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Complex analysis Wikipedia ~ Complex analysis traditionally known as the theory of functions of a complex variable is the branch of mathematical analysis that investigates functions of complex numbers It is useful in many branches of mathematics including algebraic geometry number theory analytic combinatorics applied mathematics as well as in physics including the branches of hydrodynamics thermodynamics and particularly quantum mechanics By extension use of complex analysis also has applications in engineerin
Analysis Complex analysis Britannica ~ Analysis Analysis Complex analysis In the 18th century a farreaching generalization of analysis was discovered centred on the socalled imaginary number i −1 In engineering this number is usually denoted by j The numbers commonly used in everyday life are known as real numbers but in one sense this name is misleading
Complex Analysis from Wolfram MathWorld ~ Complex analysis is an extremely powerful tool with an unexpectedly large number of practical applications to the solution of physical problems Contour integration for example provides a method of computing difficult integrals by investigating the singularities of the function in regions of the complex plane near and between the limits of integration
Introduction to Complex Analysis Coursera ~ Complex analysis is the study of functions that live in the complex plane that is functions that have complex arguments and complex outputs The main goal of this module is to familiarize ourselves with such functions
Complex Analysis Princeton Lectures in Analysis No 2 ~ Numerous examples and applications throughout its four planned volumes of which Complex Analysis is the second highlight the farreaching consequences of certain ideas in analysis to other fields of mathematics and a variety of sciences Stein and Shakarchi move from an introduction addressing Fourier series and integrals to indepth considerations of complex analysis measure and integration theory and Hilbert spaces and finally further topics such as functional analysis
Complex Analysis People ~ Chapter One Complex Numbers 11 Introduction 12 Geometry 13 Polar coordinates Chapter Two Complex Functions 21 Functions of a real variable 22 Functions of a complex variable 23 Derivatives Chapter Three Elementary Functions 31 Introduction 32 The exponential function 33 Trigonometric functions 34 Logarithms and complex exponents
Complex Analysis ~ Complex Analysis Preface §i Introduction i1 Preliminaries i1 i2 Short description of the content i3 §1 Holomorphic functions 11 Simple properties 11 12 The geometric meaning of differentiability when f′z0 6 0 14 13 The CauchyRiemann differential equations 16 14 Power series 19 15 The exponential and trigonometric functions 113 16
Lecture Notes for Complex Analysis ~ try a preliminary answer to the question ”What is complex analysis” It is clear that any short answer must be incomplete and highly subjective In these lecture notes we take the position that the core of complex analysis is the study of power series P∞ n0 anz − z0 n and of the characteristic properties of
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