Multivariate Calculus 18.022, Fall 2014, MIT
Tamuz, room E18-478. Office hours are Tuesdays 3 to 5 and
Fridays 1 to 2. More time available by appointment if
necessary. Students are encouraged to meet the instructor
during office hours, rather than communicate by
email. The Piazza
page is a good place to post questions that may interest
Lectures. Room E25-111, Tuesdays and Thursdays at 1,
Fridays at 2.
Recitations. Mondays and Wednesdays:
Trongsiriwat at 12, in 26-322.
Office hours are Mondays
5 to 6 and Tuesdays 4 to 5, in E17-401U.
Wang at 11, in 36-112.
Office hours are Wednesdays 3 to 5,
- Sam Watson at
2, in 4-159.
Office hours are Mondays from 3 to 4 and
Wednesdays from 4 to 5, in E18-466B.
Yu at 12 and at 1, in E17-128.
Office hours are Wednesdays
2 to 4, in E18-466B.
Lecture notes. Based
notes by James McKernan and on lectures by Pavel Etingof.
- Lecture 1: Vectors
and ℝ3. Given
on September 4th.
- Lecture 2: The dot
product. Given on September
- Lecture 3: The cross product. Given
on September 9th.
- Lecture 4: Planes and distances
in ℝ3. Given
on September 11th.
5: ℝn, linear
transformations and matrices. Given
on September 12th.
- Lecture 6: Cylindrical and spherical
on September 16th.
- Lecture 7: Functions. Given
on September 18th.
- Lecture 8: Limits. Given
on September 23rd.
- Lecture 9: Derivatives and partial
derivatives. Given on September
- Lecture 10: More about
derivatives. Given on September
- Lecture 11: Higher
derivaties. Given on October
- Lecture 12: The chain
rule. Given on October 3rd.
- Lecture 13: Implicit functions. Given on October 7th.
- Lecture 14: Parametrized
curves. Given on October
- Lecture 15: Curvature and
torsion. Given on October 10th.
- Lecture 16: Vector
fields. Given on October 14th.
- Lecture 17: Flow
lines. Given on October 16th.
- Lecture 18: Divergence, gradient
and curl. Given on October 17th.
- Lecture 19: Taylor polynomials. Given on October 23rd.
- Lecture 20: Maxima and minima:
I. Given on October 24th.
- Lecture 21: Maxima and minima:
II. Given on October 28th.
- Lecture 22: Double integrals. Given on October 30th.
- Lecture 23: More double integrals. Given on October 31st.
- Lecture 24: Triple
integrals. Given on November 4th.
- Lecture 25: Change of
coordinates: I. Given on November 6th.
- Lecture 26: Change of
coordinates: II. Given on November 7th.
- Lecture 27: Line
intergrals. Given on November
- Lecture 28: Green's Theorem. Given on November
- Lecture 29: More on conservative
vector fields. Given on November
- Lecture 30: Surface integrals. Given on November
- Lecture 31: Flux. Given on November
- Lecture 32: The Divergence Theorem. Given on December
- Lecture 33: Stokes's Theorem. Given on December
- Lectures 34 and 35: Calculus of
variations. First half given on December
Textbook. Colley's Vector Calculus, third edition.
Grading. The final grade will consist of 25% homework, 45%
midterms, and 30% final exam.
Homework. Homework is submitted in E17-131, and is due
every Thursday by 1. Late homework will not be accepted, but the
lowest score will be dropped. Problem sets will be posted
Collaboration on homework is encouraged, but individually written
solutions are required. Also, it is mandatory to name all
collaborators and sources of information on each assignment. Any
such named source may be used.
Midterms. Three 50 minute midterm exams will take place on
Tuesday, September 30rd, Tuesday, October
21st, and Thursday, November 13th, during
class hours, in Walker,
room 50-340. There will be no make-up exams, but the grade of
the lowest midterm exam will be disregarded, if lower than the
grade of the final exam.
Final. The 3 hour long final exam will take place on
Wednesday, December 17th, from 9am to noon, at the Johnson track.
The topics are similar to 18.02, but with more focus on mathematical
concepts and proofs.
- Vector algebra: the dot product, the cross product, matrices, determinant.
- Functions of several variables: continuity,
- Parametrized curves: arc length, curvature, torsion.
- Vector fields: gradient, curl, divergence.
- Multiple integrals, change of variables, line integrals,
- Stokes' theorem in one, two, and three dimensions.
- Calculus of variations.
Students in need of assistance or in distress. If you are
dealing with a personal or medical issue that is impacting your
ability to attend class, complete work, or take an exam, you have
the possibility of discussing this
with Student Support
Services (S3). The deans in S3 will
verify your situation, and then discuss with you how to address
the missed work. You may consult with S3 in 5-104 or at
617-253-4861. Also, S3 has walk-in hours: Monday
through Friday, 9-10am.
MIT is committed to the principle of equal access. Students who
need disability accommodations are encouraged to speak with
Kathleen Monagle, Associate Dean, prior to or early in the
semester so that accommodation requests can be evaluated and
addressed in a timely fashion. Even if you are not planning to use
accommodations, it is recommended that you meet with Student
Disability Services staff to
familiarize yourself with the services and resources of the
office. You may also consult with Student Disability Services in
5-104 or at 617-253-1674.
Math learning center. Graduate and undergraduate tutors
are available in room 4-159, Mondays through Thursdays from 3 to 5
and from 7:30 to 9:30 (pm), to help with problem sets or answer
general questions. The center is also a good place to find a study
math.mit.edu/learningcenter/ for more details.