Download or read book Geometric Differentiation written by I. R. Porteous and published by Cambridge University Press. This book was released on 2001-12-13 with total page 354 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is a revised version of the popular Geometric Differentiation, first edition.
Download or read book Geometric Algebra for Computer Science written by Leo Dorst and published by Elsevier. This book was released on 2010-07-26 with total page 664 pages. Available in PDF, EPUB and Kindle. Book excerpt: Until recently, almost all of the interactions between objects in virtual 3D worlds have been based on calculations performed using linear algebra. Linear algebra relies heavily on coordinates, however, which can make many geometric programming tasks very specific and complex-often a lot of effort is required to bring about even modest performance enhancements. Although linear algebra is an efficient way to specify low-level computations, it is not a suitable high-level language for geometric programming. Geometric Algebra for Computer Science presents a compelling alternative to the limitations of linear algebra. Geometric algebra, or GA, is a compact, time-effective, and performance-enhancing way to represent the geometry of 3D objects in computer programs. In this book you will find an introduction to GA that will give you a strong grasp of its relationship to linear algebra and its significance for your work. You will learn how to use GA to represent objects and perform geometric operations on them. And you will begin mastering proven techniques for making GA an integral part of your applications in a way that simplifies your code without slowing it down. * The first book on Geometric Algebra for programmers in computer graphics and entertainment computing * Written by leaders in the field providing essential information on this new technique for 3D graphics * This full colour book includes a website with GAViewer, a program to experiment with GA
Download or read book Guide to Geometric Algebra in Practice written by Leo Dorst and published by Springer Science & Business Media. This book was released on 2011-08-28 with total page 458 pages. Available in PDF, EPUB and Kindle. Book excerpt: This highly practical Guide to Geometric Algebra in Practice reviews algebraic techniques for geometrical problems in computer science and engineering, and the relationships between them. The topics covered range from powerful new theoretical developments, to successful applications, and the development of new software and hardware tools. Topics and features: provides hands-on review exercises throughout the book, together with helpful chapter summaries; presents a concise introductory tutorial to conformal geometric algebra (CGA) in the appendices; examines the application of CGA for the description of rigid body motion, interpolation and tracking, and image processing; reviews the employment of GA in theorem proving and combinatorics; discusses the geometric algebra of lines, lower-dimensional algebras, and other alternatives to 5-dimensional CGA; proposes applications of coordinate-free methods of GA for differential geometry.
Download or read book Covariant Differentiation of Geometric Objects written by A. Szybiak and published by . This book was released on 1967 with total page 48 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Clifford Algebra to Geometric Calculus written by D. Hestenes and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 332 pages. Available in PDF, EPUB and Kindle. Book excerpt: Matrix algebra has been called "the arithmetic of higher mathematics" [Be]. We think the basis for a better arithmetic has long been available, but its versatility has hardly been appreciated, and it has not yet been integrated into the mainstream of mathematics. We refer to the system commonly called 'Clifford Algebra', though we prefer the name 'Geometric Algebm' suggested by Clifford himself. Many distinct algebraic systems have been adapted or developed to express geometric relations and describe geometric structures. Especially notable are those algebras which have been used for this purpose in physics, in particular, the system of complex numbers, the quatemions, matrix algebra, vector, tensor and spinor algebras and the algebra of differential forms. Each of these geometric algebras has some significant advantage over the others in certain applications, so no one of them provides an adequate algebraic structure for all purposes of geometry and physics. At the same time, the algebras overlap considerably, so they provide several different mathematical representations for individual geometrical or physical ideas.
