A Comprehensive Course in Analysis by Poincare Prize winner Barry Simon is a five-volume set that can serve as a graduate-level analysis textbook with a lot of additional bonus information, including hundreds of problems and numerous notes that extend the text and provide important historical background. Depth and breadth of exposition make this set a valuable reference source for almost all areas of classical analysis. Part 2A is devoted to basic complex analysis. It interweaves three analytic threads associated with Cauchy, Riemann, and Weierstrass, respectively. Cauchy's view focuses on the differential and integral calculus of functions of a complex variable, with the key topics being the Cauchy integral formula and contour integration. For Riemann, the geometry of the complex plane is central, with key topics being fractional linear transformations and conformal mapping. For Weierstrass, the power series is king, with key topics being spaces of analytic functions, the product formulas of Weierstrass and Hadamard, and the Weierstrass theory of elliptic functions. Subjects in this volume that are often missing in other texts include the Cauchy integral theorem when the contour is the boundary of a Jordan region, continued fractions, two proofs of the big Picard theorem, the uniformization theorem, Ahlfors's function, the sheaf of analytic germs, and Jacobi, as well as Weierstrass, elliptic functions.
This book provides a modern and up-to-date treatment of the Hilbert transform of distributions and the space of periodic distributions. Taking a simple and effective approach to a complex subject, this volume is a first-rate textbook at the graduate level as well as an extremely useful reference for mathematicians, applied scientists, and engineers.<br> <br> The author, a leading authority in the field, shares with the reader many new results from his exhaustive research on the Hilbert transform of Schwartz distributions. He describes in detail how to use the Hilbert transform to solve theoretical and physical problems in a wide range of disciplines; these include aerofoil problems, dispersion relations, high-energy physics, potential theory problems, and others.<br> <br> Innovative at every step, J. N. Pandey provides a new definition for the Hilbert transform of periodic functions, which is especially useful for those working in the area of signal processing for computational purposes. This definition could also form the basis for a unified theory of the Hilbert transform of periodic, as well as nonperiodic, functions.<br> <br> The Hilbert transform and the approximate Hilbert transform of periodic functions are worked out in detail for the first time in book form and can be used to solve Laplace's equation with periodic boundary conditions. Among the many theoretical results proved in this book is a Paley-Wiener type theorem giving the characterization of functions and generalized functions whose Fourier transforms are supported in certain orthants of Rn.<br> <br> Placing a strong emphasis on easy application of theory and techniques, the book generalizes the Hilbert problem in higher dimensions and solves it in function spaces as well as in generalized function spaces. It simplifies the one-dimensional transform of distributions; provides solutions to the distributional Hilbert problems and singular integral equations; and covers the intrinsic definition of the testing function spaces and its topology.<br> <br> The book includes exercises and review material for all major topics, and incorporates classical and distributional problems into the main text. Thorough and accessible, it explores new ways to use this important integral transform, and reinforces its value in both mathematical research and applied science.<br> <br> The Hilbert transform made accessible with many new formulas and definitions<br> <br> Written by today's foremost expert on the Hilbert transform of generalized functions, this combined text and reference covers the Hilbert transform of distributions and the space of periodic distributions. The author provides a consistently accessible treatment of this advanced-level subject and teaches techniques that can be easily applied to theoretical and physical problems encountered by mathematicians, applied scientists, and graduate students in mathematics and engineering.<br> <br> Introducing many new inversion formulas that have been developed and applied by the author and his research associates, the book: <br> * Provides solutions to the distributional Hilbert problem and singular integral equations <br> * Focuses on the Hilbert transform of Schwartz distributions, giving intrinsic definitions of the space H(D) and its topology <br> * Covers the Paley-Wiener theorem and provides many important theoretical results of importance to research mathematicians <br> * Provides the characterization of functions and generalized functions whose Fourier transforms are supported in certain orthants of Rn <br> * Offers a new definition of the Hilbert transform of the periodic function that can be used for computational purposes in signal processing <br> * Develops the theory of the Hilbert transform of periodic distributions and the approximate Hilbert transform of periodic distributions <br> * Provides exercises at the end of each chapter--useful to professors in planning assignments, tests, and problems
Real Science. Real Life. Now with DSM5 coverage throughout.
This leading-edge author team, consisting of three active researchers, clinicians, and educators, take a scientist-practitioner approach emphasizing the rich blend of both the science and practice of abnormal psychology throughout the text. The developmental trajectory of each condition is discussed where appropriate and scientific findings with respect to race and gender are incorporated into discussions about each condition. Biological findings are integrated with findings from social and behavioral sciences, highlighting the complexity of abnormal behavior and how it is often influenced by a wide range of variables. The authors encourage students to look at psychological disorders along a continuum and analyze disorders in terms of whether the individual's behavior creates distress or impairs daily functioning. Importantly, an effort is made to "bring to life" the nature of these conditions by providing vivid clinical descriptions. In addition to short descriptions used liberally throughout each chapter, a fully integrated case study is presented at the end of each chapter, again illustrating the interplay of biological, psychosocial and emotional factors.
The 3rd edition includes coverage of the Diagnostic and Statistical Manual (DSM-5), with updated text references and examples throughout.
MyPsychLab is an integral part of the Beidel / Bulik / Stanley program. Key learning applications include MyPsychLab video series with new virtual case studies.
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0205968244 / 9780205968244 Abnormal Psychology Plus NEW MyPsychLab with Pearson eText -- Access Card Package
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