Calculus III, Fall 2016

Calculus III: Multivariable Calculus, Fall 2016

PDF syllabus

Course Description: This class is a continuation of Calculus I and II. We will cover the calculus of functions of several variables and vector-valued functions, including maximization/minimization; directional derivatives; gradient, curl and divergence; line, surface and volume integrals; and the classical theorems of vector calculus: Green’s Theorem, Stokes’ Theorem and the Divergence Theorem.

Reading Assignments: A reading assignment for each class will be posted on the course webpage and in the Canvas course prior to each lecture. This reading should be completed before the lecture. Unless otherwise specified, you will be responsible for all material in the reading assignment, even if it is not covered in lecture. A provisional lecture schedule appears below.

Homework: Homework problems will be assigned after each lecture, but will not be collected. Instead, a selection of these problems will appear on each weekly quiz.

Quizzes: There will be a 20 minute quiz at the beginning of lecture each Friday (excepting the two Exam days below), which will consist of two to four problems selected from the homework problems from the previous three lectures. Your lowest quiz score will be dropped when considering your overall course assessment.

Exams: There will be two in-class midterm exams, and a cumulative final. Dates are as follows:

Assessment: Your course performance (Sat/Unsat) will be evaluated based on quizzes and exams, weighted as below. Class participation and attendance will be reflected in the narrative evaluation.

Policies: A student claiming a need for special accommodations because of a disability must work with the Counseling and Wellness Center, which will establish the need for specific accommodations and communicate them to the instructor.

No student shall be compelled to attend class or sit for an examination at a day or time when he or she would normally be engaged in a religious observance or on a day or time prohibited by his or her religious belief. Students are expected to notify their instructors if they intend to be absent for a class or announced examination, in accordance with this policy, prior to the scheduled meeting.

Lecture Schedule:

Monday Wednesday Friday
8/22: 12.1, 12.2: 3D coordinates, vectors 8/24: 12.3, 12.4: Dot, cross products 8/26: 12.5, 12.6: Lines, planes, surfaces
8/29: 13.1: Curves 8/31: 13.2: Derivatives, integrals of curves 9/2: 14.1: Multi-variable functions
9/5: Labor Day 9/7: 14.2, 14.3: Limits, derivatives of functions 9/9: 14.4: Tangent planes
9/12: 14.5: Chain rule 9/14: 14.6: Gradient 9/16: 14.7: Extrema
9/19: 14.7: Extrema cont’d 9/21: Review 9/23: Exam 1
9/26: 15.1: Double integrals 9/28: 15.2: Iterated integrals 9/30: 15.3: Integrals over regions
10/3: 15.4: Polar coordinates 10/5: 15.5: Applications 10/7: 15.7: Triple integrals
10/17: No class 10/19: 15.8: Cylindrical coordinates 10/21: 15.9: Spherical coordinates
10/24: 15.8, 15.9: Special coordinates cont’d 10/26: 16.1: Vector fields 10/28: 16.2: Line integrals
10/31: 16.3: FTCLI 11/2: Review 11/4: Exam 2
11/7: 16.4: Green’s Theorem 11/9: 16.5: Curl and divergence 11/11: Veteran’s Day
11/14: 16.6: Surfaces and area 11/16: 16.6: Surfaces cont’d 11/18: 16.7: Surface Integrals
11/21: 16.8: Stokes’ Theorem 11/23: 16.9: Divergence Theorem 11/25: Thanksgiving break
11/28: Review 11/30: Review