Course info

Welcome to Math 4 – Complex Functions!

We are pleased to welcome you to this course, which introduces the fundamental concepts and applications of functions of a complex variable. Throughout the course, you will progressively develop your understanding of complex numbers and their geometric representation in the complex plane, followed by the study of complex functions, limits, and continuity. You will then explore complex differentiability, the Cauchy–Riemann equations, and holomorphic functions, which form the foundation of complex analysis. The course continues with complex integration, line integrals, Cauchy’s theorem, and Cauchy’s integral formula, before introducing more advanced topics such as power series and the classification of singularities. Along the way, you will develop your mathematical reasoning and problem-solving skills through theoretical concepts, examples, and exercises. These ideas have important applications in physics, engineering, fluid mechanics, wave theory, and signal processing. We hope this course will be an engaging and rewarding learning experience, and we encourage you to participate actively, practice regularly, and make full use of the different learning activities available throughout the course.