Complex Analysis and Functions of a Complex Variable

Complex analysis is a fundamental branch of mathematics used widely across physics, signal processing, and quantitative engineering. This course provides a clear, beginner-friendly pathway to understanding complex functions and their mathematical applications. You will begin with basic geometric concepts on the complex plane before moving step-by-step into differentiation, integration, and series expansions. What you will learn: Understand foundational terminology, regions, and curves on the complex plane; Evaluate limits, continuity, and single-valued versus multi-valued complex functions; Apply the Cauchy-Riemann conditions to test for analyticity; Calculate complex contour integrals using fundamental integration theorems; Expand functions into Taylor and Laurent series to analyze singularities; Apply residue theory to evaluate complex integrals and real improper integrals. The written explanations guide you systematically from essential definitions to key theorems and structured problem-solving patterns. This course is designed for beginners, students, and technical professionals looking for a accessible introduction to complex variables. Start reading today to build a confident working knowledge of complex analysis.