Bigeometric Calculus
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Bigeometric Calculus
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Author : Michael Grossman
language : en
Publisher: Non-Newtonian Calculus
Release Date : 1983
Bigeometric Calculus written by Michael Grossman and has been published by Non-Newtonian Calculus this book supported file pdf, txt, epub, kindle and other format this book has been release on 1983 with Mathematics categories.
This book contains a detailed account of the bigeometric calculus, a non-Newtonian calculus in which the power functions play the role that the linear functions play in the classical calculus of Newton and Leibniz. This nonlinear system provides mathematical tools for use in science, engineering, and mathematics. It appears to have considerable potential for use as an alternative to the classical calculus. It may well be that the bigeometric calculus can be used to define new concepts, to yield new or simpler laws, or to formulate or solve problems.
Non Newtonian Calculus
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Author : Michael Grossman
language : en
Publisher: Non-Newtonian Calculus
Release Date : 1972
Non Newtonian Calculus written by Michael Grossman and has been published by Non-Newtonian Calculus this book supported file pdf, txt, epub, kindle and other format this book has been release on 1972 with Mathematics categories.
The non-Newtonian calculi provide a wide variety of mathematical tools for use in science, engineering, and mathematics. They appear to have considerable potential for use as alternatives to the classical calculus of Newton and Leibniz. It may well be that these calculi can be used to define new concepts, to yield new or simpler laws, or to formulate or solve problems.
Geometric Calculus
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Author : Giuseppe Peano
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-12-01
Geometric Calculus written by Giuseppe Peano and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-12-01 with Mathematics categories.
Calcolo Geometrico, G. Peano's first publication in mathematical logic, is a model of expository writing, with a significant impact on 20th century mathematics. Kannenberg's lucid and crisp translation, Geometric Calculus, will appeal to historians of mathematics, researchers, graduate students, and general readers interested in the foundations of mathematics and the development of a formal logical language. The book has never been reprinted in its entirety, and only two chapters have ever been translated into English. Readers of this valuable translation will gain insight into the work of a distinguished mathematician and founder of mathematical logic.
Clifford Algebra To Geometric Calculus
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Author : D. Hestenes
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Clifford Algebra To Geometric Calculus written by D. Hestenes and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Science categories.
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.
Advanced Calculus
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Author : James J. Callahan
language : en
Publisher: Springer Science & Business Media
Release Date : 2010-09-09
Advanced Calculus written by James J. Callahan and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2010-09-09 with Mathematics categories.
With a fresh geometric approach that incorporates more than 250 illustrations, this textbook sets itself apart from all others in advanced calculus. Besides the classical capstones--the change of variables formula, implicit and inverse function theorems, the integral theorems of Gauss and Stokes--the text treats other important topics in differential analysis, such as Morse's lemma and the Poincaré lemma. The ideas behind most topics can be understood with just two or three variables. The book incorporates modern computational tools to give visualization real power. Using 2D and 3D graphics, the book offers new insights into fundamental elements of the calculus of differentiable maps. The geometric theme continues with an analysis of the physical meaning of the divergence and the curl at a level of detail not found in other advanced calculus books. This is a textbook for undergraduates and graduate students in mathematics, the physical sciences, and economics. Prerequisites are an introduction to linear algebra and multivariable calculus. There is enough material for a year-long course on advanced calculus and for a variety of semester courses--including topics in geometry. The measured pace of the book, with its extensive examples and illustrations, make it especially suitable for independent study.
Geometric Measure Theory And The Calculus Of Variations
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Author : William K. Allard
language : en
Publisher: American Mathematical Soc.
Release Date : 1986
Geometric Measure Theory And The Calculus Of Variations written by William K. Allard and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 1986 with Mathematics categories.
Includes twenty-six papers that survey a cross section of work in modern geometric measure theory and its applications in the calculus of variations. This title provides an access to the material, including introductions and summaries of many of the authors' much longer works and a section containing 80 open problems in the field.
