MATH 222: Calculus 3. Winter 2014


COURSE PAGE:
http://www.math.mcgill.ca/jakobson/courses/math222.html
This page is under construction
INSTRUCTORS:
  • D. Jakobson
    Office: McGill, Burnside Hall, 1220
    Office Hours: Tuesday and Wednesday, 13:30-14:30
    Tel: 398-3828
    E-mail: jakobson@math.mcgill.ca

  • LECTURES:
  • Lecture: Tuesday and Thursday, 14:35-15:55, MDHAR G-10
  • Lectures start Tuesday, January 7, 2014.
  • The last lecture is on April 10, 2014.
  • Office hours during the week of March 10 will be on Thursday, 13:30-14:30, and Friday, 11:00-12:00.
  • There will be a review session on Monday, April 14, from 12:30-13:30, in Leacock 26.
  • There will be an additional review session the week of the final exam, time to be announced.

  • MARKERS' OFFICE HOURS
  • Kade Head-Marsden: Monday, 14:30-15:30, Burnside 1234 (starting February 10)
  • Jing Yang: Friday, 12:30-13:30, Burnside 1120

  • COURSE DESCRIPTION:
  • Infinite series: Infinite sequences and series. Testing convergence and divergence of series. Power series and their use for representing functions. Taylor polynomials and Taylor series. Stewart: Chapter 11.
  • Vector functions: Review of parametric equations and polar coordinates. Review of vector geometry. Derivatives and integrals of vector functions; arc length and curvature of space curves; motion in space: velocity and acceleration. Stewart: Chapter 13 + review (parts of Chapter 12).
  • Partial derivatives: Functions of several variables and their partial derivatives. Tangent planes. The chain rule. Directional derivatives and gradient vectors. Maximal and minimal values; Lagrange multipliers. Stewart: Chapter 14.
  • Multiple integrals: Fubini's Theorem. Double integrals over general regions; double integrals in polar coordinates. Triple integrals. Change of variables. Stewart: Chapter 15.

  • Textbook:
    J. Stewart, Multivariable Calculus: Early Transcendentals (Thomson Brooks/Cole).
    Material covered in the lectures:
  • Tuesday, January 7: Stewart, 11.1, parts of 11.2.
  • Thursday, January 9: Stewart, the rest of 11.2 and parts of 11.3 and 11.4.
  • Tuesday, January 14: Stewart, rest of 11.3 and 11.4, 11.5; started 11.6 (stated the Ratio test). Estimating the remainder will be discussed later.
  • Thursday, January 16: Stewart, 11.6, parts of 11.7, started 11.8.
  • Tuesday, January 21: Stewart, 11.8 and 11.9 (as time permits)
  • Thursday, January 23: 11.10.
  • Tuesday, January 28: rest of 11.10, estimating the remainder.
  • Thursday, January 30: review.
  • Tuesday, February 4: Review, Chapter 12 (most important topics: dot and cross product, orthogonality, equations of lines and plains)
  • Thursday, February 6: Stewart 13.1, 13.2, parts of 13.3 (defined curvature)
  • Tuesday, February 11: Stewart, 13.3, 13.4
  • Thursday, February 13: Stewart, 13.4, review
  • Tuesday, February 18: Review
  • Thursday, February 20: Stewart, 14.1, 14.2.
  • Tuesday, February 25: Stewart, 14.3, started 14.4.
  • Thursday, February 27: Stewart, 14.4, 14.5 as time permits.
  • Tuesday, March 11: Stewart, 14.5.
  • Thursday, March 13: Stewart, 14.5 and 14.6.
  • Tuesday, March 18: Stewart, 14.7, start 14.8.
  • Thursday, March 20: Stewart, 14.8, 15.2.
  • Tuesday, March 25: Stewart, 15.2, 15.3, 15.4.
  • Thursday, March 27: Stewart, 15.4, 15.5.
  • Tuesday, April 1: Stewart, 15.6, started 15.7.
  • Thursday, April 3: Stewart, 15.7, 15.8.
  • Tuesday, April 8: Stewart, 15.9, 15.10 (15.10 was partly covered previously).
  • Thursday, April 10: review.

  • Midterm:
  • The midterm exam will be on Tuesday, February 25, 18:15-20:15, held in MCMED 504 and MCMED 521. Midterm solutions.
  • The midterm will cover Chapter 11 and 13 of Stewart. Things to review: pdf.
  • There will be a review/tutorial on Monday, February 24, 17:30-18:30, ENGMC 304.
  • Practice midterm: Fall 2013. Solution to Problem 6 and complete.
  • For those who cannot take the midterm on February 25 because of time conflict with another midterm or because of a trip required for your study program only there will be a make-up midterm on Tuesday, March 18, in Maass 217, from 18:15-20:15. The material covered on that exam will be similar to the material on the February 25 midterm.
  • Solutions of the make-up midterm.

  • Final:
  • There will be a three-hour final exam. Time: April 29, 14:00-17:00
  • Practice final, Fall 2013 (pdf).
  • Another practice final, Winter 2013 (pdf).

  • Grading scheme:
    Your final mark will be the largest of the following: [15% Assignments + 25% Midterm + 60% Final]; OR [15% Assignments + 85% Final].


    Assignments:
  • The course will include both written and webwork assignments.
  • There will be two webwork assignments and one written assignments before the winter break. They will cover the material in Stewart, Chapters 11, 13 (and the review part of Chapter 12).
  • There will be two webwork assignments and one written assignments after the winter break. They will cover the material in Stewart, Chapters 14 and 15.
  • Webwork link for the course. A preliminary (non-credit) assignment has been posted.
  • The first webwork assignment has been posted. It covers the material in Stewart, Chapter 11. The dealine is January 31.
  • Your score on webwork assignment 1 will be the best 35 out of 43 problems. If you do more than 35 problems, the extra problems may be credited later if you do less than the max number of problems on one of the next problem sets.
  • The second webwork assignment has been posted. It covers the material in Stewart, Chapter 13, plus some review material. The deadline is February 22, 11:59pm.
  • Your score on webwork assignment 2 will be the best 24 out of 29 problems.
  • Written assignment 1, part 1 has been posted. Please, do any 2 problems out of 3; provide detailed explanations! Part 1 is due on February 13. Solutions, part 1.
  • Written assignment 1, part 2 has been posted. Please, do both problems; provide detailed explanations! Part 2 is due on February 21.
  • Solutions for part 1 and part 2.
  • Webwork assignment 3 has been posted. It covers the material in Stewart, Chapter 14. The deadline is March 27, 11:59pm (extended by 2 days).
  • Your score on webwork assignment 3 will be the best 30 problems.
  • Written assignment 2, part 1 has been posted. Please, do any 2 problems out of 3; provide detailed explanations! Part 1 is due on March 27 (extended by 2 days). Solutions (pdf).
  • Written assignment 2, part 2 has been posted. Please, do any 2 problems out of 3; provide detailed explanations! Part 2 is due on April 11.
  • Webwork assignment 4 is due on April 12, at 11:59am. Please, do any 20 problems.

  • Web Links in Algebra, Analysis, Geometry and Differential Equations (some links may be out of date, will correct over the next few days).
    NOTICE: McGill University values academic integrity. Therefore, all students must understand the meaning and consequences of cheating, plagiarism and other academic offences under the Code of Student Conduct and Disciplinary Procedures (see McGill web page on Academic Integrity for more information).
    NOTICE: In accord with McGill University's Charter of Student Rights, students in this course have the right to submit in English or in French any work that is to be graded.
    NOTICE: In the event of extraordinary circumstances beyond the University's control, the content and/or evaluation scheme in this course is subject to change.