MAT 223: Multivariable Calculus

Spring 2023

Final exam information

1. Allowed materials

You are permitted five 3"×5" notecards or one letter-size notes sheet for use as reference during the exam.

Electronic devices (calculator, laptop, smart phone) are not allowed on exams.

2. How to study

Get enough rest during finals week and the weekend before. Create a list and schedule of what you will do each day, including enough sleep in your schedule. Start studying early enough so you can take breaks; reward yourself after working hard.

Practicing by solving problems is much more effective than reading over solutions. Going over homework/exams and correcting mistakes is also a good idea.

3. Exam content

The exam covers everything we have done. The exam is cumulative, so you should review the topics of the previous four exams. The majority of the exam will focus on what was not already tested in previous exams.

As mentioned in the syllabus, we do not have time to cover every single topic in class. You are responsible for the material in the sections even if they were not discussed in class. If we didn't talk about something and no exercise problems for a specific concept was ever assigned as homework, it is unlikely it will occur on an exam. Here are some topics we emphasized since the last exam:

polar coordinates: converting between polar and rectangular coordinates, area within polar curves, arc length
change of variables: integrating in polar, cylindrical, spherical, and arbitrary coordinates
surface integrals: scalar and vector surface integrals
fundamental theorems: Green's theorem, Stokes' theorem, divergence theorem

As usual, please note that this document is not a contract. I may have inadvertently left something off that ends up on an exam question. Moreover, I will not be able to test all of this material given the time limitations of the exam. I will have to pick and choose some subset of it.