MAT 223: Multivariable Calculus

Fall 2022

Exam 4 information

1. Allowed materials

You are permitted one 3"×5" notecard for use as reference during the exam.

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

2. How to study

Please see tips from first exam.

3. Exam content

The exam covers everything we have done, up to and including Section 14.3. (Section 14.4 will be on the next exam.) While the exam is cumulative, we will focus on what was not already tested. 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:

• double and triple integrals: rectangular domains, general domains, iterated integrals
• applications of integration: density, center of mass, work
• vector fields: divergence, curl
• line integrals: scalar and vector line integrals
• conservative vector fields: path-independence, fundamental 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.