convergence.mws About this worksheet Author and Date Content, Purpose and Use Updates and log of modifications. Convergence of series of real and complex scalars A scalar real sequence Real scalar series A sequence of complex scalars The corresponding series of complex scalars Pointwise and uniform convergence Preparations Pointwise convergence Uniform convergence Convergence of Fourier series -- visually A basic example: Fourier approximation of a rectangular wave. The effect of termwise integration The effect of termwise differentiation Convergence of Laurent series -- using color.