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Author: Daniele Antonio Di Pietro Publisher: Springer Science & Business Media ISBN: 3642229808 Category : Mathematics Languages : en Pages : 392
Book Description
This book introduces the basic ideas to build discontinuous Galerkin methods and, at the same time, incorporates several recent mathematical developments. The presentation is to a large extent self-contained and is intended for graduate students and researchers in numerical analysis. The material covers a wide range of model problems, both steady and unsteady, elaborating from advection-reaction and diffusion problems up to the Navier-Stokes equations and Friedrichs' systems. Both finite element and finite volume viewpoints are exploited to convey the main ideas underlying the design of the approximation. The analysis is presented in a rigorous mathematical setting where discrete counterparts of the key properties of the continuous problem are identified. The framework encompasses fairly general meshes regarding element shapes and hanging nodes. Salient implementation issues are also addressed.
Author: James D. Murray Publisher: Springer Science & Business Media ISBN: 3662085429 Category : Mathematics Languages : en Pages : 783
Book Description
Mathematics has always benefited from its involvement with developing sciences. Each successive interaction revitalises and enhances the field. Biomedical science is clearly the premier science of the foreseeable future. For the continuing health of their subject mathematicians must become involved with biology. With the example of how mathematics has benefited from and influenced physics, it is clear that if mathematicians do not become involved in the biosciences they will simply not be a part of what are likely to be the most important and exciting scientific discoveries of all time. Mathematical biology is a fast growing, well recognised, albeit not clearly defined, subject and is, to my mind, the most exciting modern application of mathematics. The increasing use of mathematics in biology is inevitable as biol ogy becomes more quantitative. The complexity of the biological sciences makes interdisciplinary involvement essential. For the mathematician, biology opens up new and exciting branches while for the biologist mathematical modelling offers another research tool commmensurate with a new powerful laboratory technique but only if used appropriately and its limitations recognised. However, the use of esoteric mathematics arrogantly applied to biological problems by mathemati cians who know little about the real biology, together with unsubstantiated claims as to how important such theories are, does little to promote the interdisciplinary involvement which is so essential. Mathematical biology research, to be useful and interesting, must be relevant biologically.
Author: Anna Maria Hartkopf Publisher: World Scientific ISBN: 9811253080 Category : Science Languages : en Pages : 407
Book Description
Mathematical science communication, as well as the field of science communication in general, has gained momentum over the last few decades. Mathematical science communication aims to inform the public about contemporary research, enhance factual and methodological knowledge, and foster a greater interest and support for the science of mathematics. This enables the public to apply it to their practical life, and to decision-making on a greater scale. These objectives are met in the various formats and media through which mathematical science communication is brought to the public.The first 13 chapters of the book consist of best-practice examples from the areas of informal math education, museums and exhibitions, and the arts. The final 5 chapters discuss the structural aspects of mathematical science communication and contribute to the basis for its theoretical framework.
Author: Ke Chen Publisher: Springer Nature ISBN: 3030986616 Category : Mathematics Languages : en Pages : 1981
Book Description
This handbook gathers together the state of the art on mathematical models and algorithms for imaging and vision. Its emphasis lies on rigorous mathematical methods, which represent the optimal solutions to a class of imaging and vision problems, and on effective algorithms, which are necessary for the methods to be translated to practical use in various applications. Viewing discrete images as data sampled from functional surfaces enables the use of advanced tools from calculus, functions and calculus of variations, and nonlinear optimization, and provides the basis of high-resolution imaging through geometry and variational models. Besides, optimization naturally connects traditional model-driven approaches to the emerging data-driven approaches of machine and deep learning. No other framework can provide comparable accuracy and precision to imaging and vision. Written by leading researchers in imaging and vision, the chapters in this handbook all start with gentle introductions, which make this work accessible to graduate students. For newcomers to the field, the book provides a comprehensive and fast-track introduction to the content, to save time and get on with tackling new and emerging challenges. For researchers, exposure to the state of the art of research works leads to an overall view of the entire field so as to guide new research directions and avoid pitfalls in moving the field forward and looking into the next decades of imaging and information services. This work can greatly benefit graduate students, researchers, and practitioners in imaging and vision; applied mathematicians; medical imagers; engineers; and computer scientists.
Author: Georg Glaeser Publisher: Springer ISBN: 9783642146473 Category : Mathematics Languages : en Pages : 339
Book Description
How can one visualize a curve that fills the entire plane or all of space? Can a polyhedron be smoothly turned inside out? What is the projective plane? What does four-dimensional space look like? Can soap bubbles exist that are not spherical? How can one better understand the structure of vortices and currents? In this book you will experience mathematics from the visual point of view, discovering fascinating and never previously published images that offer illustrative examples to the above questions. Every picture is accompanied by a brief explanatory text, references to further reading, and a number of web links where you can obtain further information. This book is intended for all friends of mathematics—students, teachers, amateurs, and professionals—who want to see something beyond dry text and endless formulas. It will provide inspiration for pursuing further one or another topic that may previously have seemed inaccessible. You will get to know mathematics from a totally new and colorful viewpoint.
Author: Jerzy Pogonowski Publisher: LIT Verlag Münster ISBN: 3643913109 Category : Languages : en Pages :
Book Description
This volume contains four essays which may attract the attention of those readers, who are interested in mathematical cognition The main issues and questions addressed include: How do we achieve understanding of mathematical notions and ideas? What benefits can be obtained from mistakes of great mathematicians? Which mathematical objects are standard and which are pathological? Is it possible characterize the intended models of mathematical theories in a unique way?