Continues the rigorous theoretical introduction to analysis in several variables, including basic linear algebra, begun in MAT216.
Topics to be covered:
- Real analytic mappings and series, power series, Dirichlet series, Stone-Weierstrass theorem
- Vector spaces, bilinear functions, endomorphisms, minimal and characteristic polynomials
- Geometry of mappings between n-dimensional real vector spaces, inverse mapping theorem, implicit functions, rank theorem, submanifolds and manifolds
- Riemann integral, integration over Jordan domains, Fubini's theorem, limits and improper integrals, change of variables
- line integrals, differential forms, Stokes's Theorem in general dimensions