Download or read book An Introduction to Differentiable Manifolds and Riemannian Geometry written by and published by Academic Press. This book was released on 1975-08-22 with total page 441 pages. Available in PDF, EPUB and Kindle. Book excerpt: An Introduction to Differentiable Manifolds and Riemannian Geometry
Download or read book Differentiation in Practice A Resource Guide for Differentiating Curriculum Grades K 5 written by Carol Ann Tomlinson and published by ASCD. This book was released on 2003-06-15 with total page 217 pages. Available in PDF, EPUB and Kindle. Book excerpt: Join Carol Ann Tomlinson and Caroline Cunningham Eidson in their continuing exploration of how real teachers incorporate differentiation principles and strategies throughout an entire instructional unit. Focusing on the elementary grades, but applicable at all levels, Differentiation in Practice, Grades K-5 will teach anyone interested in designing and implementing differentiated curriculum how to do so or how to do so more effectively. Included are * Annotated lesson plans for differentiated units in language arts, social studies, science, and mathematics. * Samples of differentiated product assignments, learning contracts, rubrics, and homework handouts. * An overview of the non-negotiables in differentiated classrooms and guidelines for using the book as a learning tool. * An extended glossary and recommended readings for further exploration of key ideas and strategies. Each unit highlights underlying standards, delineates learning goals, and takes you step by step through the instructional process. Unit developers provide running commentary on their use of flexible grouping and pacing, tiered assignments and assessments, learning contracts, and numerous other strategies. The models and insight presented will inform your own differentiation efforts and help you meet the challenge of mixed-ability classrooms with academically responsive curriculum appropriate for all learners. Note: This product listing is for the Adobe Acrobat (PDF) version of the book.
Download or read book Yet Another Calculus Text written by Dan Sloughter and published by Orange Grove Texts Plus. This book was released on 2009-09-24 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book An Introduction to Differentiable Manifolds and Riemannian Geometry Revised written by William Munger Boothby and published by Gulf Professional Publishing. This book was released on 2003 with total page 444 pages. Available in PDF, EPUB and Kindle. Book excerpt: The second edition of An Introduction to Differentiable Manifolds and Riemannian Geometry, Revised has sold over 6,000 copies since publication in 1986 and this revision will make it even more useful. This is the only book available that is approachable by "beginners" in this subject. It has become an essential introduction to the subject for mathematics students, engineers, physicists, and economists who need to learn how to apply these vital methods. It is also the only book that thoroughly reviews certain areas of advanced calculus that are necessary to understand the subject. Line and surface integrals Divergence and curl of vector fields
Download or read book Calculus with Analytic Geometry written by Murray H. Protter and published by Jones & Bartlett Learning. This book was released on 1988 with total page 990 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Geometry Geodesics and the Universe written by Robert G. Bill and published by Xlibris Corporation. This book was released on 2023-03-19 with total page 267 pages. Available in PDF, EPUB and Kindle. Book excerpt: The story of the development of geometry is told as it emerged from the concepts of the ancient Greeks, familiar from high school, to the four-dimensional space-time that is central to our modern vision of the universe. The reader is first reacquainted with the geometric system compiled by Euclid with its postulates thought to be self-evident truths. A particular focus is on Euclid’s fifth postulate, the Parallel Postulate and the many efforts to improve Euclid’s system over hundreds of years by proving it from the first four postulates. Two thousand years after Euclid, in the process that would reveal the Parallel Postulate as an independent postulate, a new geometry was discovered that changed the understanding of geometry and mathematics, while paving the way for Einstein’s General Relativity. The mathematics to describe the non-Euclidean geometries and the geometric universe of General Relativity is initiated in the language of mathematics available to a general audience. The story is told as a mathematical narrative, bringing the reader along step by step with all the background needed in analytic geometry, the calculus, vectors, and Newton’s laws to allow the reader to move forward to the revolutionary extension of geometry by Riemann that would supply Einstein with the language needed to overthrow Newton’s universe. Using the mathematics acquired for Riemannian geometry, the principles behind Einstein’s General Relativity are described and their realization in the Field Equations is presented. From the Field Equations, it is shown how they govern the curved paths of light and that of planets along the geodesics formed from the geometry of space-time, and how they provide a picture of the universe’s birth, expansion, and future. Thus, Euclid’s geometry while no longer thought to spring from perceived absolute truths as the ancients believed, ultimately provided the seed for a new understanding of geometry that in its infinite variety became central to the description of the universe, marking mathematics as a one of the great modes of human expression.
