AS/SC/AK/ MATH 3010 3.0 W

Vector Integral Calculus

      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 change-of-variables 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.