Gabriel's Turd

Multivariate Calculus 18.022, Fall 2014, MIT

See also the course Stellar page, the Piazza page, and Sam Watson's recitation page.

Instructor. Omer 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 others.

Lectures. Room E25-111, Tuesdays and Thursdays at 1, Fridays at 2.

Recitations. Mondays and Wednesdays:

Wuttisak Trongsiriwat at 12, in 26-322.
Office hours are Mondays 5 to 6 and Tuesdays 4 to 5, in E17-401U.
Menglu Wang at 11, in 36-112.
Office hours are Wednesdays 3 to 5, in E18-466B.
Sam Watson at 2, in 4-159.
Office hours are Mondays from 3 to 4 and Wednesdays from 4 to 5, in E18-466B.
Jun Yu at 12 and at 1, in E17-128.
Office hours are Wednesdays 2 to 4, in E18-466B.

Lecture notes. Based on lecture notes by James McKernan and on lectures by Pavel Etingof.

Lecture 1: Vectors in ℝ² and ℝ³. Given on September 4^th.
Lecture 2: The dot product. Given on September 5^th.
Lecture 3: The cross product. Given on September 9^th.
Lecture 4: Planes and distances in ℝ³. Given on September 11^th.
Lecture 5: ℝⁿ, linear transformations and matrices. Given on September 12^th.
Lecture 6: Cylindrical and spherical coordinates. Given on September 16^th.
Lecture 7: Functions. Given on September 18^th.
Lecture 8: Limits. Given on September 23^rd.
Lecture 9: Derivatives and partial derivatives. Given on September 25^th.
Lecture 10: More about derivatives. Given on September 26^th.
Lecture 11: Higher derivaties. Given on October 2^nd.
Lecture 12: The chain rule. Given on October 3^rd.
Lecture 13: Implicit functions. Given on October 7^th.
Lecture 14: Parametrized curves. Given on October 9^th.
Lecture 15: Curvature and torsion. Given on October 10^th.
Lecture 16: Vector fields. Given on October 14^th.
Lecture 17: Flow lines. Given on October 16^th.
Lecture 18: Divergence, gradient and curl. Given on October 17^th.
Lecture 19: Taylor polynomials. Given on October 23^rd.
Lecture 20: Maxima and minima: I. Given on October 24^th.
Lecture 21: Maxima and minima: II. Given on October 28^th.
Lecture 22: Double integrals. Given on October 30^th.
Lecture 23: More double integrals. Given on October 31^st.
Lecture 24: Triple integrals. Given on November 4^th.
Lecture 25: Change of coordinates: I. Given on November 6^th.
Lecture 26: Change of coordinates: II. Given on November 7^th.
Lecture 27: Line intergrals. Given on November 13^th.
Lecture 28: Green's Theorem. Given on November 18^th.
Lecture 29: More on conservative vector fields. Given on November 20^th.
Lecture 30: Surface integrals. Given on November 21^st.
Lecture 31: Flux. Given on November 25^th.
Lecture 32: The Divergence Theorem. Given on December 2^nd.
Lecture 33: Stokes's Theorem. Given on December 4^th.
Lectures 34 and 35: Calculus of variations. First half given on December 5^th.

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 on Stellar. 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.

Homework 1. Due September 18^th.
Homework 2. Due September 25^th.
Homework 3. Due October 2^nd.
Homework 4. Due October 9^th.
Homework 5. Due October 16^th.
Homework 6. Due October 23^th.
Homework 7. Due October 30^th.
Homework 8. Due November 6^th.
Homework 9. Due November 12^th.
Homework 10. Due November 20^th.
Homework 11. Due December 1^st.

Midterms. Three 50 minute midterm exams will take place on Tuesday, September 30^rd, Tuesday, October 21^st, and Thursday, November 13^th, 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.

First midterm exam.
Second midterm exam.
Third midterm exam.
Fourth midterm exam. This is an extra credit, take home exam, due on Friday, December 5^th at 11pm. It will count as an additional midterm for those who hand it in, provided it raises the grade.

Final. The 3 hour long final exam will take place on Wednesday, December 17^th, from 9am to noon, at the Johnson track.

Syllabus.

Vector algebra: the dot product, the cross product, matrices, determinant.
Functions of several variables: continuity, differentiability, derivatives.
Parametrized curves: arc length, curvature, torsion.
Vector fields: gradient, curl, divergence.
Multiple integrals, change of variables, line integrals, surface integrals.
Stokes' theorem in one, two, and three dimensions.
Calculus of variations.

The topics are similar to 18.02, but with more focus on mathematical concepts and proofs.

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 group. See math.mit.edu/learningcenter/ for more details.