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Complex
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Complex Analysis
With this second volume, we enter the intriguing world of complex analysis.From the first theorems on, the elegance and sweep of the results is evident.The starting point is the simple idea of extending a function initially given for real values of the argument to one that is defined when the argument is complex.From there, one proceeds to the main properties of holomorphic functions, whose proofs are generally short and quite illuminating: the Cauchy theorems, residues, analytic continuation, the argument principle.With this background, the reader is ready to learn a wealth of additional material connecting the subject with other areas of mathematics: the Fourier transform treated by contour integration, the zeta function and the prime number theorem, and an introduction to elliptic functions culminating in their application to combinatorics and number theory.Thoroughly developing a subject with many ramifications, while striking a careful balance between conceptual insights and the technical underpinnings of rigorous analysis, Complex Analysis will be welcomed by students of mathematics, physics, engineering and other sciences. The Princeton Lectures in Analysis represents a sustained effort to introduce the core areas of mathematical analysis while also illustrating the organic unity between them.Numerous examples and applications throughout its four planned volumes, of which Complex Analysis is the second, highlight the far-reaching 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 in-depth considerations of complex analysis; measure and integration theory, and Hilbert spaces; and, finally, further topics such as functional analysis, distributions and elements of probability theory.
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God Complex
LONGLISTED FOR THE LAUREL PRIZEGod Complex is a sweeping and corrosive epic, a narrative poem that tells the story of the breakdown of a relationship against a backdrop of progressive environmental degradation.A grieving body moves through states of toxicity, becoming an instrument for measuring the impact of pollutants. an entwining of human and non-human, built environment and natural landscape blurs perspective and distorts logic, creating an erratic decline into disorder.Loss is divined everywhere: in human relations, in the ruptures of class and privilege, and the poisoning of the planet. It is through a purgatorial leavening of pain that the narrator comes to terms with the delicate, shifting states of the ecological systems that merge with and surround us to create new forms of being and devotion.The result is visionary - a book that vibrates with urgency and feeling. 'This is a very fine book, quite unlike anything I've seen for a long time.It deserves to be read, and read again, and savoured.' Matt Merritt, Magma
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Elephant Complex
A gripping account of an under-reported island' Spectator, Book of the Year '[A] brilliant new book about an island that has a geography from heaven and a history from hell' Daily Telegraph'A brilliant work of travel, history and psychological insight . . . astute and sympathetic . . . very funny' Wall Street Journal Everyone has wanted a piece of paradiseJohn Gimlette - winner of the Dolman Prize and the Shiva Naipaul Prize for Travel Writing - is the kind of traveller you'd want by your side.Whether hacking a centuries-old path through the jungle, interrogating the surviving members of the Tamil Tigers or observing the stranger social mores of Colombo's city life, he brings his own unique insight to the page: a treasure-chest of research and a gift for wry amusement.Through him, Sri Lanka - all at once dazzling, strange, conflicted and beautiful - comes to life as never before.
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Which kitchen appliances also have a long lifespan, such as mixers, etc.?
Kitchen appliances such as mixers, blenders, and food processors are known for their long lifespan. These appliances are designed to withstand heavy use and are built with durable materials, making them reliable for many years. Additionally, high-quality brands and models of these appliances are often built to last, making them a worthwhile investment for any kitchen. Regular maintenance and proper care can also help extend the lifespan of these appliances.
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What is the Oedipus complex and the father complex?
The Oedipus complex is a concept in psychoanalytic theory proposed by Sigmund Freud. It refers to a child's unconscious desire for their opposite-sex parent, along with feelings of jealousy and rivalry towards their same-sex parent. The Oedipus complex is said to occur during the phallic stage of psychosexual development, typically between the ages of 3 and 6. The father complex, on the other hand, is a term used to describe a child's feelings and attitudes towards their father. It can encompass a range of emotions, including admiration, fear, and competition. The father complex is also a concept within psychoanalytic theory, and it is seen as a counterpart to the Oedipus complex. Both of these concepts are central to Freud's ideas about the development of personality and the formation of relationships.
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What is the complex conjugate of a complex number?
The complex conjugate of a complex number is obtained by changing the sign of the imaginary part of the number. For a complex number of the form a + bi, where a is the real part and b is the imaginary part, the complex conjugate is a - bi. In other words, the complex conjugate of a complex number is the reflection of the number across the real axis in the complex plane. The complex conjugate is denoted by adding a bar over the number, for example, the complex conjugate of z is denoted as z̅.
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Applied Complex Variable
First half of this highly-regarded book covers complex number plane; functions and limits; Riemann surfaces, the definite integral; power series; meromorphic functions, and much more.The second half deals with potential theory; ordinary differential equations; Fourier transforms; Laplace transforms and asymptotic expansion.Exercises included.
