18.022: Multivariable Calculus

Table of contents

  1. Course Info
  2. Realistic Prerequisites
  3. Subject Matter
  4. Course Staff
  5. Lectures
  6. Problem Sets
  7. Exams
  8. Resources
  9. Grading
  10. Advice to Future Students

Course Info

Class Size 46
Hours/Week 9.8 (18 responses)
Instructors Alexei Borodin
Overall Rating 6.7/7.0

Realistic Prerequisites

  • The content of 18.01 is a hard prerequisite.
  • Experience with vector operations and set notation was helpful.

Subject Matter

  • Lectures were more theoretical with an emphasis on proofs, while PSET and test questions were computational and rarely had proofs.

Course Staff

  • Both Professor Borodin and the TA were described as caring and helpful, and willing to put in the time to help students.
  • Students were encouraged to ask questions during class.
  • Flexible and understanding, especially in regards to accommodations and schedules.


  • Students agreed that Professor Borodin was a fantastic lecturer.
  • Lectures were entertaining, engaging, and well-paced. They were good for a theoretical overview of the topic, and questions that “consistently challenge assumptions of mathematics.”
  • Textbook (Vector Calculus by Susan Colley) closely followed lectures and helped clarify explanations.
  • Office hours and PSETS helped reinforce what was learned in lecture and developed application skills.

Problem Sets

  • PSETS always consisted of textbook problems.
  • Students typically spent 2-3 hours a week on psets.
  • Most students agreed the problem sets were mostly computational or routine applications of course material. They were not perceived as very fun, challenging, or creative, but instead described as tedious, repetitive, or boring.
  • Lectures prepared students for psets.


  • Students described the exams as standard, straightforward, and fair.
  • Studying materials such as practice problems were provided.
  • Lectures prepared students for the exams.
  • Practice problems and OCW materials are useful in preparing for exams.
  • Difficulty of exams varied highly. Students agreed the second exam covered more complicated material and was more of a time crunch. Grade cutoffs were lowered to account for this.


  • Susan Jane Colley’s Vector Calculus (4th ed.) was used in the class, and was helpful and provided clear explanations.
  • Professor McKernan’s 2010 lecture notes were also provided but did not always align with what was covered in class.


  • Students felt that grading was fair and transparent.
  • Students mentioned that there was no credit for late work, and regrades were not openly offered.

Advice to Future Students

  1. “Spend time thinking about the material outside of class or you will become lost easily”
  2. “I would recommend taking this instead of 18.02 if you enjoy seeing proofs in lecture.”