Theory of functions of a complex variable pdf
Complex VariablesSkip to search form Skip to main content. Carrier and Max Krook and Carl E. Carrier , Max Krook , Carl E. Pearson Published DOI: Complex numbers and their elementary properties 2. Analytic functions 3. Contour integration 4.
Complex Analysis - Fundamental(Lecture1)
Functions of a complex variable are used to solve applications in various branches of mathematics, science, and engineering. Functions of a Complex Variable: Theory and Technique is a book in a special category of influential classics because it is based on the authors' extensive experience in modeling complicated situations and providing analytic solutions. The book makes available to readers a comprehensive range of these analytical techniques based upon complex variable theory. Proficiency in these techniques requires practice. The authors provide many exercises, incorporating them into the body of the text. By completing a substantial number of these exercises, the reader will more fully benefit from this book.
In mathematics , a holomorphic function is a complex-valued function of one or more complex variables that is, at every point of its domain , complex differentiable in a neighbourhood of the point. The existence of a complex derivative in a neighbourhood is a very strong condition, for it implies that any holomorphic function is actually infinitely differentiable and equal, locally, to its own Taylor series analytic. Holomorphic functions are the central objects of study in complex analysis. Though the term analytic function is often used interchangeably with "holomorphic function", the word "analytic" is defined in a broader sense to denote any function real, complex, or of more general type that can be written as a convergent power series in a neighbourhood of each point in its domain. The fact that all holomorphic functions are complex analytic functions, and vice versa, is a major theorem in complex analysis. Holomorphic functions are also sometimes referred to as regular functions. The phrase "holomorphic at a point z 0 " means not just differentiable at z 0 , but differentiable everywhere within some neighbourhood of z 0 in the complex plane.
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