Welcome to the permanent home page for Sections ES31 and WBP01 of MATH-2080 (Calculus 3) at Southeast Community College in the Spring term of 2021. I am Toby Bartels, your instructor.

Course administration

Contact information


The official textbook for the course is the 4th Edition of University Calculus: Early Transcendentals by Hass et al published by Addison Wesley (Pearson). There is also a packet of course notes (DjVu).

Curves and functions

  1. General review:
  2. Parametrized curves:
  3. Standard parametrizations:
  4. Integrating parametrized curves:
  5. Arclength:
  6. Functions of several variables:
  7. Topology in several variables:
  8. Limits in several variables:
  9. Vector fields:
  10. Linear differential forms:
  11. Differentials:
Quiz 1, covering the material in Problem Sets 1–11, is available on February 4 Thursday.


  1. Partial derivatives:
  2. Levels of differentiability:
  3. Directional derivatives:
  4. Gradient vector fields:
  5. Matrices:
  6. The Chain Rule:
  7. Tangent flats and normal lines:
  8. Linearization:
  9. Estimation:
  10. Local optimization:
  11. Constrained optimization:
  12. Lagrange multipliers:
Quiz 2, covering the material in Problem Sets 12–23, is available on March 4 Thursday.


  1. Integration on curves:
  2. Integrating vector fields:
  3. Integrating scalar fields:
  4. Double integrals on rectangles:
  5. Double integrals:
  6. Systems of inequalities:
  7. Triple integrals:
  8. Areas, volumes, and averages:
  9. The area element:
  10. Coordinate transformations:
  11. Polar coordinates:
  12. Area integrals in polar coordinates:
  13. Volume integrals in polar coordinates:
Quiz 3, covering the material in Problem Sets 24–36, is available on April 1 Thursday.

More integration

  1. Parametrized surfaces:
  2. Integrals along surfaces:
  3. Flux across surfaces:
  4. Integrals on surfaces:
  5. Moments:
  6. Conservative vector fields and exact differential forms:
  7. Exterior differentials:
  8. Green's Theorem:
  9. Stokes's Theorem:
  10. Gauss's Theorem:
  11. Cohomology:
Quiz 4, covering the material in Problem Sets 37–47, is available on April 22 Thursday.


  1. Curves and functions:
  2. Differentiation:
  3. Integration:
  4. More integration:

Final exam

A comprehensive final exam is on December 16 Wednesday from 9:00 to 10:40 (face-to-face), or whenever you schedule with me to take it by December 17 Thursday. The exam will consist of questions similar in style and content to those in the practice final exam.
This web page and the files linked from it were written by Toby Bartels, last edited on 2021 April 12. Toby reserves no legal rights to them.

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