Math 31BH - Honors Multivariable Calculus

Welcome to Math 31BH!

Course description:

This course is the second in the Mathematics Department's Honors sequence. We will cover multivariable calculus: point-set topology, limits and continuity, derivatives in several variables, tangent spaces, Taylor polynomials, Min/max in several variables, Lagrange multipliers, manifolds.
The three courses in the Honors sequence, Math 31ABC, cover essentially the same material as do Math 20F, 20C, and 20E, respectively, but at a more sophisticated conceptual level. The Honors sequence emphasizes proofs, so students completing it will be exempt from taking Math 109 (Mathematical Reasoning).
The Honors sequence is intended for mathematics majors and prospective mathematics majors (although others are very welcome) and gives a much better view of what upper-division mathematics is like than does the standard Math 20 sequence.

Instructor: Dragos Oprea, doprea "at", AP&M 6-101.

Lectures: MWF, 2pm-2:50pm, AP&M B-412.

Office hours:

Monday 3-4, Friday 3-4 in AP&M 6-101.
I am available for questions after lecture or by appointment. Also, feel free to drop in if you see me in my office.

Teaching Assistant:

Daniel Vallieres dvallieres "at" you know where.
Daniel's Office Hours: Thursday 12 - 2pm, Office: APM 5132.


A grade of B- or better in Math 31AH.

Textbook: J. H. Hubbard and B. B. Hubbard, Vector Calculus, Linear Algebra, and Differential Forms: A Unified Approach, Fourth Edition.


Homework (20%), two midterms (20% each), final (40%).


There will be weekly homework assignments, due in section on Tuesdays, or before then in the drop box on the sixth floor of AP&M. Students are allowed to discuss the homework assignments among themselves, but are expected to turn in their own work - copying someone else's is not acceptable

Important Dates and Holidays:

  • Monday, January 3: First lecture
  • Monday, January 17: Martin Luther King Holiday
  • Friday, January 28: Midterm I
  • Saturday, January 29: Drop deadline
  • Monday, February 21: Presidents' Day
  • Friday, February 25: Midterm II
  • Sunday, March 5: Withdrawal date
  • Friday, March 11: Last lecture
  • Monday, March 14: Final exam (3-6pm).

  • Lecture Summaries