MATH 262: Intermediate Calculus

Fall 2004



January 2005

Dmitry Jakobson's office hours to discuss the final marks for Math 262:

  • Monday, January 10, 1-3pm
  • Tuesday, January 11, 12noon-1pm
  • Wednesday, January 12, 11am-12:30pm
  • Later office hours to be announced.

  • Course web page: http://www.math.mcgill.ca/jakobson/courses/math262.html
    Instructors:
  • D. Jakobson (course coordinator), Lectures MWF 9:30-10:30, RPHYS 112
    Office: BH1212, Office Hours: Mon 10:30-11:30, Wed. 13:00-14:00
    Tel: 398-3828
    E-mail: jakobson@math.mcgill.ca
    Web Page: www.math.mcgill.ca/jakobson
  • V. Jaksic, Lectures MWF 9:30-10:30, ENGMC 204
    Office: BH1209, Office Hours: Mon. and Wed. 12:00-13:00
    Tel: 398-3827
    E-mail: jaksic@math.mcgill.ca
    Web Page: www.math.mcgill.ca/jaksic
  • B. Moore, Lectures MWF 9:30-10:30, ENGMD 279
    Office: BH1248, Office Hours: Wed. 10:30-11:30, Fri. 13:00-14:00
    Tel: 398-2998
    E-mail: moore@math.mcgill.ca
    Web Page: www.math.mcgill.ca/~moore

  • Tutorials
  • Monday, 12:30-13:30, ENGMC 210, Gaurav Gupta
  • Monday, 14:30-15:30, ENGMC 210, Sameer Ishtiaq
  • Wednesday, 12:30-13:30, ENGMD 280, Patrick Kechichian
  • Wednesday, 12:30-13:30, ENGMC 210, Andrew Di Battista
  • Wednesday, 13:30-14:30, ENGMC 304, Amit Monga

  • Undergraduate student assistants
  • Andrew Di Battista
  • Gaurav Gupta
  • Sameer Ishtiaq
  • Patrick Kechichian
  • Amit Monga

  • Prerequisites: Math 133 and Math 141.
    Text: Calculus: A Complete Course (5th ed.) by Robert Adams
    Syllabus: Chapters 9,10.1-10.4,11,12,13.1-13.4 of the Text. The following topics will be covered:
  • Series and power series. Series: geometric and p-series; integral, comparison and ratio tests for absolute convergence; alternating series test. Power series: operations on series, Taylor's theorem with remainder, Taylor and Maclaurin series for elementary functions, binomial theorem and series. Series solutions to ODEs at ordinary points.
  • Vector geometry. Lines, planes, dot and cross products.
  • Vector functions and curves. Differentiation of vector-valued functions. Curves and parametrization, arclength. Tangent, normal and conormal vectors and Frenet formulas. Tangent and Normal accelerations. Kepler's laws (if time permits).
  • Partial differentiation and differential calculus for vector-valued functions. Functions of several variables: visualisation, limits and continuity. Partial derivatives of 1st and higher order, tangent planes and normal lines, wave and Laplace equation. Linear approximation, differentiability, functions from n-space to m-space with Jacobian matrices. Gradients and directional derivatives. Implicit and inverse functions, Taylor polynomials and series in several variables.
  • Unconstrained and constrained extremal problems. Critical points and their classification. Extreme values on restricted domains. Method of Lagrange multipliers with one or more constraints.

  • WeBWorK assignments: These assignments will be available on the Web and will be answered on the Web. The WebWorK assignments will be posted at http://msr05.math.mcgill.ca/webwork/m262f04/
    The initial login/password is your 9 digit student number. Please CHANGE your password the first time you log in. There are eight assignments and seven best will count for the grade. Missed assignments cannot be redone. The WeBWorK assignments are worth 17% of your grade. The additional information about WeBWorK assignments is available at http://www.math.mcgill.ca/~jaksic/webwork.html. If you experience technical problems with WeBWorK please contact the administrator at wwadmin@math.mcgill.ca.
    Due dates
  • Assignment 1: September 23
  • Solutions to problems 9, 10: page 1, page 2, page 3, page 4
  • Assignment 2: September 29
  • Assignment 3: October 17
  • Solutions to problems 7, 11: page 1, page 2, page 3
  • Assignment 4: October 27
  • Solutions to problems 1, 4: page 1, page 2, page 3, page 4, page 5
  • Assignment 5: November 10
  • Assignment 6: November 18
  • Solutions to problem 2: page 1
  • Assignment 7: November 24
  • Solutions to problem 4: page 1, page 2, page 3
  • Assignment 8: December 2
  • Solutions to problem 3: page 1, page 2

