“…Additionally: It provides an accessible introduction to the two most useful exact solutions of Einstein's vacuum field equations describing black holes, using only basic tensor calculus Explores the geometry and physical properties of these spacetimes through the motion of particles and light Explains the use of different coordinate systems, maximal extensions and Penrose diagrams Discusses the association of the surface area of a black hole with its entropy and shows that, with the introduction of quantum mechanics, black holes cease to be black and can radiate. …”
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“…The only background required of the reader is a good knowledge of advanced calculus and linear algebra.…”
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“…Students using this text should be familiar with the principles of physics, chemistry, and geology, and have taken a year of differential and integral calculus. Mathematical Modeling of Earth's Dynamical Systems helps earth scientists develop a philosophical framework and strong foundations for conceptualizing complex geologic systems. * Step-by-step lessons for representing complex Earth systems as dynamical models * Explains geologic processes in terms of fundamental laws of physics and chemistry * Numerical solutions to differential equations through the finite difference technique * A philosophical approach to quantitative problem-solving * Various examples of processes and systems, including the evolution of sandy coastlines, the global carbon cycle, and much more * Professors: A supplementary Instructor's Manual is available for this book. …”
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“…Required mathematical background for the book includes a knowledge of functional calculus, spectral theory (essentially reduced to the case of finite matrices) and basic probability theory. …”
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“…The 12th conference on "Variational Calculus, Optimal Control and Applications" took place September 23-27, 1996, in Trassenheide on the Baltic Sea island of Use­ dom. …”
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“…It presupposes little background: the reader is only expected to master basic differential calculus, and a little point-set topology. The book covers the main topics of differential geometry: manifolds, tangent space, vector fields, differential forms, Lie groups, and a few more sophisticated topics such as de Rham cohomology, degree theory and the Gauss-Bonnet theorem for surfaces. …”
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“…It provides a basic introduction to theoretical physics as applied to soft matter, explaining the concepts of symmetry, broken symmetry, and order parameters; phases and phase transitions; mean-field theory; and the mathematics of variational calculus and tensors. It is written in an informal, conversational style, which is accessible to students from a diverse range of backgrounds. …”
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“…The mathematical model, known as the "Fluent Calculus,'' describes how to use classical first-order logic to set up symbolic models of dynamic worlds and to represent knowledge of actions and their effects. …”
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“…As previous knowledge just the basic facts of calculus and algebra are supposed. Parts where somewhat more (measure theory) is needed and sketches of lengthier calcula­ tions are set in fine print. …”
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“…Equipped with only a basic knowledge of calculus, functional analysis, and partial differential equations, the reader is introduced to the concept and applications of the Navier–Stokes equations through a series of fully self-contained chapters. …”
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“…While only an understanding of calculus is required to appreciate it, there are more technical sections that will charm even specialists in harmonic analysis. …”
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“…The interest in these topics is related to the need to produce “analogue” electronic devices characterized by non-integer order impedance, and to the characterization of natural phenomena, which are systems with memory or aftereffects and for which the fractional-order calculus tool is the ideal choice for analysis. FOEs represent the building blocks for designing and realizing analogue integrated electronic circuits, which the authors believe hold the potential for a wealth of mass-market applications. …”
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“…Drawing on a wealth of primary sources, the author presents a fascinating and erudite picture of Kepler's scientific accomplishments, his public life (work with Tycho Brahe, the Danish astronomer; mathematical appointments at Graz, Prague, and Linz; pioneering work with calculus and optics, and more) and his personal life: childhood and youth, financial situation, his mother's trial as a witch, his own lifelong fear of religious persecution, his difficulties in choosing one of eleven possible young women as his second wife, and more, through his last years in Ulm and death in Regensburg. …”
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“…The use of Euler’s method makes nonlinear examples tractable and accessible to a broad spectrum of early-stage undergraduates, thus providing a practical alternative to the procedural approach of a traditional Calculus curriculum. Tools are developed within numerous, relevant examples, with an emphasis on the construction, evaluation, and interpretation of mathematical models throughout. …”
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“…Basic algebra is required to master most of the material. But, the calculus is used in derivation of some of the equations. …”
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“…They can be analyzed pathwise with deterministic calculus, but require further treatment beyond that of classical ODE theory due to the lack of smoothness in their time variable. …”
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“…The problems show how mathematics―including algebra, trigonometry, geometry, and calculus―can be united with physical laws to solve both real and theoretical problems. …”
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“…Designed for upper-division undergraduates in mathematics or computer science classes, the textbook assumes that students have prior knowledge of linear algebra and calculus, although these topics are reviewed in the text. …”
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“…No previous knowledge of linear algebra is needed to approach this text, with single-variable calculus as the only formal prerequisite. However, the reader will need to draw upon some mathematical maturity to engage in the increasing abstraction inherent to the subject. …”
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“…Assuming only multivariable calculus and linear algebra as prerequisites, this book introduces the reader to the KdV Equation and its multisoliton solutions, elliptic curves and Weierstrass \wp-functions, the algebra of differential operators, Lax Pairs and their use in discovering other soliton equations, wedge products and decomposability, the KP Equation and Sato's theory relating the Bilinear KP Equation to the geometry of Grassmannians. …”
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