Calculus III, Fall 2020

Calculus III: Multivariable Calculus, Fall 2020

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 is best 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 in order for you to practice and gain facility with the material. A selection of three to four of these problems will be collected weekly to provide feedback. Note: while you will receive scores on your returned homework, these numerical homework scores will not be used in your final evaluation; only your homework participation rate matters for evaluation purposes. This gives you a safe and low stakes opportunity for a regular appraisal of your performance leading up to the exams.

Workshop: An additional problem set will be given in the optional weekly workshop, providing an opportunity for additional practice and real time assistance. Along with office hours, this is also a good time to get help with homework problems.

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 assessed based on the following criteria, in descending order of significance:

You are always encouraged to check in if you have any concerns.

Tips for Success: These are based on the experience of past students in this class.

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 they 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
8/24: 12.1, 12.2, 12.3: Vectors, dot prod 8/26: 12.4, 12.5: Cross prod, lines, planes 8/28: 12.6: Surfaces
8/31: 13.1, 13.2: Curves and velocity 9/2: 13.3: Arc length 9/4: 14.1: Multivariable functions
9/7: Labor Day 9/9: 14.2, 14.3: Limits, partial derivatives 9/11: 14.4, 14.5: Tan. planes, chain rule
9/14: 14.6: Gradient 9/16: 14.7: Local extrema 9/18: 14.8: Lagrange Multipliers
9/21: 14.7, 14.8 Extrema continued 9/23: Review 9/25: Exam 1
9/28: 15.1: Double integrals 9/30: 15.2: Integrals over regions 10/2: 15.3: Polar coordinates
10/5: 15.4: Applications 10/7: 15.6: Triple Integrals 10/9: 15.7: Cylindrical coordinates
10/12: Fall Break 10/14: 15.8: Spherical coordinates 10/16: 15.6-15.8: Triple integral wrap-up
10/19:: Review 10/21: Exam 2 10/23: 16.1: Vector fields
10/26: 16.2: Line integrals 10/28: 16.3: FTCLI 10/30: Green’s Theorem
11/2: 16.5 Curl and divergence 11/4: 16.6: Surfaces and area 11/6: 16.7: Surface integrals
11/9: 16.6, 16.7: Surfaces cont’d 11/11: Veteran’s Day 11/14: 16.8: Stokes’ Theorem
11/16: 16.9: Divergence Theorem 11/18: 16.8, 16.9 Stokes’/Div. cont’d 11/20: Review
11/23: Review 11/25: Review 11/27: Thanksgiving