From the algebraic properties of a complete number field to the Cauchy integral formula to conformal mapping, this text explores all facets of complex variables, with particular emphasis on using theory in practice. It presents complex analysis as a natural continuation of calculus, discusses the use of computer algebra systems in complex analysis, and integrates MATLAB exercises and examples throughout. Each chapter features applications from physics and engineering, including those involving differential equations. The text also includes stimulating exercises at the drill, theory, and exploration levels as well as numerous figures to clarify key concepts in complex variable theory.
