This course equips sophomores in mathematics with a further background in mathematical analysis. Topics include series of functions, uniform continuity, double series, uniform convergence, differentiation of series of functions, integration of series of functions, special functions, Gamma functions, Hilbert space, Fourier series, orthogonality, completeness, transformations, the inverse function theorem, the implicit function theorem, vector analysis, multiple integration, line integration, and some basic concepts of differentiable manifolds.