Libros de Matemáticas, página 6 de 470

Clarity, readability and rigor combine in the second edition of this widely-used textbook to provide the first step into general relativity for undergraduate students with a minimal background in mathematics. Topics within relativity that fascinate astrophysical researchers and students alike are covered with Schutz's characteristic ease and authority - from black holes to gravitational lenses, from pulsars to the study of the Universe as a whole. This edition now contains discoveries by astronomers that require general relativity for their explanation; a revised chapter on relativistic stars, including new information on pulsars; an entirely rewritten chapter on cosmology; and an extended, comprehensive treatment of modern detectors and expected sources. Over 300 exercises, many new to this edition, give students the confidence to work with general relativity and the necessary mathematics, whilst the informal writing style makes the subject matter easily accessible. Password protected solutions for instructors are available at www.cambridge.org/9780521887052.

This unique book is an excellent introduction to the basic properties of wavelets. The fundamental construction of these functions by means of "multiresolution analyses" is presented; in particular, this method is used for introducing the spline wavelets and the compactly supported wavelets. An important feature of this book, however, is the use of the Fourier transform for studying wavelets on the real line. A simple characterization of all wavelets is presented which is most useful for the construction of new families of wavelets. This technique can also be used for obtaining characterizations of low pass filters and scaling functions. Another feature is the use of wavelets for representing those function spaces that are most often encountered in analysis: the Lebesgue spaces, Hardy spaces, and more generally, the Besov spaces, the Sobolev, and the Lipschitz spaces. Other topics, some related to applications, are also included: the Fast Fourier Transform, wavelet packets, frames, local cosine and sine bases and their discrete versions are just some examples. Wavelet theory had its origin in quantum field theory, signal analysis, and function space theory. In these areas wavelet-like algorithms replace the classical Fourier-type expansion of a function. This unique new book is an excellent introduction to the basic properties of wavelets, from background math to powerful applications. The authors provide elementary methods for constructing wavelets, and illustrate several new classes of wavelets. The text begins with a description of local sine and cosine bases that have been shown to be very effective in applications. Very little mathematical background is needed to follow this material. A complete treatment of band-limited wavelets follows. These are characterized by some elementary equations, allowing the authors to introduce many new wavelets. Next, the idea of multiresolution analysis (MRA) is developed, and the authors include simplified presentations of previous studies, particularly for compactly supported wavelets. Some of the topics treated include: oSeveral bases generated by a single function via translations and dilations oMultiresolution analysis, compactly supported wavelets, and spline wavelets oBand-limited wavelets oUnconditionality of wavelet bases oCharacterizations of many of the principal objects in the theory of wavelets, such as low-pass filters and scaling functions The authors also presen

Mathematical methods are essential tools for all physical scientists. This second edition provides a comprehensive tour of the mathematical knowledge and techniques that are needed by students in this area. In contrast to more traditional textbooks, all the material is presented in the form of problems. Within these problems the basic mathematical theory and its physical applications are well integrated. The mathematical insights that the student acquires are therefore driven by their physical insight. Topics that are covered include vector calculus, linear algebra, Fourier analysis, scale analysis, complex integration, Greens functions, normal modes, tensor calculus, and perturbation theory. The second edition contains new chapters on dimensional analysis, variational calculus, and the asymptotic evaluation of integrals. This book can be used by undergraduates, and lower-level graduate students in the physical sciences. It can serve as a stand-alone text, or as a source of problems and examples to complement other textbooks.

Lawrence Potter nos introduce en el fabuloso mundo de las matemáticas, desde los aspectos históricos más apasionantes -como la manera que tenían de contar los pitagóricos, el origen árabe del álgebra o la forma como aplicamos tecnicas arabes, chinas y babilonicas para solventar ecuaciones- hasta la manera de resolver Sudokus. El autor demuestra que las matematicas no son un campo aislado del pensamiento abstracto sino una ciencia con unas conexiones fascinantes con el mundo que nos rodea. ¿Que significa la coma de los decimales? ¿Como se pueden multiplicar de memoria numeros de varias cifras? ¿Que logica hay tras las ecuaciones simultaneas? ¿Como se puede ganar apostando a los caballos? ¿Como se puede resolver un Sudoku?

This text attempts to change the way logic and discrete math are taught in computer science and mathematics. While many books treat logic simply as another topic of study, this book''s uniqueness is its willingness to take it one step further. In the book, logic is treated as a basic tool, to be applied in essentially every other area. "This is a rather extraordinary book, and deserves to be read by everyone involved in computer science and - perhaps more importantly - software engineering. I recommend it highly. The book will be of value not only to beginning students, but also to hardened programmers with many years of experience - in Fortran, Cobol, C, C++, or whatever. If the book is taken seriously, the rigor that it unfolds and the clarity of its concepts could have a significant impact on the way in which software is conceived and developed. " -Peter G. Neumann-

Medramos coa presenza limpa das rectas, tan simples, tan útiles, sen dubidar da súa consistencia, malia vivirmos nunha superficie curva, aceptando o seu carácter ilimitado, ao abeiro dun espazo infinito, teimosos na ignorancia. Se cadra asumimos a ficcion como necesaria, presos de ideas primitivas, nacidas de experiencias limitadas que sufriron xeneralizacions abusivas e se converteron en principios inmutabeis, conturbando a nosa razon. Agora sabemos que non, que a recta e unha aparencia, aquela precisa simplicidade da xeometria escolar. E xorden outras xeometrias, outras teorias fisicas... Aprendemos que o universo non se corresponde coa idea de espazo plano e infinito, que a sua xeometria varia dun lugar a outro e muda permanentemente coas diversas configuracions materiais! Estas paxinas percorren unha longa marcha, a longa historia da evolucion das teorias xeometricas, desde os albores da civilizacion ata esa modernidade que fai eclosion no seculo XIX. Unha andaina instrutiva que arriba a unha abstraccion insospeitada, derrubando a ilusion dunha xeometria natural.