COMPLEX ANALYSIS: Demystified and Simplified gives a new approach to local complex analysis, which is based on generalization of method of solution of Dirichlet’s problem for the Unit Disc. We explicitly construct an analytic function locally, giving its characteristic properties such as Cauchy’s theorem/integral formula; power series development; Poisson’s integral formula; maximum modulus principle, in one stroke. In the process, we present and develop the theory of exponential Fourier series as a generalization of trigonometric Fourier series and show that locally, analytic and elementary methods are the same.

Preface, Intent and Introduction / Complex Numbers and Functions / Riemann-Stieltjes Integration, Functions of Bounded Variation, Curves and Line Integrals / Differentiability, Analytic Functions and Moebius Transformations / Power Series, Exponential Function and Logarithm / Generalised Euler’s Summation formula, the Basic Fourier Series and Exponential Fourier Series / From Fourier Series to Laurent Series and Isolated Singularities / Dirichlet’s Problem for a Disc, Local Complex Analysis and Generalisations / Cauchy’s Theorem and its Consequences / Notations and Definitions.

Undergraduate and Postgraduate Students & Researchers