Math 2233: Multivariable Calculus
Section 20
Summer 2026

Contact Info
Summer 2026

Office: Phillips Hall 720E
Email: jaydaigle@gwu.edu

Office Hours:

Course Information

Lecture:

Official textbook:

Daily Assignments

Week 1: Vectors
June 29: Vectors and the Dot Product
June 30: Dot Product and Cross Product
  • Finish section 1.3, and read sections 1.4 and 1.5 of the online notes
    • See also sections 2.3, 2.4, and 2.5 of Gilbert and Strang
July 1: Vector Functions
  • Mastery Quiz 1
    • M1, S1
  • Read section 2.1 of the online notes
    • See also section 3.1 of Gilbert and Strang
July 2: Calculus of Vector Functions
Week 2: Multivariable Functions
July 6: Multivariable Functions and their Limits
  • Mastery Quiz 2
    • M1, S1, S2
  • Read Sections 3.1-2 of the online notes
    • See also sections 4.1 and 4.2 of Gilbert and Strang
    • Work through the [worksheet on graphing multivariable functions]
July 7: Partial Derivatives, Linear Approximation, and the Gradient
  • Read the [solutions] to Mastery Quiz 2.
  • Read sections 3.3-5 of the online notes
  • See also sections 4.3 and 4.4 of Gilbert and Strang
July 8: The Chain Rule and Second Partials
  • Mastery Quiz 3
    • M1, M2, S2, S3
  • Read sections 3.6-7 of the online notes
  • See also section 4.6 of Gilbert and Strang, and look back at 4.3
July 9: Test 1
  • Read the [solutions] to Mastery Quiz 3.
  • You may bring a one-sided, handwritten cheat sheet on letter-size or A4-size paper.
  • You may not use a calculator.
  • Practice Midterm 1
Week 3: Optimization and Integration
July 13: Maxima and Minima
  • Mastery Quiz 4
    • M1, M2, S3
  • Read sections 4.1-2 of the online notes
  • See also section 4.7 of Gilbert and Strang
July 14: Global Extrema and Constrained Optimization
  • Read the [solutions] to Mastery Quiz 4
  • Read sections 4.2-3 of the online notes
  • See also section 4.8 of Gilbert and Strang
July 15: Riemann Sums and Multivariable Integrals
  • Mastery Quiz 5
    • M2, M3
  • Read section 5.1 of the online notes
  • See also section 5.1 of Gilbert and Strang
July 16: Double and Triple Integrals
  • Read the [solutions] to Mastery Quiz 5
  • Read section 5.2 of the online notes
    • See also section 5.2 and 5.4 of Gilbert and Strang
Week 4: Integration
July 20: Polar, Cylindrical, and Spherical Integrals
  • Mastery Quiz 6
    • M2, M3, M4
  • Read the rest of sections 5.3-4 of the online notes
    • See also section 5.3 and 5.5 of Gilbert and Strang
July 21: Integrals and Change of Variables
  • Read the [solutions] to Mastery Quiz 6
  • Read the section 5.5 of the online notes
    • See also section 5.7 of Gilbert and Strang
July 22: Integral Applications
  • Mastery Quiz 7
    • M3, M4
  • Read section 5.6 of the online notes
    • See also section 5.6 of Gilbert and Strang
July 23: Test 2
Week 5: Vector Calculus
July 27: Vector Fields and Line Integrals
  • Mastery Quiz 8
    • M3, M4, S4
  • Read sections 6.1-2 of the online notes
    • See also sections 6.2.1 and 6.1 of Gilbert and Strang
July 28: Conservative Vector Fields
  • Read the [solutions] to Mastery Quiz 8
  • Read sections 6.3-4 of the online notes
    • See also the rest of section 6.2 and section 6.3 of Gilbert and Strang
July 29: The Curl and Green’s Theorem
  • Mastery Quiz 9
    • M4, M5, S4
  • Read sections 6.5-6 of the online notes
    • See also the middle section 6.5.2 of 6.5, and then section 6.4 of Gilbert and Strang
July 30: Surface Parametrization and Surface Integrals
  • Read the [solutions] to Mastery Quiz 9
  • Read sections 7.1-2 of the online notes
    • See also (sub)sections 6.6.1-6.6.3 of Gilbert and Strang
Week 6: Flux Integrals
August 3: Flux Integrals
  • Mastery Quiz 10
    • M5, S5
  • Read section 7.3 of the online notes
    • See also (sub)sections 6.6.4-6.6.6 of Gilbert and Strang
August 4: Stokes’s Theorem
  • Read the [solutions] to Mastery Quiz 10
  • Read section 7.4 of the online notes
    • See also (sub)sections 6.7 of Gilbert and Strang
August 5: Divergence and the Divergence Theorem
  • Mastery Quiz 11
    • M5, S5
  • Read section 8.1-3 of the online notes
    • See also (sub)sections 6.5.1 and sections 6.8 of Gilbert and Strang
  • Bonus Section 8.4 of the online notes discusses an advanced perspective on vector calculus. We will not be substantially covering it in this course, and we certainly won’t be testing on it, but you might find it interesting or enlightening.
August 6: Final Exam
August 8: Wrap-up

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

The course syllabus is available here.

Course notes

Mastery Quizzes

Allocation of topics is tentative and may change as the course progresses.

Major Topics

  1. Vectors
  2. Partial Derivatives
  3. Optimization
  4. Multiple Integrals
  5. Line Integrals
  6. Surface Integrals

Secondary Topics

  1. Lines and Planes
  2. Vector Functions
  3. Multivariable Functions
  4. Integral Applications
  5. Vector Fields
  6. The Divergence Theorem

Tests

Calculators of any sort will not be allowed on tests. I will allow you to bring a cheat sheet in your own handwriting. For midterms I will allow a one-sided cheat sheet, and for the final I will allow a two-sided cheat sheet.

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.

We will be using a (free!) online homework system called WeBWorK this term. You can access it by going to Blackboard, then to “Course Links”, and clicking the WeBWorK link. This will automatically create an account for you and log you in. You may continue to log in through Blackboard, or if you wish you may create a password within WeBWorK to log in directly.