Uniform convergence of sequences, series of functions and improper integrals, applications to the gamma function and Fourier series; Weierstrass Approximation Theorem. Differentiation of transforms: inverse and implicit function theorems. Applications to geometry and analysis: transformations of multiple integrals, integrals over curves and surfaces. Differential geometry: differential forms, the theorems of Green, Gauss and Stokes; exact and closed forms.
Text: Principles of Mathematical Analysis (3rd edition) by Walter Rudin.