Math 2233: Multivariable Calculus
Section 12
Fall 2022

Contact Info
Fall 2022

Office: Phillips Hall 720E

Office Hours:

Often in office:

Course Information



TA Office Hours:

Official textbook:


Section 36:

Section 37:

Section 38:

Daily Assignments

Final Exam on Monday, December 19, 12:40 - 2:40 PM

December 12: The Divergence Theorem and Vector Calculus

December 9: Recitation 14 on Stokes’s Theorem and Divergence

December 7: Divergence

December 5: Stokes’s Theorem

December 2: Recitation 13 on Surface Integrals

November 30: Flux Integrals

November 28: Surfaces and Scalar Surface Integrals

November 21: Curl and Green’s Theorem

November 18: Recitation 12 on Conservative Vector Fields

November 16: Conservative Vector Fields

November 14: Midterm 2

November 11: Recitation 11 on Line Integrals

November 9: Vector Fields and Line Integrals

November 7: Probability and Scalar Line Integrals

November 4: Recitation 10 on change of coordinates and center of mass

November 2: Integral Applications

October 31: Spherical Integrals and Alternate Coordinate Systems

October 28: Recitation 9 on Polar and Cylindrical Integrals

October 26: Polar, Cylindrical, and Spherical Coordinates

Recitation 8 on Iterated Integrals

October 19: Double Integrals 2

October 17: Double Integrals

Recitation 7 on Optimization

October 12: Lagrange Multipliers and Riemann Sums

October 10: Constrained Optimization

October 7: Recitation 6 on optimization

October 5: Optimization

October 3: Midterm 1

September 30: Recitation 5 on the Gradient and Second Partials

September 28: The Chain Rule and Second Partials

September 26: The Gradient and the Chain Rule

September 23: Recitation on Multivariable Limits and Derivatives

September 21: Linear Approximation and the Gradient

September 19: Limits and Continuity of Multivariable Functions

September 16: Recitation on Graphing 3D functions

September 14: Calculus of Vector Functions

September 12: Vector Functions

September 9: Recitation 2 on Cross Products

September 7: Cross Products and Planes

September 2: Recitation on Projections

August 31: The Dot Product

August 29: Syllabus and Vectors

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


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.


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.