Complex Integration, Cauchy and Residue Theorems - Essence of Complex Analysis

This course on complex integration, Cauchy and residue theorems aims to provide a crash course in complex analysis leading up to the Residue theorem. The learning outcomes include gaining a more intuitive understanding of complex integration using Pólya vector field, comprehending the importance of Jacobian in complex differentiation and Cauchy-Riemann equations, and understanding the relationships between Cauchy integral formula and Laurent coefficients. The course teaches skills such as parametrization, complex differentiation, and applying the Residue theorem. The teaching method involves a slower-paced explanation to ensure better comprehension, with a focus on more "applicable" concepts in complex analysis. The intended audience for this course includes individuals interested in advanced mathematics, particularly in the field of complex analysis.