Complex Variables I,

Complex analysis is the branch of mathematics that investigates functions of complex numbers, that is, functions whose independent and dependent variables are both complex numbers. The course extends concepts from the analysis of real valued functions to complex functions. Complex Analysis is of enormous practical use in applied mathematics and in Physics. Course Objectives:By the end of the course, the student should be able to: 

• Extend concepts of analysis of real variables, like sequences, limits of functions, continuity of function, series of real numbers, to complex numbers.
• Determine which functions are differentiable using Cauchy- Riemann equations.
• Solve equations involving elementary functions like e^z, log z, cos z, sin z, tan z, cosh z, sihn z.
• Integrate a complex function from definition, using the Cauchy Integral theorem, using the Deformation of contour theorem, using the Multiple Annulus theorem and using the Cauchy Integral formula.