Course DescriptionComplex analysis is one of the most beautiful and useful disciplines of mathematics, with applications in engineering, physics, and astronomy, as well as other branches of mathematics. This introductory course reviews the basic algebra and geometry of complex numbers; develops the theory of complex differential and integral calculus; and concludes by discussing a number of elegant theorems, including many--the fundamental theorem of algebra is one example--that are consequences of Cauchy's integral formula. Other topics include De Moivre's theorem, Euler's formula, Riemann surfaces, Cauchy-Riemann equations, harmonic functions, residues, and meromorphic functions. The course should appeal to those whose work involves the application of mathematics to engineering problems as well as individuals who are interested in how complex analysis helps explain the structure and behavior of the more familiar real number system and real-variable calculus.
Course OutlineThis introductory course reviews the basic algebra and geometry of complex numbers, the theory of complex differential and integral calculus, and a variety of theorems that are consequences of Cauchy’s integral formula.
PrerequisitesFamiliarity with differentiation and integration of real-valued functions.
Applies Towards the Following Certificates
- Study Abroad at UCLA Program : Required