Complex analysis is one of the most central subjects in mathematics. It is compelling and rich in its own right, but it is also remarkably useful in a wide variety of other mathematical subjects, both pure and applied. This book is different from others in that it treats complex variables as a direct development from multivariable real calculus. As each new idea is introduced, it is related to the corresponding idea from real analysis and calculus. The text is rich with examples andexercises that illustrate this point. The authors have systematically separated the analysis from the topology, as can be seen in their proof of the Cauchy theorem. The book concludes with several chapters on special topics, including full treatments of special functions, the prime number theorem,and the Bergman kernel. The authors also treat $Hp$ spaces and Painleve's theorem on smoothness to the boundary for conformal maps. This book is a text for a first-year graduate course in complex analysis. It is an engaging and modern introduction to the subject, reflecting the authors' expertise both as mathematicians and as expositors.

This volume is a collection of articles translated from Russian editions of the journal "Kvant"--T.p. verso.

Most of the matter in our solar system, and, probably, within the whole universe, exists in the form of ionized particles. On the other hand, in our natural environ ment, gaseous matter generally consists of neutral atoms and molecules. Only under certain conditions, such as within the path oflightning or in several technical devices (e. g. gas discharges, rocket engines, etc. ) will some of the atoms and molecules be ionized. It is also believed that the chemistry of the earth's troposphere predomi nantly proceeds via reactions between neutral particles. (The complex system of atmospheric chemistry will be treated in one of the forthcoming volumes to this series. ) Why, then, are ions considered so important that hundreds oflaboratories all over the world (including some of the most prestigious) are involved in research pro grams on ions, covering many different facets, from biochemistry to physics? One may obtain as many different answers as there are research groups busy in this field. There is, however, one simple, common feature which makes it attractive to work with ions: since they carry one or more net elementary charges, they can easily be gui ded, focused or separated by appropriate electric and magnetic fields, and, last but not least, they can easily be detected. Apart from these advantages, which are welcome and appreciated by the researcher, the study of molecular ions can provide insight into very fundamental aspects of the general behavior of molecules.

Finite-dimensional Morse theory is easier to present fundamental ideas than in infinite-dimensional Morse theory, which is theoretically more involved. However, finite-dimensional Morse theory has its own significance. This volume explains the finte-dimensional Morse theory.

Dr. Richard Polin's Neonatology Questions and Controversies series highlights the most challenging aspects of neonatal care, offering trustworthy guidance on up-to-date diagnostic and treatment options in the field. In each volume, renowned experts address the clinical problems of greatest concern to today's practitioners, helping you handle difficult practice issues and provide optimal, evidence-based care to every patient. - Stay fully up to date in this fast-changing field with Gastroenterology and Nutrition, 3rd Edition. - Emerging knowledge about the basic developmental physiology of upper intestinal motility as it relates to reflux and feeding tolerance, and immaturities in motility by altering composition of feedings and pharmacologic means. - New content on genetics and pharmacology, the role of inflammation in systemic diseases in other organs as well as necrotizing enterocolitis, optimizing administration of lipids to preterm infants, and administering lipids to infants who are at high risk for complications secondary to suboptimal lipid therapies. - Current coverage of the composition of human milk and clinical trials that address the efficacy of donor milk in comparison to formula and own mother's milk. - Consistent chapter organization to help you find information quickly and easily. - The most authoritative advice available from world-class neonatologists who share their knowledge of new trends and developments in neonatal care. Purchase each volume individually, or get the entire 7-volume set!Gastroenterology and NutritionHematology, Immunology and GeneticsHemodynamics and CardiologyInfectious Disease and Pharmacology New Volume!Nephrology and Fluid/Electrolyte PhysiologyNeurologyThe Newborn Lung

Classroom Discourse and the Space of Learning is about learning in schools and the central role of language in learning. The investigations of learning it reports are based on two premises: First, whatever you are trying to learn, there are certain necessary conditions for succeeding--although you cannot be sure that learning will take place when those conditions are met, you can be sure that no learning will occur if they are not. The limits of what is possible to learn is what the authors call "the space of learning." Second, language plays a central role in learning--it does not merely convey meaning, it also creates meaning. The book explicates the necessary conditions for successful learning and employs investigations of classroom discourse data to demonstrate how the space of learning is linguistically constituted in the classroom. Classroom Discourse and the Space of Learning: *makes the case that an understanding of how the space of learning is linguistically constituted in the classroom is best achieved through investigating "classroom discourse" and that finding out what the conditions are for successful learning and bringing them about should be the teacher's primary professional task. Thus, it is fundamentally important for teachers and student teachers to be given opportunities to observe different teachers teaching the same thing, and to analyze and reflect on whether the classroom discourse in which they are engaged maximizes or minimizes the conditions for learning; *is both more culturally situated and more generalizable than many other studies of learning in schools. Each case of classroom teaching clearly demonstrates how the specific language, culture, and pedagogy molds what is happening in the classroom, yet at the same time it is possible to generalize from these culturally specific examples the necessary conditions that must be met for the development of any specific capability regardless of where the learning is taking place and what other conditions might be present; and *encompasses both theory and practice--providing a detailed explication of the theory of learning underlying the analyses of classroom teaching reported, along with close analyses of a number of authentic cases of classroom teaching driven by classroom discourse data which have practical relevance for teachers. Intended for researchers and graduate students in education, teacher educators, and student teachers, Classroom Discourse and the Space of Learning is practice- and content-oriented, theoretical, qualitative, empirical, and focused on language, and links teaching and learning in significant new ways.