Complex Variables and Applications

This course is intended to provide computational techniques and a concise theory of functions of one complex variable. Topics are selected from: complex numbers and functions, analytic functions, Cauchy-Riemann equations, elementary functions, contour integration, Cauchy integral formula, series expansion, zeros, singularities, residue theorem and definite integrals, linear fractional transformation, harmonic functions and their applications. Students taking this course are expected to have knowledge in advanced calculus.