“…However, it also offers a valuable resource for students with a solid background in vector calculus, complex analysis and functional analysis.…”
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“…Features include a reader-friendly introduction to tensor calculus and the concept of manifolds; a simple and robust treatment for dimensional regularization; a consistent explanation of the renormalization procedure, step by step and in a transparent manner at all orders, using the QED Lagrangian; and extensive treatment of infrared as well as ultraviolet divergences. …”
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“…To facilitate comprehension the text is divided into three broad areas –  reproducing kernel Hilbert spaces, Cramér-Hida representations and stochastic calculus – for which a somewhat different approach was used than in their usual stand-alone context. …”
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“…This leads naturally to use analysis tools from K-theory and non-commutative geometry, such as cyclic cohomology, quantized calculus with Fredholm modules and index pairings. …”
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“…Key features of this Second Edition: -Five new chapters -Treatment of the basic principles of the modern risk LP theory (the LP-calculus, the LP-methods and the risk LP-theory with GIE) using uniform methodology and terminology with a practical orientation towards both engineering and economics, for the first time in book form -Clear definitions and notations, revised sections and chapters, an extended list of references, and a new subject index -More than a hundred illustrations and tables which motivate the presentation Specialists in risk management in economics, banking and business, as well as graduates and post-graduates in economics and engineering, will benefit from this book.…”
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“…Problems cover areas of single-variable differential and integral calculus, linear algebra, advanced algebra, analytic geometry, combinatorics, basic group theory, and number theory. …”
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“…It is mainly addressed to students who have already studied these mappings in the setting of metric spaces, as well as multidimensional differential calculus. The needed background facts about sets, metric spaces and linear algebra are developed in detail, so as to provide a seamless transition between students' previous studies and new material. …”
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“…The most obvious, and the first context in which major new techniques depended on formulating infinite processes, is calculus. But there are many others, for example Fourier analysis and fractals. …”
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“…Bibliographic notes, updated and expanded from the first edition, are included at the end of every chapter for further reading on Monge-Ampère-type equations and their diverse applications in the areas of differential geometry, the calculus of variations, optimization problems, optimal mass transport, and geometric optics. …”
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“…With emphasis placed on physical understanding rather than on rigorous mathematical derivations, the content is accessible to graduate students and researchers in the broad areas of materials science and engineering, chemistry, chemical and biomolecular engineering, applied mathematics, condensed-matter physics, without specific training in theoretical physics or calculus of variations.…”
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“…In addition to classical results of functional analysis, differential calculus and integration, Analysis discusses topics such as convex analysis, dissipative operators and semigroups which are often absent from classical treatises. …”
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“…The exercises are at the level of undergraduate students and only require knowledge of elementary Euclidean geometry and pre-calculus algebra. It is especially well-suited for those students who are thinking of becoming a mathematics teacher and for mathematics teachers.…”
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“…Instructors and educators teaching problem-solving courses or organizing mathematics clubs, as well as motivated mathematics students from high school juniors to college seniors, will find Mathematical Bridges a useful resource in calculus, linear and abstract algebra, analysis and differential equations. …”
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“…Rafelski presents Special Relativity in a language deemed accessible to students without any topical preparation - avoiding the burden of geometry, tensor calculus, and space-time symmetries – and yet advancing in highly contemporary context all the way to research frontiers. …”
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“…Two supplemental chapters, the first on continuum mechanics of three-dimensional continua and the second on methods from variational calculus, are included to provide relevant background for students. …”
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“…The prerequisites for this text are linear algebra and a calculus based course in statistics. .…”
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“…Mathematical introduction : arithmetic and algebra ; geometry, trigonometry, and analytic geometry ; calculus ; matter and force ; the Earth as an astronomical body ; the celestial sphere and measurement of time ; Moon and eclipses ; the solar system and celestial mechanics ; energy and work ; heat and the kinetic molecular theory ; the atomic constitution of matter ; electricity and magnetism ; electrical nature of matter ; wave motion and light ; electromagnetic waves ; spectra ; astronomical spectroscopy : astrophysics ; properties of more important elements ; oxidation and reduction ; reaction velocity and chemical equilibrium ; ionogens : acids, bases, salts ; atomic structure and chemical behavior ; electromotive series of the elements ; carbon and its compounds ; silicon and the structure of rocks ; Earth materials and processes ; gradation ; geologic work of the ocean : the sedimentary rocks ; diastrophism and earthquakes ; volcanism, the deep-seated rocks, and the rock cycle ; principles of Earth history ; fossils and ancient climates ; geological time ; geosynclines and mountains ; pre-cambrian and early paleozoic times ; late paleozoic and the Appalachian revolution ; the mesozoic era ; the cenozoic era ; mapping the Earth ; weather and weather maps ; climate ; nature of soils.…”
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“…By introducing protomodular categories and Mal’tsev categories, which form a larger class, the structural properties of the category Gp of groups, show how they emerge from four very basic observations about the algebraic litteral calculus and how, studied for themselves at the conceptual categorical level, they lead to the main striking features of the category Gp of groups. …”
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“…While covering all the standard material expected of such a course, efforts have been made to illustrate the use of various theorems via examples taken from differential equations and the calculus of variations, either through brief sections or through exercises. …”
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“…Its discussion of the problems of passive observation, the calculus of observation, the two-model problem, and model-based consensus uses illustrations drawn primarily from economics. …”
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