  • Written assignments: There will be 3 written assignments posted on this web page (in .ps, .pdf and .dvi format). These assignments contain more difficult theoretical problems. Your solutions should be written in a clear, complete and logical way -- you must convince the marker that your solutions are correct. The assignments will be collected and returned in the class. After the due date the solutions will be posted on this web page. Missed assignments cannot be redone--instead, two best out of three will count for the grade. The written assignments are worth 3% of your grade.
    Due dates
  • Written Assignment 1 (dvi, ps, pdf): September 29.
  • Solutions for Assignment 1 in dvi, ps, pdf. Please note that there will be two points for each problem (and not ten points as was announced on the problem sheet by mistake).
  • Written Assignment 2 (dvi, ps, pdf): October 27.
  • Solutions for Assignment 2 in dvi, ps, pdf.
  • Written Assignment 3 (dvi, ps, pdf): November 22.
  • Solutions for Assignment 3 in dvi, ps, pdf.

  • Midterm: There will a midterm on October 21, 18:40-20:40, Rooms MD-HAR G-01, ENGMC 204, ENGTR 1100, ENGTR 1080, ENGTR 1090, ENGTR 2110, ENGTR 2120. The midterm will cover the material on series and power series; vector geometry; vector functions and curves in the Syllabus, i.e. Chapters 9,10.1-10.4,11.1 and 11.3 of the Text.

    Midterm solutions: dvi, ps, pdf

    Rooms for midterm:

  • ENGMC 204, Ab - Har (proctor: Jaksic)
  • ENGTR 1080, Hen - Laga (proctor: MGupta)
  • ENGTR 1090, Lagu - Mah (proctor: Ishtiaq)
  • ENGTR 1100, Man - Poit (proctor: Di Battista)
  • ENGTR 2110, Pol - Sim (proctor: Kechichian)
  • ENGTR 2120, Siv - Wam (proctor: Monga)
  • MD-HAR G-01, Wan - Z (proctor: Moore)
  • Jakobson will rotate between the rooms in ENGTR

  • Missed midterm cannot be redone. If you miss the midterm for any reason, the weights for your mark will be: Assignments 20%, Final 80%.
    Final: There will be a three hour final exam. Date: Thursday, December 9, 14:00-17:00

    Tutorial: Wednesday, December 8, Burnside 1B45, 18:00-20:00

    Supplemental: There will be a supplemental exam, counting 100% of the supplemental grade. No additional work will be accepted for D, F, or J.


    Old Finals: Go to SUMS, then click on "Exam Archive" (look for math 260 and math 222).
    Grading:
  • Your final mark will be the largest of the following: [20% Assignments + 20% Midterm + 60% Final]; OR [20% Assignments + 80% Final].
  • The Assignment mark (worth 20% of the final grade) will consist of your mark for Webwork (17%) and your mark for written assignments (3%).

  • WebCT: Your scores on assignments, midterm, final, and your final mark will be posted on WebCT
    TUTORIAL: Here is a nice tutorial.
    Course material from previous courses at McGill:
  • Random handouts from other courses taught by D. Jakobson. Linear algebra review: A note about determinants, ps and pdf. Computing curvature and torsion for curves that are not parametrized by arclength (solution of Problem 12 on p. 25 in do Carmo's book on Differential Geometry, see also section 11.4 of the Text), ps and pdf
  • Material from old Math 265 Course Pak (Prepared by Taylor and Labute): Chain Rule pdf and ps. Implicit Function Theorem pdf and ps
  • Sam Drury's web page for MATH 222
  • John Labute's web pages for Math 222: page 1 and page 2

  • HELPDESK and their email: helpdesk@math.mcgill.ca
    WEB LINKS in Calculus, Algebra, Geometry and Differential Equations.
    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).