The Final examination will take place at 12:30 pm on Tuesday, May 2, 2023.

The exam is 150 minutes long. No notes, books, computers, phones, calculators or other aids are allowed. Full credit will not be awarded for insufficient accompanying work.

The exam is cumulative. You are expected to know all the material from prerequisite math courses as well as the material covered in the midterms. In addition, the following new material will be on the exam:

• 5.7 Change of Variables in Multiple Integrals
• 6.1 Vector Fields
• 6.2 Line Integrals
• 6.3 Conservative Vector Fields
• 6.4 Green’s Theorem

All material in the course will have roughly equal weighting on the exam.

• You do not need to know Laplace’s equation in 6.4.
• You do not need to know how to apply Green’s theorem to regions that are not simply connected.

Two practice exams have been posted in the resources section, which have similar length, difficulty, and format to your exam.

Midterm 3 will take place during the scheduled class period on Thursday, April 6, 2023.

The exam is 75 minutes long. No notes, books, computers, phones, calculators or other aids are allowed. Full credit will not be awarded for insufficient accompanying work.

The midterm will focus on the following sections from the text:

• 4.8 Lagrange Multipliers
• 5.1 Double Integrals over Rectangular Regions
• 5.2 Double Integrals over General Regions
• 5.3 Double Integrals in Polar Coordinates
• 5.4 Triple Integrals
• 5.5 Triple Integrals in Cylindrical and Spherical Coordinates

You are expected to know all the material from prerequisite math courses as well as the material covered in midterms 1 and 2.

• You do not need to know the “Type I” or “Type II” nomenclature in 5.2.
• You do not need to know the applications to probability in 5.2.

Two practice exams have been posted in the resources section, which have similar length, difficulty, and format to your exam.

Midterm 2 will take place during the scheduled class period on Thursday, March 2, 2023.

The exam is 75 minutes long. No notes, books, computers, phones, calculators or other aids are allowed. Full credit will not be awarded for insufficient accompanying work.

The midterm will focus on the following sections from the text:

• 4.1 Functions of Several Variables
• 4.2 Limits and Continuity
• 4.3 Partial Derivatives
• 4.4 Tangent Planes and Linear Approximations
• 4.5 The Chain Rule
• 4.6 Directional Derivatives and the Gradient
• 4.7 Maxima/Minima Problems

You are expected to know all the material from prerequisite math courses as well as the material covered in midterm 1.

• You do not need to know the formal definition of the limit from 4.2, but of course you should know all the limit rules etc. and have a conceptual understanding.
• You do not need to know the material about partial differential equations from 4.3.
• You do not need to know the formal definition of the “differentiable” from 4.4, but you should know how to apply Theorem 4.7.

Two practice exams have been posted in the resources section, which have similar length, difficulty, and format to your exam.

Midterm 1 will take place during the scheduled class period on Thursday, February 2, 2023.

The exam is 75 minutes long. No notes, books, computers, phones, calculators or other aids are allowed. Full credit will not be awarded for insufficient accompanying work.

The midterm will focus on the following sections from the text:

• 2.1 Vectors in the Plane
• 2.2 Vectors in Three Dimensions
• 2.3 The Dot Product
• 2.4 The Cross Product
• 2.5 Equations of Lines and Planes in Space
• 3.1 Vector-Valued Functions and Space Curves
• 3.2 Calculus of Vector-Valued Functions
• 3.3 Arc Length and Curvature

You are expected to know all the material from prerequisite math courses). In particular, see Calculus: Volume 1 for material from Math 141 and Calculus: Volume 2 for material from Math 142.

You do not need to know the “distance between skew lines” from 2.5.

Two practice exams have been posted in the resources section, which have similar length, difficulty, and format to your exam.

This website will be the main source of information for the course outside of lecture. Announcements for the course will be posted on the website here. You can also find the course syllabus, lecture schedule, and additional resources. As the course progresses, you can check your grades on Blackboard