Functions of complex variables and their applications
Foundations of the complex number system
The exponential form and finding complex roots
Functions of a complex variable
Limits and continuity in the complex plane
Analytic functions and the Cauchy-Riemann equations
Line integrals in the complex plane
The fundamental theorems of complex analysis
Taylor and Laurent series in the complex plane
Classification of singularities and residue theory
Applications of residues to integration
Angle-preserving transformations
Special functions and advanced theorems
Review and synthesis of complex analysis