Complex Integration and Cauchy's Theorem


Book Description

Originally published in 1914, this book provides a concise proof of Cauchy's Theorem, with applications of the theorem to the evaluation of definite integrals.




Lectures on Complex Integration


Book Description

The theory of complex functions is a strikingly beautiful and powerful area of mathematics. Some particularly fascinating examples are seemingly complicated integrals which are effortlessly computed after reshaping them into integrals along contours, as well as apparently difficult differential and integral equations, which can be elegantly solved using similar methods. To use them is sometimes routine but in many cases it borders on an art. The goal of the book is to introduce the reader to this beautiful area of mathematics and to teach him or her how to use these methods to solve a variety of problems ranging from computation of integrals to solving difficult integral equations. This is done with a help of numerous examples and problems with detailed solutions.




Complex Integration of Multiple Brain Systems in Therapy (IPNB)


Book Description

Enabling patients’ minds to change the structure of their brains. Beatriz and Albert Sheldon have spent the last 20 years developing the novel therapeutic paradigm called Complex Integration of Multiple Brain Systems (CIMBS). They have pioneered new methodology for "reading" and assessing emotional states using their patients’ carefully observed psychophysiological phenomena as empirical evidence. CIMBS also incorporates the latest groundbreaking research on neuroplasticity, brain development, and therapeutic change. This book details their novel neurobiological and psychotherapeutic paradigm—and reveals how therapists can use it for more successful treatment. Clients come to therapy troubled by deeply ingrained neural circuits and emotional habits. The authors demonstrate how they use psychophysiological perspectives to recognize limitations in brain systems that are interfering with their patients’ functioning. And through “physiopsychotherapy,” they activate self-affirming, nonconscious emotional resources to change rigid, maladaptive neural circuits. CIMBS offers a way of “integrating” these [brain system] resources to foster more complex and flexible mental functioning and to produce more successful psychotherapeutic outcomes. The therapeutic attachment relationship between therapist and patient, and “present moment” experiences within the session rather than recollections of past trauma, are key elements in this unique emotional resource-based mode of therapy. This book is wide-ranging in documenting CIMBS' success at operationalizing neuroscience research. Translating their academic, scientific, and clinical research and successful training courses into a reference work that you can hold in your hands and savor at leisure, the Sheldons have produced an approachable, intriguing, yet comprehensive milestone in the psychotherapeutic literature.




Complex Integration of Multiple Brain Systems in Therapy


Book Description

Enabling patients’ minds to change the structure of their brains. Beatriz and Albert Sheldon have spent the last 20 years developing the novel therapeutic paradigm called Complex Integration of Multiple Brain Systems (CIMBS). They have pioneered new methodology for "reading" and assessing emotional states using their patients’ carefully observed psychophysiological phenomena as empirical evidence. CIMBS also incorporates the latest groundbreaking research on neuroplasticity, brain development, and therapeutic change. This book details their novel neurobiological and psychotherapeutic paradigm—and reveals how therapists can use it for more successful treatment. Clients come to therapy troubled by deeply ingrained neural circuits and emotional habits. The authors demonstrate how they use psychophysiological perspectives to recognize limitations in brain systems that are interfering with their patients’ functioning. And through “physiopsychotherapy,” they activate self-affirming, nonconscious emotional resources to change rigid, maladaptive neural circuits. CIMBS offers a way of “integrating” these [brain system] resources to foster more complex and flexible mental functioning and to produce more successful psychotherapeutic outcomes. The therapeutic attachment relationship between therapist and patient, and “present moment” experiences within the session rather than recollections of past trauma, are key elements in this unique emotional resource-based mode of therapy. This book is wide-ranging in documenting CIMBS' success at operationalizing neuroscience research. Translating their academic, scientific, and clinical research and successful training courses into a reference work that you can hold in your hands and savor at leisure, the Sheldons have produced an approachable, intriguing, yet comprehensive milestone in the psychotherapeutic literature.




Introduction to Complex Analysis


Book Description

This book describes a classical introductory part of complex analysis for university students in the sciences and engineering and could serve as a text or reference book. It places emphasis on rigorous proofs, presenting the subject as a fundamental mathematical theory. The volume begins with a problem dealing with curves related to Cauchy's integral theorem. To deal with it rigorously, the author gives detailed descriptions of the homotopy of plane curves. Since the residue theorem is important in both pure and applied mathematics, the author gives a fairly detailed explanation of how to apply it to numerical calculations; this should be sufficient for those who are studying complex analysis as a tool.




Phenotypic Integration


Book Description

The interface of evolution and development has attracted the attention of evolutionary and developmental biologists, geneticists, and organismal biologists. Pigliucci (ecology, evolutionary biology, University of Tennessee) and Preston (botany, Standford University) bring together work by experts in the field of phenotype integration, shedding ligh.




Policy Integration for Complex Environmental Problems


Book Description

This book proposes a comprehensive conceptualization of policy integration and negotiates pertinent theoretical, methodological and applied issues from the perspective of selected EU policies - rural development, regional development, transport, social, economic, environmental, water resources, and biodiversity policy.




Irresistible Integrals


Book Description

This book, first published in 2004, uses the problem of exact evaluation of definite integrals as a starting point for exploring many areas of mathematics.




Managing Complex Projects


Book Description

Concerned with the management of complex long-term engineering projects, this important volume, of great interest to postgraduate students of business, technology management and engineering, reports on a set of rich, novel and unique findings concerning the conduct and management of three high profile and complex projects. The major investments which constitute complex long-term projects represent an increasingly important source of economic activity, often with particularly significant consequences for economic growth and public policy. This informative volume expertly contributes to broader debates concerning new organizational forms, knowledge management and organizational learning and the management of innovation in project-based settings.




Complex Analysis


Book Description

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.