Calculus III, Fall 2018

Calculus III: Multivariable Calculus, Fall 2018

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 Fridays following Exams 1 and 2), which will consist of two to four problems selected from the homework problems from the previous three lectures.

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: Students in need of academic accommodations for a disability may consult with the office of Students Disability Services (SDS) to arrange appropriate accommodations. Students are required to give reasonable notice prior to requesting an accommodation. Students may request an appointment with SDS in-person (HCL3), via phone at 941-487-4496 or via email at

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, well in advance of the scheduled meeting.

Lecture Schedule:

Monday Wednesday Friday
8/27: 12.1-12.3: Vectors, dot products 8/29: 12.4, 12.5: Cross products, lines, planes 8/31: 12.6: Surfaces
9/1: Labor Day 9/5: 13.1, 13.2: Curves and velocity 9/7: 13.3: Arc length
9/10: 14.1: Multivariable functions 9/12: 14.2, 14.3: Limits, partial derivatives 9/14: 14.4, 14.5: Tangent planes, chain rule
9/17: No Class 9/19: No Class 9/21: No Class
9/24: 14.6: Gradient 9/26: 14.7: Local extrema 9/28: 14.8: Lagrange Multipliers
10/1: Review 10/3: Exam 1 10/5: 15.1: Double integrals over rectangles
10/8: 15.2: Integrals over regions 10/10: 15.3: Polar coordinates 10/12: 15.4: Applications
10/22: 15.6: Triple Integrals 10/24: 15.7: Cylindrical coordinates 10/26: 15.8: Spherical coordinates
10/29: 16.1: Vector fields 10/31: 16.2: Line integrals 11/2: 16.3: FTCLI
11/5: Review 11/7: Exam 2 11/9: 16.4: Green’s Theorem
11/12: Veteran’s Day 11/14: 16.5 Curl and divergence 11/16: 16.6: Surfaces and area
11/19: 16.6: Surfaces continued 11/21: 16.7: Surface integrals 11/23: Thanksgiving break
11/26: 16.7: Surface integrals cont’d 11/28: 16.8: Stokes’ Theorem 11/30: 16.9: Divergence Theorem
12/3: Review 12/5: Review