Mathematics

Complex Analysis (L6)

Module code: G5261
Level 6
15 credits in spring semester
Teaching method: Lecture
Assessment modes: Unseen examination, Coursework

This module will explore the extension of mathematical analysis from the real numbers to the larger field of complex numbers, with an appeal to planar geometry for some intuition. The module will focus on complex differentiation and path integrals, including the deep theorem of Cauchy and its consequences such as the fundamental theorem of algebra, analytic continuation and the residue theorem.

Module learning outcomes

• Systematically understand the key algebraic structures and geometric interpretations of the field of complex numbers including de Moivre’s identity and complex roots of unity
• Systematically recognize and appreciate the differences between differentiable real functions and holomorphic complex functions
• Understand and be able to apply the deep theorem of Cauchy and its consequences to solve standard problems in complex analysis
• Evaluate certain real integrals via the residue theorem for complex path integrals