rest of section 4.7 of Gilbert and Strang

September 28: Critical Points and Local Extrema

• Read the solutions to quiz 2
• Read Section 4.1 of the online notes
  • See also section 4.7 of Gilbert and Strang, through Checkpoint 4.35

September 23: The Chain Rule and Second Partials

• Due in class: Mastery Quiz 2
  • Topics: 1, 2, 3
• Read Section 3.4-5 of the online notes
  • See also section 4.5 of Gilbert and Strang

September 21: The Gradient

• Read Section 3.3 of the online notes
  • See also section 4.6 of Gilbert and Strang
    • Note that we skipped 4.5

September 16: Partial Derivatives and Linear Approximation

• Read Sections 3.1-2 of the online notes
  • See also sections 4.3 and 4.4 of Gilbert and Strang
• Read the solutions to quiz 1

September 15: Mastery Quiz due

• Mastery Quiz 1: Topic 1
  • Due in recitation

September 14: The Dot Product and the Cross Product

• Read Sections 2.3-4 of the online notes
  • See also sections 2.3 and 2.4 of Gilbert and Strang

September 10: Edfinity due

September 9: Vectors and the Dot Product

• Read Section 2.1-2 of the online notes, and maybe glance at 2.3
  • Or read sections 2.1 and 2.2 of Gilbert and Strang

September 7: Limits and Continuity of Multivariable Functions

• Read Section 1.4 of the online notes
  • Or read section 4.2 of Gilbert and Strang

September 2: Lines and Planes

• Read Section 1.3 of the online notes
  • Or read section 2.5 of Gilbert and Strang, but note they approach this material in a different way that assumes you’ve already seen vector operations.

August 31: Syllabus and Multivariable Functions

• Please read the syllabus
• Claim your account on Edfinity
• Read Section 1.1-2 of the online notes
  • Or read section 4.1 of Gilbert and Strang

Course Goals

In this course we will extend our theory of calculus to cover functions of multiple variables. We will understand these functions algebraically and geometrically, and learn how to use the tools of differential and integral calculus to further understand them.

Topics will include: 3D graphing, planes, partial derivatives, vectors, directional derivatives, gradients, the chain rule, optimization and Lagrange multipliers, integration, parametrization, vector fields, line and surface integrals, and Green’s, Stokes’s, and the Divergence theorem.

The course syllabus is available here.

Course notes

• Course Notes
• Section 1: Multivariable Functions
  • Section 1 Mathematica Notebook
• Section 2: Vectors
• Section 3: Derivatives
  • Section 3 Mathematica Notebook
• Section 4: optimization
  • Section 4 Mathematica Notebook
• Section 5: Multivariable Integrals
  • Section 5 Mathematica Notebook
• Section 6: Parametrization and Vector Fields
  • Section 6 Mathematica Notebook
• Section 7: Line Integrals
  • Section 7 Mathematica Notebook
• Section 8: Surface Integrals
  • Section 8 Mathematica Notebook
• Section 9: Divergence
  • Section 9 Mathematica Notebook

Mastery Quizzes

• Mastery Quiz 1: Topic 1
  • Solutions
• Mastery Quiz 2: Topics 1, 2, 3
  • Solutions
• Mastery Quiz 3: Topics 1, 2, 3, 4
  • Solutions
• Mastery Quiz 4: Topics 2, 3, 4, 5, 6
  • Solutions
• Mastery Quiz 5: Topics 4, 5, 6, 7
  • Solutions
• Mastery Quiz 6: Topics 5, 6, 7, 8, 9
  • Do up to 4
  • Solutions
• Mastery Quiz 7: Topics 7, 8, 9, 10
  • Do up to 3
  • Solutions
• Mastery Quiz 8
  • Topics 8, 9, 10, 11, 12
  • Do up to 4
  • Solutions
• Mastery Quiz 9
  • Topics 10, 11, 12, 13, 14
  • Do up to 4
  • Solutions
• Mastery Quiz 10
  • Topics 11, 12, 13, 14
  • Do up to 4
  • Solutions

Topics

1. Lines and planes
2. Vector operations
3. Partial Derivatives and Linear Approximation
4. Gradient and directional derivatives
5. Multivariable optimization
6. Constrained optimization
7. Multivariable integrals
8. Integrals in other coordinate systems
9. Calculus of curves
10. Integral change of variables
11. Line integrals
12. Conservative Vector Fields
13. Surface integrals
14. Green’s and Stokes’s theorems
15. Divergence theorem

Tests

• Midterm on October 5
  • Practice Midterm 1
  • Solutions to practice midterm 1
  • Midterm 1 Solutions
• Midterm on November 11
  • Practice Midterm 2
  • Solutions to practice midterm 2
  • Solutions to midterm 2
• Final Exam
  • Tuesday Dec 14, 12:40–2:40 PM
  • Practice Final
  • Solutions to practice final

Graphing calculators will not be allowed on tests. Scientific, non-programmable calculators will be allowed. I will have some to share, but not enough for everyone.

Edfinity online homework system

We will be using Edfinity for Math 2233-11. To enroll, please follow the steps below:

1. If you already have an Edfinity account from a previous course, please sign into it. Otherwise, go to step 2.
2. Go to the following registration link: https://edfinity.com/join/WJF6876B
3. You will be prompted to pay (I believe the fee is $25) and enroll in our section.
4. Start working on your assignments :)

Textbook

The official textbook for Math 2233 is OpenStax Calculus Volume 3 by Gilbert Strang and Edwin Herman. It is available for free online here. You can also buy copies from Amazon; a paperback is a little under $30.

I will be loosely following the textbook, but will often be giving my own take or focusing on topics the textbook doesn’t emphasize. All my course notes will be posted to the course web page.

This section of Math 2233 will use the Edfinity online homework platform. You will need to buy a license, which I believe is $25.