Welcome to the permanent home page for Sections ES31 and WBP01 of MATH-2080 (Calculus 3) at Southeast Community College in the Fall term of 2020. I am Toby Bartels, your instructor.

Course administration:

Contact information:

Reading homework

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).
  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 September 17 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 October 15 Thursday.


  1. Integration on curves:
  2. Integrating vector fields:
  3. Integrating scalar fields:
  4. Double integrals on rectangles:
  5. Double integrals:
  6. Triple integrals:
  7. Systems of inequalities:
  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 November 12 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 December 3 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 (TBA).
This web page and the files linked from it were written by Toby Bartels, last edited on 2020 November 23. Toby reserves no legal rights to them.

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