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This is a textbook for 3rd quarter calculus covering the three main topics of (1) calculus with polar coordinates and parametric equations, (2) infinite series, and (3) vectors in 3D. It has explanations, examples, worked solutions, problem sets and answers. It has been reviewed by calculus instructors and class-tested by them and the author. Besides technique practice and applications of the techniques, the examples and problem sets are also designed to help students develop a visual and conceptual understanding of the main ideas. The exposition and problem sets have been highly rated by reviewers.
A self-contained text for an introductory course, this volume places strong emphasis on physical applications. Key elements of differential equations and linear algebra are introduced early and are consistently referenced, all theorems are proved using elementary methods, and numerous worked-out examples appear throughout. The highly readable text approaches calculus from the student's viewpoint and points out potential stumbling blocks before they develop. A collection of more than 1,600 problems ranges from exercise material to exploration of new points of theory — many of the answers are found at the end of the book; some of them worked out fully so that the entire process can be followed. This well-organized, unified text is copiously illustrated, amply cross-referenced, and fully indexed.
An authorised reissue of the long out of print classic textbook, Advanced Calculus by the late Dr Lynn Loomis and Dr Shlomo Sternberg both of Harvard University has been a revered but hard to find textbook for the advanced calculus course for decades.This book is based on an honors course in advanced calculus that the authors gave in the 1960's. The foundational material, presented in the unstarred sections of Chapters 1 through 11, was normally covered, but different applications of this basic material were stressed from year to year, and the book therefore contains more material than was covered in any one year. It can accordingly be used (with omissions) as a text for a year's course in advanced calculus, or as a text for a three-semester introduction to analysis.The prerequisites are a good grounding in the calculus of one variable from a mathematically rigorous point of view, together with some acquaintance with linear algebra. The reader should be familiar with limit and continuity type arguments and have a certain amount of mathematical sophistication. As possible introductory texts, we mention Differential and Integral Calculus by R Courant, Calculus by T Apostol, Calculus by M Spivak, and Pure Mathematics by G Hardy. The reader should also have some experience with partial derivatives.In overall plan the book divides roughly into a first half which develops the calculus (principally the differential calculus) in the setting of normed vector spaces, and a second half which deals with the calculus of differentiable manifolds.
A print version of Chapters 0-3 from Dale Hoffman's Contemporary Calculus, an open-source calculus text. These chapters cover the concepts of differential calculus (limits, definition of derivative, differentiation rules, and applications). Newly edited and typeset in LaTeX for improved readability. March 23, 2015, printing corrects 14 minor typos and adds 40 problems. Free PDF version available at: www.contemporarycalculus.com
This book uses elementary versions of modern methods found in sophisticated mathematics to discuss portions of "advanced calculus" in which the subtlety of the concepts and methods makes rigor difficult to attain at an elementary level.
This book explores the major techniques involved in optimization, control theory, and calculus of variations. The book serves as a concise contemporary guide to optimal control theory, optimization, numerical methods and beyond. As such, it is a valuable source to learn mathematical modeling and the mathematical nature of optimization and optimal control. The presence of a variety of exercises solved down to numerical values is one of the main characteristic features of the book. Another one is its compactness, and the material’s usefulness in preparing and teaching several different university courses. The investigation of trends and their formation undertaken in the book leads seamlessly into extrapolation techniques and rigorous methods of scientific prediction. The research for this book was accomplished at the Russian Technological University (RTU) MIREA, based on the courses which have been taught at the RTU for many years.
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Since September 11, 2001, the imagination of "low probability, high consequence" events has become a distinctive feature of contemporary politics. Uncertain futures—devastation by terrorist attack, cyber crime, flood, financial market collapse—must be discerned and responded to as possibilities, however improbable they may be. In The Politics of Possibility, Louise Amoore examines this development, tracing its genealogy through the diverse worlds of risk management consulting, computer science, commercial logistics, and data visualization. She focuses on the increasingly symbiotic relationship between commercial opportunities and state security threats, a relation that turns the trusted, iris-scanned traveler into "a person of national security interest," and the designer of risk algorithms for casino and insurance fraud into a homeland security resource. Juxtaposing new readings of Agamben, Foucault, Derrida, Massumi, and Connolly with interpretations of post–9/11 novels and artworks, Amoore analyzes the "politics of possibility" and its far-reaching implications for society, associative life, and political accountability.
Originally published in 1987. The Consumption Theory of Land Rent or CTLR is a comprehensive model of the urban landscape developed by Grant Ian Thrall. Working from the basic idea that the same underlying processes account for the spatial structure of all places, Thrall shows how CTLR can be used as a tool to explain and predict the long-term consequences of policy decisions by governments, such as introducing light rail rapid transit, or parameter changes in the economy, such as a general rise in real income. Thrall’s methodology for the analysis of land rent and land use in a significant research accomplishment and a major analytical tool for students and professionals within city planning, regional science, urban geography, and urban economics.