Vector Calculus

University of Melbourne

Course Description

  • Course Name

    Vector Calculus

  • Host University

    University of Melbourne

  • Location

    Melbourne, Australia

  • Area of Study

    Calculus, Mathematics

  • Language Level

    Taught In English

    Hours & Credits

  • Credit Points

  • Recommended U.S. Semester Credits
    3 - 4
  • Recommended U.S. Quarter Units
    4 - 6
  • Overview

    This subject studies the fundamental concepts of functions of several variables and vector calculus. It develops the manipulation of partial derivatives and vector differential operators. The gradient vector is used to obtain constrained extrema of functions of several variables. Line, surface and volume integrals are evaluated and related by various integral theorems. Vector differential operators are also studied using curvilinear coordinates.

    Functions of several variables topics include limits, continuity, differentiability, the chain rule, Jacobian, Taylor polynomials and Lagrange multipliers. Vector calculus topics include vector fields, flow lines, curvature, torsion, gradient, divergence, curl and Laplacian. Integrals over paths and surfaces topics include line, surface and volume integrals; change of variables; applications including averages, moments of inertia, centre of mass; Green's theorem, Divergence theorem in the plane, Gauss' divergence theorem, Stokes' theorem; and curvilinear coordinates.

Course Disclaimer

Courses and course hours of instruction are subject to change.

Credits earned vary according to the policies of the students' home institutions. According to ISA policy and possible visa requirements, students must maintain full-time enrollment status, as determined by their home institutions, for the duration of the program.