This second edition continues to emphasise learning by doing and the development of students' ability to use mathematics with understanding to solve engineering problems. Extensive treatment of some advanced engineering topics, particularly as tools for computer-based system modelling, analysis and design. *Follow on text from Modern Engineering Mathematics, 2E - over 20,000 copies sold *Changing student needs catered for by some easier examples and exercises plus new introductory sections on matrix algebra and vector spaces *New chapter on Numerical Solution of Ordinary Differential Equations *Engineering applications covered in specific sections in each chapter *The increasing importance of digital techniques and statistics is recognised throughout
For a two-semester or a three-quarter calculus-based Introduction to the Mathematics of Statistics course. This classic, calculus-based introduction to the theory - and application - of statistics provides an unusually comprehensive depth and breadth of coverage and reflects the state-of-the-art in statistical thinking, the teaching of statistics, and current practices - including the use of the computer. *NEW - Places greater emphasis on the use of computers in performing statistical calculations. *NEW - Includes new exercises - many of which require the use of a computer. *NEW - Expands coverage of Analysis of Variance to include the two-way analysis-of-variance model with interaction and a discussion of multiple comparisons. *NEW - Adds appendices which summarize the properties of the special probability distributions and density functions that appear in the text. *Places greater emphasis on the use of computers in performing statistical calculations. *Comprehensive coverage of statistical theories. *Features more than 1,100 problems and exercises - divided into theory and applications.
E-mail: [email protected] Las ecuaciones de la Física no relacionan sin más números, vectores o tensores de índole matemática, sino cantidades diádicas formadas con esos componentes vinculados a unidades diversas que indican cantidades de magnitudes naturales. Entonces, ¿por qué se opera con los entes diádicos de la Física como si fuesen elementos matemáticos puros?, ¿no supone esta ficción una aberración que envilece todo el conocimiento científico? Algunos autores han advertido de esta laguna crítica, que oculta a la Física un pilar tan fundamental. Pueden citarse preeminentes físicos como Clerk Maxwell o Max Planck, entre otros clásicos. Todos manifestaron a su manera los escrúpulos suscitados por la tradicional e injustificada forma de operar con las magnitudes físicas y sus unidades. Aquí se descubre, describe y resuelve tan notable paradoja de «aritmetización» de la Física y se construye un álgebra rigurosa y coherente para las cantidades de magnitudes. La Primera álgebra de magnitudes resuelve la hipótesis falsa del Sistema Internacional de Unidades, consistente en suponer negligentemente que las magnitudes físicas presenten estructura multiplicativa de grupo abeliano. No puede ser así, como se demuestra en este trabajo. Finalmente, se pone de manifiesto el camino lógico e inapelable que conduce del álgebra de magnitudes a los espacios «dismétricos», que se estudian con mayor profundidad en el segundo volumen de esta obra. La «dismetría» es una nueva y poderosa herramienta para representar con precisión los fenómenos físicos de un universo variable. Esta nueva Física acoge multitud de innovaciones, que sin duda sabrán apreciar muchos investigadores emprendedores. The equations of Physics do not simply relate numbers, vectors or tensors of a mathematical nature, but rather dyadic quantities formed with these components linked to various units that indicate quantities of natural magnitudes. So, why do we operate with the dyadic entities of Physics as if they were pure mathematical elements? Doesn't this fiction suppose an aberration that debases all scientific knowledge? Some authors have warned of this critical gap, which hides such a fundamental pillar from Physics. Pre-eminent physicists such as Clerk Maxwell or Max Planck, among other classics, can be cited. All of them expressed in their own way the scruples aroused by the traditional and unjustified way of operating with physical quantities and their units. Here such a remarkable «arithmeticization» paradox of Physics is discovered, described and solved and a rigorous and coherent algebra is constructed for the quantities of magnitudes. The First Algebra of Magnitudes resolves the false hypothesis of the International System of Units, consisting of negligently assuming that physical magnitudes have a multiplicative abelian group structure. It cannot be like that, as demonstrated in this work. Finally, the logical and unappealable path that leads from the algebra of magnitudes to the «dysmetric» spaces is revealed, which are studied in greater depth in the second volume of this work. «Dysmetry» is a powerful new tool for accurately representing the physical phenomena of a variable universe. This new Physics welcomes a multitude of innovations, which will undoubtedly be appreciated by many enterprising researchers.
