Real Analysis I (Mathematical Analysis I)
Metric spaces and the topology of R^n. Compact sets, the geometry of Euclidean Spaces, limits and continuous mappings. Rigorous definitions of limits using filter bases. Heine-Borel Theorem, Bolzanno-Weirstrass Theorem. Partial differentiation. Vector valued functions, extrema, the inverse and implicit function theorems, and multiple integrals. Line integral and surface integrals, the theorems of Green, Gauss, and Stokes.
