Rouche's theorem in complex analysis book

In the rest of the book, the calculus of complex numbers will be built on the properties that we develop in this. An extension of rouches theorem via a korovkin type theorem 110. A function of the complex variable is analytic in an open set if it has a derivative at. Management accounting by aggarwal, aggarwal and jain, ramesh book. I hope you enjoy this video and find it beneficial for your studies in complex analysis. Rouches theorem states that if two functions fz and gz are analytic inside and on a simple closed curve c and if gz smaller than fz for. So, i just know some basic theorems about holomorphic functions. The book provides an introduction to complex analysis for students with some familiarity with complex numbers from high school. Unlike real analysis, complex differentiable functions have a large number of.

Complex analysis series in pure mathematics world scientific. In two years since the first edition of this book appeared some new suggestions. The first part comprises the basic core of a course in complex analysis for junior and senior undergraduates. The second part includes various more specialized topics as the argument principle, the schwarz lemma and hyperbolic geometry, the poisson integral, and the riemann mapping theorem. An extension of rouches theorem via a korovkin type theorem. Complex analysis related to locating the roots of functions. Arriving as a corollary of the argument principle, rouch. I apologize for some parts where the sound quality isnt too great. Support consider subscribing and liking if you enjoyed this video or if it helped you understand the subject. This is a textbook for a first course in functions of complex variable, assuming a. In complex analysis, rouches theorem gives a method for telling when two holomorphic functions have the same number of zeros in a region of the plane bounded by some curve.