Nowadays we are facing numerous and important imaging problems: nondestructive testing of materials, monitoring of industrial processes, enhancement of oil production by efficient reservoir characterization, emerging developments in noninvasive imaging techniques for medical purposes - computerized tomography (CT), magnetic resonance imaging (MRI), positron emission tomography (PET), X-ray and ultrasound tomography, etc. In the CIME Summer School on Imaging (Martina Franca, Italy 2002), leading experts in mathematical techniques and applications presented broad and useful introductions for non-experts and practitioners alike to many aspects of this exciting field. The volume contains part of the above lectures completed and updated by additional contributions on other related topics.
It is a great pleasure to share with you the Springer CCIS 111 proceedings of the Third World Summit on the Knowledge Society––WSKS 2010––that was organized by the International Scientific Council for the Knowledge Society, and supported by the Open Research Society, NGO, (http://www.open-knowledge-society.org) and the Int- national Journal of the Knowledge Society Research, (http://www.igi-global.com/ijksr), and took place in Aquis Corfu Holiday Palace Hotel, on Corfu island, Greece, September 22–24, 2010. The Third World Summit on the Knowledge Society (WSKS 2010) was an inter- tional scientific event devoted to promoting the dialogue on the main aspects of the knowledge society towards a better world for all. The multidimensional economic and social crisis of the last couple years brings to the fore the need to discuss in depth new policies and strategies for a human-centric developmental process in the global c- text. This annual summit brings together key stakeholders of knowledge society dev- opment worldwide, from academia, industry, government, policy makers, and active citizens to look at the impact and prospects of it information technology, and the knowledge-based era it is creating, on key facets of living, working, learning, innovating, and collaborating in today’s hyper-complex world.
El texto contiene una colección de ejercicios y problemas resueltos en detalle y se ajusta al programa de la asignatura Fundamentos Matemáticos de las Tecnologías de la Información del Grado en Ingeniería de las Tecnologías de la Información, y se ha incluido un tema inicial de puesta al día y repaso que se considera importante para poder seguir el curso. El contenido se estructura en seis temas. En el Tema 1 se revisan algunos contenidos de cursos anteriores relativos a matrices, determinantes y sistemas de ecuaciones lineales. El Tema 2 se centra en el estudio de la estructura de espacio vectorial, fundamental en Álgebra Lineal. El Tema 3 trata las aplicaciones lineales entre espacios vectoriales. Los Temas 4, 5 y 6 se dedican al Cálculo Infinitesimal, el Tema 4 a las funciones de una variable y el Tema 5 a las funciones de varias variables. Finalmente, en el Tema 6 se desarrollan las técnicas básicas del cálculo integral.
This book treats Modelling of CFD problems, Numerical tools for PDE, and Scientific Computing and Systems of ODE for Epidemiology, topics that are closely related to the scientific activities and interests of Prof. William Fitzgibbon, Prof. Yuri Kuznetsov, and Prof. O. Pironneau, whose outstanding achievements are recognised in this volume. It contains 20 contributions from leading scientists in applied mathematics dealing with partial differential equations and their applications to engineering, ab-initio chemistry and life sciences. It includes the mathematical and numerical contributions to PDE for applications presented at the ECCOMAS thematic conference "Contributions to PDE for Applications" held at Laboratoire Jacques Louis Lions in Paris, France, August 31- September 1, 2015, and at the Department of Mathematics, University of Houston, Texas, USA, February 26-27, 2016. This event brought together specialists from universities and research institutions who are developing or applying numerical PDE or ODE methods with an emphasis on industrial and societal applications. This volume is of interest to researchers and practitioners as well as advanced students or engineers in applied and computational mathematics. All contributions are written at an advanced scientific level with no effort made by the editors to make this volume self-contained. It is assumed that the reader is a specialist already who knows the basis of this field of research and has the capability of understanding and appreciating the latest developments in this field.
