MTH305 - Complex Analysis I
Complex Analysis I introduces the fundamental concepts of functions of a complex variable, focusing on analytic functions and their properties. The course explores complex numbers, limits, continuity, differentiability, and the formulation of functions in the complex plane. Emphasis is placed on understanding the behavior of complex functions, including elementary functions, mappings, and the geometric interpretation of analytic functions. Key topics such as the Cauchy-Riemann equations, complex integration, and contour integrals are developed to provide a strong theoretical foundation for further studies in mathematics, engineering, and applied sciences.
Mathematics and Statistics
School of Pure and Applied Sciences
Adewole Kayode
Objectives
The objective of this course is to equip students with a solid understanding of the theory and techniques of complex variable analysis. It aims to develop students’ ability to analyze and solve problems involving complex functions, understand the conditions for analyticity, and apply fundamental theorems of complex analysis. The course also seeks to build analytical thinking and prepare students for advanced topics in pure and applied mathematics.
Learning Outcomes
By the end of the course, students should be able to demonstrate proficiency in performing operations with complex numbers, determine the analyticity of complex functions using the Cauchy-Riemann equations, evaluate complex integrals using standard techniques, and apply key theorems such as Cauchy’s theorem and integral formula. Students will also be able to represent complex functions graphically, analyze conformal mappings, and solve practical problems involving complex variables in scientific and engineering contexts.