Calendar description

Functions of several variables, Lagrange multipliers, vector valued functions, directional derivatives, gradient, divergence, curl, transformations, Jacobians, inverse and implicit function theorems, multiple integration including change of variables using polar, cylindrical and spherical co-ordinates, Green's theorem, Stoke's theorem, divergence theorem, line integrals, arc length.

Prerequisite:

Mathematics 2000 and 2050

Course objectives

Students are expected to be able to learn various tools of vector calculus.

How do you get additional help?

  • Please drop by my office (HH-3035) during the office hours ( Mon and Wed 11:00-12:00).
  • If you need to speak to me outside of those times, I am mostly available in my office (HH-3035) on Mondays, Wednesdays, and Fridays between 09:00 and 16:00. You may simply drop by my office on these days. However, it is not guaranteed that I will be in the office outside office hours, unless you make an appointment.
  • Please feel free to email me any time (any day) for quick questions, but I may reply your email(s) only on working days.

    • Outline of the course

    Vector functions
    		 Section(s)
    • Curves defined by parametric equations
    • Vector functions and space curves
    • Derivatives and integrals of vector functions
    • Arc length and curvature
    • Motion in space: velocity and acceleration
      10.1
      13.1
      13.2
      13.3
      13.4
    Partial derivatives
    • Functions of several variables
    • Partial derivatives
    • Linear approximations
    • Directional derivatives and the gradient vector
    • Lagrange Multipliers
      12.6,14.1
      14.3
      14.4
      14.6
      14.8
    Multiple integrals
    • Double integral over general region
    • Double integral in polar coordinates
    • Applications of double integrals
    • Triple integrals
    • Change of variables in multiple integrals
      15.3
      15.4
      15.5
      15.6-15.8
      15.9
    Vector calculus
    • Vector fields
    • Line integrals
    • The fundamental theorem of line integrals
    • Green's Theorem
    • Curl and divergence
    • Parametric surfaces and their areas
    • Surface integrals
    • Stoke's theorem
    • Divergence theorem
      16.1
      16.2
      16.3
      16.4
      16.5
      16.6
      16.7
      16.8
      16.9

    Marking scheme

  • 6 home works
  • One mid-term test
  • The final exam
    		•  20%
    30%
    50%

    Text book

    Calculus: Early Transcendentals (6E) by Stewart, J., Thomson Brooks/Coles

    This is the standard text book for this course. The following books are also useful:
  • Multivariable calculus: Early transcendentals (6E) by Stewart, J
  • Vector Calculus by Marsden, J
  • Vector Calculus by Lovric, M
    •

    Home work assignments [top]

  • Please report any typo if you notince in the solution

    • Assignment 1 Due Sep 19 Solution 1
    Assignment 2 Due Oct 3 Solution 2
    Assignment 3 Due Oct 15 Solution 3
    There was a typo in Q3(a) of home work 3
    Midterm test Oct 20 Solution
    Assignment 4 Due Oct 29 Solution 4
    Assignment 5 Due Nov 17 Solution 5
    Assignment 6 Due Dec 1 Solution 6
    Assignment 7 DO NOT HAND IN No solutions will be posted.

    Remarks:

  • Homework assignments must be handed in at the start of class on the due date. No late assignments will be marked.
  • If you miss the mid term test for acceptable reasons, the corresponding weighting may be shifted to the final exam. You need to send me an email explaining the circumstances. Make sure to write "Your full name -- missed work" in the subject line. A doctor's note is required if you were sick. The missed work has to be settled no later than one week of the event.