Integrability
of continuous functions over suitable domains, iterated
integrals and Fubini's theorem, counterexamples, change of variables,
Jacobian determinants, polar and spherical coordinates, volumes, vector
fields, divergence, curl, line and surface integrals, Green's and Stokes's
theorems, differential forms, general Stokes's theorem.
The course continues the study of vector calculus, begun in the first
and second year calculus courses.
It will begin by reviewing some of the vector differential calculus
studied in second year, without restricting
attention solely to dimensions 2 and 3. This
portion of the course closes with a treatment of the implicit function
theorem. The course then continues the study
of multiple integrals by treating the
changeofvariables formula and Jacobian determinants. It concludes by
treating line and surface integrals, including the versions of the
fundamental
theorem of calculus that they obey, namely Green's theorem, Stokes's
theorem,
and the divergence theorem. General differential forms will be covered
only if time permits.
The textbook is still to be determined.
Prerequisite:AS/SC/MATH 2010 3.0; or AS/SC/AK/MATH
2310 3.0; or
AS/SC/MATH 2015 3.0 and written permission of the Mathematics
Undergraduate Director (normally granted only to students
proceeding in Honours programmes in Mathematics or in the
Specialized Honours Programme in Statistics).
Corequistite (or prerequisite):AS/SC/MATH 2022 3.0 or AS/SC/AK/MATH 2222 3.0.
Coordinator: T. Salisbury
