Calculus III, Fall 2017

Calculus III: Multivariable Calculus, Fall 2017

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 with 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 (unless there is an exam, as below), which will consist of two to four problems selected from the homework problems assigned with 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
8/28: 1.1, 1.2: Vector algebra 8/30: 1.3, 1.4: Dot, cross products 9/1: 1.5: Lines and planes
9/4: Labor Day 9/6: 1.6: Surfaces 9/8: 1.8: Vector-valued functions
9/11: 1.9: Arc length 9/13: 2.1: Multi-variable functions 9/15: 2.2: Partial derivatives
9/18: 2.3: Tangent planes 9/20: 2.4: Gradient, directional derivatives 9/22: 2.5: Maxima and minima
9/25: 2.7: Lagrange multipliers 9/27: Review 9/29: Exam 1
10/2: 3.1: Double integrals 10/4: 3.2: Double integrals cont’d 10/6: 3.3: Triple integrals
10/9: 1.7: Curvilinear coords 10/11: 3.5: Change of variables 10/13: 3.6, 3.7: Applications
10/16: Fall break 10/18: Fall break 10/20: Fall break
10/23: 4.1: Line integrals 10/25: Line integrals cont’d 10/27: 4.2: Properties of line int’s
10/30: 4.2: Properties cont’d 11/1: 4.3: Green’s theorem 11/3: 4.3: Green’s thm cont’d
11/6: Review 11/8: Exam 2 11/10: Veteran’s Day
11/13: 4.4: Surface integrals 11/15: 4.4: Divergence theorem 11/17: 4.6: Div, grad, curl
11/20: 4.5: Stokes’ theorem 11/22: 4.5: Stokes’ cont’d 11/24: Thanksgiving break
11/27: Review/Extension 11/29: Review/extension 12/1: Review/extension
12/4: Review/Extension 12/6: Review/extension