Factorization Calculus And Geometric Probability
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Author : R. V. Ambartzumian
language : en
Publisher: Cambridge University Press
Release Date : 1990-09-28
Factorization Calculus And Geometric Probability written by R. V. Ambartzumian and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1990-09-28 with Mathematics categories.
The classical subjects of geometric probability and integral geometry, and the more modern one of stochastic geometry, are developed here in a novel way to provide a framework in which they can be studied. The author focuses on factorization properties of measures and probabilities implied by the assumption of their invariance with respect to a group, in order to investigate nontrivial factors. The study of these properties is the central theme of the book. Basic facts about integral geometry and random point process theory are developed in a simple geometric way, so that the whole approach is suitable for a nonspecialist audience. Even in the later chapters, where the factorization principles are applied to geometrical processes, the only prerequisites are standard courses on probability and analysis. The main ideas presented have application to such areas as stereology and geometrical statistics and this book will be a useful reference book for university students studying probability theory and stochastic geometry, and research mathematicians interested in this area.
Geometric Methods And Optimization Problems
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Author : Vladimir Boltyanski
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-12-11
Geometric Methods And Optimization Problems written by Vladimir Boltyanski and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-12-11 with Mathematics categories.
VII Preface In many fields of mathematics, geometry has established itself as a fruitful method and common language for describing basic phenomena and problems as well as suggesting ways of solutions. Especially in pure mathematics this is ob vious and well-known (examples are the much discussed interplay between lin ear algebra and analytical geometry and several problems in multidimensional analysis). On the other hand, many specialists from applied mathematics seem to prefer more formal analytical and numerical methods and representations. Nevertheless, very often the internal development of disciplines from applied mathematics led to geometric models, and occasionally breakthroughs were b~ed on geometric insights. An excellent example is the Klee-Minty cube, solving a problem of linear programming by transforming it into a geomet ric problem. Also the development of convex programming in recent decades demonstrated the power of methods that evolved within the field of convex geometry. The present book focuses on three applied disciplines: control theory, location science and computational geometry. It is our aim to demonstrate how methods and topics from convex geometry in a wider sense (separation theory of convex cones, Minkowski geometry, convex partitionings, etc.) can help to solve various problems from these disciplines.
Multivariable Calculus
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Author : F. Beatrous
language : en
Publisher:
Release Date : 2002
Multivariable Calculus written by F. Beatrous and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2002 with Mathematics categories.
For a one-semester sophomore-level course in multivariable calculus, for Engineering, Mathematics, or Science students. Reform ideas, traditional ideas, and original ideas are combined in this text that is designed to teach concepts and computations, especially intuitive ones about the geometry of 3 space. The core concepts of multivariable calculus are presented in a straightforward, but never simplistic language that will familiarize students with the thinking and speaking habits of mathematicians and ease their access to the mathematics of applications and higher mathematics courses. *Students are engaged through formulas and geometric reasoning-In addition to calculating accurately, students are asked to draw accurately in both two and three dimensions, reason geometrically from figures, make estimates based on ruler-and pencil-constructions, and present their results verbally. *Helps students learn conceptual reasoning and reinforces learning by asking students to work the material in two different modes. *This is a spiral bound text. *Lays flat so students can draw in blank diagrams while reading the text. *A multitude of exercises are interwoven within the flow of the text-T
Calculus Of Variations And Geometric Evolution Problems
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Author : F. Bethuel
language : en
Publisher: Springer
Release Date : 2006-11-14
Calculus Of Variations And Geometric Evolution Problems written by F. Bethuel and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-11-14 with Mathematics categories.
The international summer school on Calculus of Variations and Geometric Evolution Problems was held at Cetraro, Italy, 1996. The contributions to this volume reflect quite closely the lectures given at Cetraro which have provided an image of a fairly broad field in analysis where in recent years we have seen many important contributions. Among the topics treated in the courses were variational methods for Ginzburg-Landau equations, variational models for microstructure and phase transitions, a variational treatment of the Plateau problem for surfaces of prescribed mean curvature in Riemannian manifolds - both from the classical point of view and in the setting of geometric measure theory.