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.
- Complete Notes
- Section 1: Multivariable Functions
- Section 2: Vectors
- Section 3: Derivatives
- Section 4: Optimization
- Section 5: Integrals
- Section 6: Parametrization
- Section 7: Line Integrals
- Section 8: Surface Integrals
- Section 9: Divergence and Differential Forms
The primary way this course will handle homework assignments is through the MAA’s online WeBWork interface. You will need to go here and log in to your account; your login is the same as your Oxy login name, and your password is your student ID. (Please change this as soon as possible.)
I currently plan to have weekly homework assignments, generally due on Tuesdays. (We do not have class on Tuesday, but the homework system is online so that’s fine. I’ll be on campus to answer questions on Tuesday afternoons.)
There is a very brief assignment due this Friday, January 24, just to make sure you have gotten into the system.
- Friday, January 24: A brief assignment to make sure you can use the system
- Tuesday, January 28: Homework 1, on multivariable functions.
- Tuesday, February 4: Homework 2, on limits, continuity, vectors, and the dot product
Each week you will have a written assignment due, generally on Wednesdays.
- Written Homework 1, due Wednesday, January 29
- Written Homework 2, due Wednesday, February 5
- Written Homework 3, due Wednesday, February 12
- Written Homework 4, due Wednesday, February 19
Tentative midterm dates are February 21, March 21, and April 11.
The final exam will be held in our usual classroom according to the official schedule.
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.
You don’t need Mathematica at any point in the course, but it can be very helpful to do calculations or experiment with visualizations. Occidental has a license that allows you to install Mathematica on your personal computer.
You can download Mathematica by following this link. You will be asked to create an account. After you have created an account and logged in, return to that link to download Mathematica for your computer.
There is no official textbook for this course. If you would like references or other perspectives, I recommend the following free online textbooks: