MAT 223: Multivariable Calculus

Spring 2021

Exam 2 information

1. Allowed materials

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

Calculators are not allowed on exams.

You may only use other electronic devices (computer, smart phone) to the extent of following exam logistics (below).

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 12.3. (Section 12.4 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:

• vector-valued functions: limit, continuity, derivative, integral, tangent vector
• arc length, speed, arc length parametrization
• curvature; TNB frame, osculating plane and circle
• motion in 3-space: velocity, acceleration, tangential and normal components
• multivariable function basics: domain, range, graph, trace, level curve, contour map
• limits, continuity: finding a limit, showing a limit does not exist
• partial derivative: equality of mixed partials

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.

4. Logistics

Logistics will be identical to Exam 1; review it if you don't remember the procedure.

Change: there will not be a 10-minute head-start option.