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Complex Analysis
The book provides an introduction to complex analysis for students with some familiarity with complex numbers from high school.It conists of sixteen chapters. The first eleven chapters are aimed at an Upper Division undergraduate audience.The remaining five chapters are designed to complete the coverage of all background necessary for passing PhD qualifying exams in complex analysis.Topics studied in the book include Julia sets and the Mandelbrot set, Dirichlet series and the prime number theorem, and the uniformization theorem for Riemann surfaces.The three geometries, spherical, euclidean, and hyperbolic, are stressed.Exercises range from the very simple to the quite challenging, in all chapters.The book is based on lectures given over the years by the author at several places, including UCLA, Brown University, the universities at La Plata and Buenos Aires, Argentina; and the Universidad Autonomo de Valencia, Spain.
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Complex Analysis
The present book is meant as a text for a course on complex analysis at the advanced undergraduate level, or first-year graduate level.The first half, more or less, can be used for a one-semester course addressed to undergraduates.The second half can be used for a second semester, at either level.Somewhat more material has been included than can be covered at leisure in one or two terms, to give opportunities for the instructor to exercise individual taste, and to lead the course in whatever directions strikes the instructor's fancy at the time as well as extra read ing material for students on their own.A large number of routine exer cises are included for the more standard portions, and a few harder exercises of striking theoretical interest are also included, but may be omitted in courses addressed to less advanced students.In some sense, I think the classical German prewar texts were the best (Hurwitz-Courant, Knopp, Bieberbach, etc. ) and I would recommend to anyone to look through them.More recent texts have emphasized connections with real analysis, which is important, but at the cost of exhibiting succinctly and clearly what is peculiar about complex analysis: the power series expansion, the uniqueness of analytic continuation, and the calculus of residues.
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Complex Analysis
Beginning with the ?rst edition of Complex Analysis, we have attempted to present the classical and beautiful theory of complex variables in the clearest and most intuitive form possible.The changes inthisedition, which include additions to ten of the nineteen chapters, are intended to provide the additional insights that can be obtainedby seeing a little more of the “bigpicture”.This includesadditional related results and occasional generalizations that place the results inaslightly broader context.The Fundamental Theorem of Algebra is enhanced by three related results.Section 1.3 offers a detailed look at the solution of the cubic equation and its role in the acceptance of complex numbers.While there is no formula for determining the rootsof a generalpolynomial,we added a section on Newton’sMethod,a numerical technique for approximating the zeroes of any polynomial. And the Gauss-Lucas Theorem provides an insight into the location of the zeroes of a polynomial and those of its derivative.Aseries of new results relate to the mapping properties of analytic functions.Arevised proof of Theorem 6.15 leads naturally to a discussion of the connection between critical points and saddle points in the complex plane.The proof of the SchwarzRe?ectionPrinciplehasbeenexpandedtoincludere?ectionacrossanalytic arcs, which plays a key role in a new section (14.3) on the mapping properties of analytic functions on closed domains. And our treatment of special mappings has been enhanced by the inclusion of Schwarz-Christoffel transformations.
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What are complex numbers and what does complex conjugate mean?
Complex numbers are numbers that can be expressed in the form a + bi, where a and b are real numbers and i is the imaginary unit (√-1). The complex conjugate of a complex number a + bi is denoted as a - bi, where the sign of the imaginary part is flipped. Geometrically, the complex conjugate reflects the original complex number across the real axis on the complex plane. The product of a complex number and its complex conjugate is always a real number.
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What is a pi complex and what is a sigma complex?
A pi complex is a type of coordination complex in which the metal ion is coordinated to a ligand through pi bonds. This type of complex typically involves the interaction of a metal ion with a ligand that contains a pi-bonding system, such as an aromatic ring or an alkene group. On the other hand, a sigma complex is a type of coordination complex in which the metal ion is coordinated to a ligand through sigma bonds. This type of complex typically involves the direct interaction of a metal ion with a ligand through the overlap of atomic orbitals, resulting in the formation of a sigma bond. Both pi and sigma complexes are important in the field of coordination chemistry and play a crucial role in the reactivity and stability of coordination compounds.
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Is 1z complex differentiable?
No, 1z is not complex differentiable. In order for a function to be complex differentiable at a point, it must satisfy the Cauchy-Riemann equations, which require the function to be holomorphic. Since 1z is not holomorphic (as it does not satisfy the Cauchy-Riemann equations), it is not complex differentiable.
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What are complex numbers?
Complex numbers are numbers that consist of a real part and an imaginary part, usually written in the form a + bi, where 'a' is the real part, 'b' is the imaginary part, and 'i' is the imaginary unit (√-1). These numbers are used in mathematics to solve equations that have no real solutions, such as the square root of a negative number. Complex numbers can be added, subtracted, multiplied, and divided, just like real numbers. They are an essential part of many branches of mathematics and physics.
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