Vol. 7, Issue 1, Part A (2025)

Real and Complex Analysis are two fundamental branches of mathematical analysis that play a critical role in both theoretical and applied mathematics. Real Analysis focuses on real-valued functions, sequences, and series, providing a rigorous foundation for calculus and a deeper understanding of continuity, integration, and differentiation. Complex Analysis, on the other hand, extends these concepts to the complex plane, where functions of a complex variable exhibit powerful and often surprising properties. This paper explores key concepts in both fields, including measure theory, Lebesgue integration, analytic functions, and contour integration. Through examples and applications, we highlight how Real and Complex Analysis contribute to advancements in physics, engineering, and other scientific disciplines.