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

Text book

The main text book is: Calculus: Early Transcendentals (6E) by Stewart, J., Thomson Brooks/Coles

There are two supplementary text books:

  • Vector Calculus by Marsden, J
  • Vector Calculus by Lovric, M

    • 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