Download PDF by Robert C. Gunning, Hugo Rossi: Analytic Functions of Several Complex Variables

By Robert C. Gunning, Hugo Rossi

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In this chapter we basically concern ourselves with functions that take numerical values as f ( z ) ,where the argument, z, is called the independent variable. We usually define a new variable, y, as which is called the dependent variable. Functions with multiple variables, that is, multivariate functions, can also be defined. For example, for each point (z,y) in some region of the zy-plane we may assign a unique real number, f ( z ,y), according t o the rule We now say that f (z, y) is a function with two independent variables, 2 and y.

Xxvii This Page Intentionally Left Blank CHAPTER 1 FUNCTIONAL ANALYSIS A function is basically a rule that relates the members of one set of objects to the members of another set. In this regard, it has a very wide range of applications in both science and mathematics. Functional analysis is basically the branch of mathematics that deals with the functions of numbers. In this chapter, we confine ourselves t o the real domain and introduce some of the most commonly used techniques in functional analysis.

I am indebted to Prof. L. Leach for his insightful comments and for meticulously reading two of the chapters. I am grateful to Wiley for a grant to prepare the camera-ready copy, and I would like to thank my editor Susanne SteitzFiller for sharing my excitement. My work on the two books Mathematical Meth,ods in Science and Engineering and Essentials of Mathematical Methods in Science and Engineering has spanned an uninterrupted period of 6 years. With the time spent on my two books in Turkish published in the years 2000 and 2004, which were basically the forerunners of my first book, this project has dominated my life for almost a decade.

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Analytic Functions of Several Complex Variables by Robert C. Gunning, Hugo Rossi


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