معلومات المقرر

Math 4 “Complex Functions” is a foundational course that introduces the theory and applications of functions of a complex variable. It begins with the structure of complex numbers and their geometric representation in the complex plane, then develops the concept of complex functions, including limits and continuity. The course emphasizes differentiability in the complex sense, leading to the study of the Cauchy–Riemann equations and analytic (holomorphic) functions, which possess strong properties such as infinite differentiability. It further explores integration in the complex plane through line integrals, Cauchy’s theorem, and Cauchy’s integral formula. Advanced topics include power series expansions and the classification of singularities. Throughout the course, students learn how these concepts are applied in fields such as physics, engineering, and applied mathematics, particularly in solving problems involving waves, fluid flow, and signal processing.