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Differential equations.

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This book, one of the first on G2 manifolds in decades, collects introductory lectures and survey articles largely based on talks given at a workshop held at the Fields Institute in August 2017, as part of the major thematic program on geometric analysis. It provides an accessible introduction to various aspects of the geometry of G2 manifolds, including the construction of examples, as well as the intimate relations with calibrated geometry, Yang-Mills gauge theory, and geometric flows. It also features the inclusion of a survey on the new topological and analytic invariants of G2 manifolds that have been recently discovered. The first half of the book, consisting of several introductory lectures, is aimed at experienced graduate students or early career researchers in geometry and topology who wish to familiarize themselves with this burgeoning field. The second half, consisting of numerous survey articles, is intended to be useful to both beginners and experts in the field.

Geometry, Differential. --- Differential geometry --- Differential geometry. --- Algebraic geometry. --- Differential Geometry. --- Algebraic Geometry. --- Algebraic geometry --- Geometry

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Outside back cover : "Chapman & Nakielny's Aids to Radiological Differential Diagnosis is a well-loved radiology resource, used by trainees and practitioners worldwide to hone their knowledge of radiological differential diagnosis for the most commonly encountered conditions throughout the body. It is an invaluable quick-reference companion in everyday practice, as well as an essential study tool when preparing for the FRCR or similar examinations. First published 35 years ago Stephen Chapman and Richard Nakielny's original aims remain as relevant today as when the book was originally conceived. However radiology has expanded rapidly in recent years and this Seventh Edition is the biggest revision this book has had in its long history with major changes incorporated into nearly every section. Comprehensive lists of differential diagnoses to aid effective diagnoses Closely aligned to the needs of current FRCR curriculum Brief, to the point text and clear page format allows for rapid access to key information Part 2 of the book has been restructured to focus on multisystem disorders which cannot be fully covered in the individual chapters in Part 1. A new chapter on Nuclear Medicine has been added to reflect its importance in modern medical imaging. The chapter on head and neck conditions has been significantly expanded. Important discriminating features have been added to nearly every differential to aid the reader in developing a strategy for reaching a diagnosis. The top differentials in each list which are considered important for radiology trainees to learn for exams are underlined."

Radiography --- Diagnosis, Differential

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This book presents a concise introduction to a unified Hilbert space approach to the mathematical modelling of physical phenomena which has been developed over recent years by Picard and his co-workers. The main focus is on time-dependent partial differential equations with a particular structure in the Hilbert space setting that ensures well-posedness and causality, two essential properties of any reasonable model in mathematical physics or engineering. As a unique feature, this powerful tool for tackling time-dependent partial differential equations is subsequently applied to many equations. By means of illustrative examples, from the straightforward to the more complex, the authors show that many of the classical models in mathematical physics as well as more recent models of novel materials and interactions are covered, or can be restructured to be covered, by this unified Hilbert space approach. The reader should require only a basic foundation in the theory of Hilbert spaces and operators therein. For convenience, however, some of the more technical background requirements are covered in detail in the appendix. The theory is kept as elementary as possible, making the material suitable for a senior undergraduate or master’s level course. In addition, researchers in a variety of fields whose work involves partial differential equations and applied operator theory will also greatly benefit from this approach to structuring their mathematical models in order that the general theory can be applied to ensure the essential properties of well-posedness and causality.

Partial differential equations --- differentiaalvergelijkingen

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When one has to deal with fluid flows, magnetic fields or heat transfer in stars, one faces the partial differential equations that govern these processes. These phenomena are naturally multi-dimensional and their study requires new and sophisticated models. This volume gathers the lecture notes which summarize the essence of the lectures and conferences given by world experts in the field of multi-dimensional modelling of stars, during the 2018 Evry Schatzman School held in Roscoff, France. It gives the present status of our understanding of several processes that occur in stars, like thermal convection, double-diffusive convection, dynamo effect or baroclinic flows. Every subject is discussed under the light of the most recent results of nowadays research and is made accessible to all newcomers, either students or researchers who wish to join the field.

Differential equations, Partial