MATH 264: Advanced Calculus

Winter 2008

This web page:

Lectures (start January 3): Tu, Thur 10:00-11:30, Arts Building W-120 (D. Jakobson's section)
There are no lectures on March 20
There will be a make-up lecture on Thursday, April 3, 18:30-20:00, in LEA 26.
For those who cannot come from 18:30-20:00 on April 3, there will be an earlier lecture (same material), from 14:00-15:30, in Burnside 934.
There will be no lecture on Thursday, April 10.
There will be a PDE review lecture on Wednesday, April 16, 18:00-20:00, in LEA 26.

  • Jian-Jun Xu
    Office: BH1247, Office Hours: Tue. Thur. 1:00-2:00pm
    Tel: 398-3849
    E-mail: xu AT
    Web Page:
  • D. Jakobson (course coordinator)
    Office: BH1212, Office Hours: Tue. 13:15-14:15 (time has changed!), Thur. 11:40-12:40 or by appointment
    Office hours during the week of April 14 to be announced
    Tel: 398-3828
    E-mail: jakobson AT
    Web Page:

  • Tutorials: There will be five tutorials per week. Tutorials start during the second week of classes.
  • Monday, 1:30-2:30pm, Burnside 1B24, Forhad Hasnat
  • Tuesday, 1-2pm, Arts 145, Bassel Hakoura
  • Wednesday, 1:30-2:30pm, Burnside 1B24, Hamza Bari
  • Thursday, 1-2pm, Arts 145, Saad Ahmad
  • Friday, 1:30-2:30pm, Burnside 1B23, Yevgeniy Goldenberg

  • Prerequisites: MATH 260 or MATH 262 or MATH 151 or MATH 152 or equivalent.
    Restrictions: Open only to students in the Faculty of Engineering. Not open to students taking or having taken MATH 248, MATH 265 or MATH 314.
    Text: "Calculus: A Complete Course", by Robert A. Adams. Chapters 14,15,16.
    Lecture Notes
  • L. Laayouni's notes, Winter 2007
  • J-J. Xu's notes on PDE, Fall 2007
  • Heat equation: a short summary (D. Jakobson): pdf and ps
  • Wave equation, a short summary (D. Jakobson).
    Part 1: pdf and ps.
    Part 2: pdf and ps.
    Part 3: pdf and ps.
    Part 4: pdf and ps.

  • Syllabus: Multiple Integration: double and triple integrals, change of variables, surface integrals. Vector fields: conservative fields, line integrals, flux. Vector calculus: grad, div, curl, Green's theorem, divergence theorem, Stokes' theorem, potentials. PDE and Fourier series: heat equation, separation of variables (possibly other topics as time permits).
    Assignments: There will be be 5 written assignments. Due dates will be announced in class and on the course web page. Late assignments will not be accepted, except in cases of emergency. Depending on availability of TA and other factors, some problems may not be marked.
  • Assignment 1, due Thursday, January 17. ps and pdf.
    Adams sec. 14.2 no. 18; sec. 14.3 no. 11; sec. 14.4 no. 20, 25; sec. 14.6 no. 19, 20. Solutions: ps and pdf.
  • Assignment 2, due Thursday, February 14 (extended!): ps and pdf. Solution of the problem on field lines: ps and pdf. Solutions: ps and pdf
  • Assignment 3, due Thursday, March 13 (extended): ps and pdf. Solutions: ps and pdf
  • Assignment 4, due Tuesday, March 25 (extended): ps and pdf. Solutions: ps and pdf
  • The following formulas may be useful:
    ∫ sinn(x) dx =-sinn-1(x)*cos(x)/n+((n-1)/n)* ∫ sinn-2(x) dx;
    ∫ cosn(x) dx =cosn-1(x)*sin(x)/n+((n-1)/n)* ∫ cosn-2(x) dx.
  • Assignment 5, CANCELLED (solutions to selected problems will be provided shortly): ps and pdf. Solutions: pdf
  • Table of integrals: pdf and ps
  • Solutions of winter 2006 PDE assignment: pdf
  • A quick review of differential equations: 2nd order constant coefficient; method of undetermined coefficients; method of variation of parameters.

  • Webwork: There will be additional problems on Webwork (computer-graded).
  • Assignment 1, due January 17.
  • Assignment 2, due February 5 (extended).
  • Assignment 3, due February 12 (extended).
  • Assignment 4, due Tuesday, March 11.
  • Assignment 5, due Thursday, March 27 (extended).
  • Assignment 6, due Thursday, April 3. The following formulas may be useful:
    ∫ x sin(x) dx =sin(x)-x*cos(x); AND ∫ xn sin(x) dx = -xn cos(x)+n* ∫ xn-1 cos(x) dx
    ∫ x cos(x) dx =cos(x)+x*sin(x); AND ∫ xn cos(x) dx = xn sin(x)-n* ∫ xn-1 sin(x) dx
    ∫ eax sin(nx) dx = eax[a sin(nx) - n cos(nx)]/(a2+n2)
    ∫ eax cos(nx) dx = eax[a cos(nx) + n sin(nx)]/(a2+n2)
    The following three formulas hold if a2 != b2:
    ∫ sin(ax) sin(bx)dx = -sin((a+b)x)/(2(a+b)) + sin((a-b)x)/(2(a-b))
    ∫ cos(ax) cos(bx)dx = sin((a+b)x)/(2(a+b)) + sin((a-b)x)/(2(a-b))
    ∫ sin(ax) cos(bx)dx = -cos((a+b)x)/(2(a+b)) - cos((a-b)x)/(2(a-b))

  • Midterm: Thursday, February 21, 2008, 18:00-21:00. Rooms STBIO S1/4 and S1/3. McGill approved calculators are permitted. Missed midterm cannot be redone. If you miss the midterm for any reason, the weights for your mark will be: Assignments 20%, Final 80%.
    Midterm solutions: ps and pdf
    Old Midterms: A year ago: Solutions, version 1: ps and pdf; version 2: ps and pdf
    Another old midterm: problems and solutions.
    Final: April 18, 9-12am. Solutions: pdf

    No additional work will be accepted for D, F, or J.
    Solutions of old finals:
  • 2006 final: pdf
  • 2007 final: pdf and ps

  • Grading scheme: Your final mark will be the largest of the following: [20% Assignments + 20% Midterm + 60% Final]; OR [20% Assignments + 80% Final].
    WebCT: Your scores on assignments, midterm, final, and your final mark will be posted on WebCT
    Related course material from previous courses at McGill:
  • Old Math 265 Course Pack, by J.C. Taylor and J. Labute. Here is another version.
  • Math 264, Fall 2007 web page (J.J. Xu)

  • HELPDESK and their email:
    WEB LINKS in Calculus, Algebra, Geometry and Differential Equations.
    Paul's online notes in Advanced Calculus (Lamar university)
    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).