Download or read book Encyclopaedia of Mathematics written by M. Hazewinkel and published by Springer. This book was released on 2013-11-11 with total page 952 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Differential and Riemannian Geometry written by Detlef Laugwitz and published by Academic Press. This book was released on 2014-05-12 with total page 251 pages. Available in PDF, EPUB and Kindle. Book excerpt: Differential and Riemannian Geometry focuses on the methodologies, calculations, applications, and approaches involved in differential and Riemannian geometry. The book first offers information on local differential geometry of space curves and surfaces and tensor calculus and Riemannian geometry. Discussions focus on tensor algebra and analysis, concept of a differentiable manifold, geometry of a space with affine connection, intrinsic geometry of surfaces, curvature of surfaces, and surfaces and curves on surfaces. The manuscript then examines further development and applications of Riemannian geometry and selections from differential geometry in the large, including curves and surfaces in the large, spaces of constant curvature and non-Euclidean geometry, Riemannian spaces and analytical dynamics, and metric differential geometry and characterizations of Riemannian geometry. The publication elaborates on prerequisite theorems of analysis, as well as the existence and uniqueness theorem for ordinary first-order differential equations and systems of equations and integrability theory for systems of first-order partial differential equations. The book is a valuable reference for researchers interested in differential and Riemannian geometry.
Download or read book The Geometric Induction of Bone Formation written by Ugo Ripamonti and published by CRC Press. This book was released on 2020-12-23 with total page 208 pages. Available in PDF, EPUB and Kindle. Book excerpt: The Geometric Induction of Bone Formation describes new biomimetic biomaterials that offer mechanistic osteogenic surfaces for the autonomous and spontaneous induction of bone formation without the addition of osteogenic soluble molecular signals of the transforming growth factor-β supergene family. The chapters frame our understanding of regenerative medicine in primate species, including humans. The goal is to unravel the fundamental biological mechanisms of bone formation unique to non-human and human primates. The broad target audience dovetails with several disciplines both in the academic and private biotech sectors primarily involved in molecular biology, tissue biology, tissue engineering, biomaterial science, and reconstructive, orthopedic, plastic, and dental surgery. Key Features Includes outstanding images of undecalcified whole mounted sections Summarizes non-human primate research – ideal for clinical translation Reviews methods for creating devices capable of making bone autonomously, i.e. an intrinsically osteo-inductive bioreactor and/or biomaterial Describes the spontaneous induction of bone formation including a whole spectrum of tissue biology, from basic molecular biology to clear-cut morphology and pre-clinical application in non-human primate species Intended for audiences in both academic research and the biotech industry
Download or read book Activities for a Differentiated Classroom Level 1 written by Wendy Conklin and published by Teacher Created Materials. This book was released on 2011-02-01 with total page 174 pages. Available in PDF, EPUB and Kindle. Book excerpt: Easily implement grade appropriate lessons suitable for Grade 1 classrooms. Based on current research, these easy-to-use lessons are based on a variety of strategies to differentiate your instruction. Activities are included to allow access to all learners. Includes interactive whiteboard-compatible Resource CD with sample projects, templates, and assessment rubrics. 160pp. plus Teacher Resource CD.
Download or read book Cameos for Calculus written by Roger B. Nelsen and published by American Mathematical Soc.. This book was released on 2015-12-31 with total page 187 pages. Available in PDF, EPUB and Kindle. Book excerpt: A thespian or cinematographer might define a cameo as a brief appearance of a known figure, while a gemologist or lapidary might define it as a precious or semiprecious stone. This book presents fifty short enhancements or supplements (the cameos) for the first-year calculus course in which a geometric figure briefly appears. Some of the cameos illustrate mainstream topics such as the derivative, combinatorial formulas used to compute Riemann sums, or the geometry behind many geometric series. Other cameos present topics accessible to students at the calculus level but not usually encountered in the course, such as the Cauchy-Schwarz inequality, the arithmetic mean-geometric mean inequality, and the Euler-Mascheroni constant. There are fifty cameos in the book, grouped into five sections: Part I. Limits and Differentiation, Part II. Integration, Part III. Infinite Series, Part IV. Additional Topics, and Part V. Appendix: Some Precalculus Topics. Many of the cameos include exercises, so Solutions to all the Exercises follows Part V. The book concludes with references and an index. Many of the cameos are adapted from articles published in journals of the MAA, such as The American Mathematical Monthly, Mathematics Magazine, and The College Mathematics Journal. Some come from other mathematical journals, and some were created for this book. By gathering the cameos into a book the [Author]; hopes that they will be more accessible to teachers of calculus, both for use in the classroom and as supplementary explorations for students.
Download or read book Differential and Integral Calculus written by Daniel Alexander Murray and published by . This book was released on 1908 with total page 522 pages. Available in PDF, EPUB and Kindle. Book excerpt:
