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| Author | : Gilbert de B. Robinson |
| Publisher | : Courier Corporation |
| Total Pages | : 194 |
| Release | : 2013-10-10 |
| Genre | : Mathematics |
| ISBN | : 0486321045 |
Concise undergraduate-level text by a prominent mathematician explores the relationship between algebra and geometry. An elementary course in plane geometry is the sole requirement. Includes answers to exercises. 1962 edition.
| Author | : Melvin Hausner |
| Publisher | : Courier Dover Publications |
| Total Pages | : 417 |
| Release | : 2018-10-17 |
| Genre | : Mathematics |
| ISBN | : 0486835391 |
A fascinating exploration of the correlation between geometry and linear algebra, this text portrays the former as a subject better understood by the use and development of the latter rather than as an independent field. The treatment offers elementary explanations of the role of geometry in other branches of math and science — including physics, analysis, and group theory — as well as its value in understanding probability, determinant theory, and function spaces. Outstanding features of this volume include discussions of systematic geometric motivations in vector space theory and matrix theory; the use of the center of mass in geometry, with an introduction to barycentric coordinates; axiomatic development of determinants in a chapter dealing with area and volume; and a careful consideration of the particle problem. Students and other mathematically inclined readers will find that this inquiry into the interplay between geometry and other areas offers an enriched appreciation of both subjects.
| Author | : Seymour Schuster |
| Publisher | : |
| Total Pages | : 213 |
| Release | : 1962-01-01 |
| Genre | : Geometry |
| ISBN | : 9780471764946 |
| Author | : Anastasios Mallios |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 457 |
| Release | : 2012-12-06 |
| Genre | : Mathematics |
| ISBN | : 9401150060 |
This two-volume monograph obtains fundamental notions and results of the standard differential geometry of smooth (CINFINITY) manifolds, without using differential calculus. Here, the sheaf-theoretic character is emphasised. This has theoretical advantages such as greater perspective, clarity and unification, but also practical benefits ranging from elementary particle physics, via gauge theories and theoretical cosmology (`differential spaces'), to non-linear PDEs (generalised functions). Thus, more general applications, which are no longer `smooth' in the classical sense, can be coped with. The treatise might also be construed as a new systematic endeavour to confront the ever-increasing notion that the `world around us is far from being smooth enough'. Audience: This work is intended for postgraduate students and researchers whose work involves differential geometry, global analysis, analysis on manifolds, algebraic topology, sheaf theory, cohomology, functional analysis or abstract harmonic analysis.
| Author | : Serge Lang |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 624 |
| Release | : 2012-12-06 |
| Genre | : Mathematics |
| ISBN | : 1461210682 |
This new, revised edition covers all of the basic topics in calculus of several variables, including vectors, curves, functions of several variables, gradient, tangent plane, maxima and minima, potential functions, curve integrals, Green’s theorem, multiple integrals, surface integrals, Stokes’ theorem, and the inverse mapping theorem and its consequences. It includes many completely worked-out problems.
| Author | : Gabriel Weinreich |
| Publisher | : University of Chicago Press |
| Total Pages | : 132 |
| Release | : 1998-07-06 |
| Genre | : Mathematics |
| ISBN | : 9780226890487 |
Every advanced undergraduate and graduate student of physics must master the concepts of vectors and vector analysis. Yet most books cover this topic by merely repeating the introductory-level treatment based on a limited algebraic or analytic view of the subject. Geometrical Vectors introduces a more sophisticated approach, which not only brings together many loose ends of the traditional treatment, but also leads directly into the practical use of vectors in general curvilinear coordinates by carefully separating those relationships which are topologically invariant from those which are not. Based on the essentially geometric nature of the subject, this approach builds consistently on students' prior knowledge and geometrical intuition. Written in an informal and personal style, Geometrical Vectors provides a handy guide for any student of vector analysis. Clear, carefully constructed line drawings illustrate key points in the text, and problem sets as well as physical examples are provided.
| Author | : C. E. Springer |
| Publisher | : Courier Corporation |
| Total Pages | : 258 |
| Release | : 2013-09-26 |
| Genre | : Mathematics |
| ISBN | : 048632091X |
Assuming only a knowledge of basic calculus, this text's elementary development of tensor theory focuses on concepts related to vector analysis. The book also forms an introduction to metric differential geometry. 1962 edition.
| Author | : Shoshichi Kobayashi |
| Publisher | : Princeton University Press |
| Total Pages | : 317 |
| Release | : 2014-07-14 |
| Genre | : Mathematics |
| ISBN | : 1400858682 |
Holomorphic vector bundles have become objects of interest not only to algebraic and differential geometers and complex analysts but also to low dimensional topologists and mathematical physicists working on gauge theory. This book, which grew out of the author's lectures and seminars in Berkeley and Japan, is written for researchers and graduate students in these various fields of mathematics. Originally published in 1987. The Princeton Legacy Library uses the latest print-on-demand technology to again make available previously out-of-print books from the distinguished backlist of Princeton University Press. These editions preserve the original texts of these important books while presenting them in durable paperback and hardcover editions. The goal of the Princeton Legacy Library is to vastly increase access to the rich scholarly heritage found in the thousands of books published by Princeton University Press since its founding in 1905.
| Author | : Alan Macdonald |
| Publisher | : Createspace Independent Publishing Platform |
| Total Pages | : 0 |
| Release | : 2012 |
| Genre | : Calculus |
| ISBN | : 9781480132450 |
This textbook for the undergraduate vector calculus course presents a unified treatment of vector and geometric calculus. This is the printing of August 2022. The book is a sequel to the text Linear and Geometric Algebra by the same author. That text is a prerequisite for this one. Its web page is at faculty.luther.edu/ macdonal/laga. Linear algebra and vector calculus have provided the basic vocabulary of mathematics in dimensions greater than one for the past one hundred years. Just as geometric algebra generalizes linear algebra in powerful ways, geometric calculus generalizes vector calculus in powerful ways. Traditional vector calculus topics are covered, as they must be, since readers will encounter them in other texts and out in the world. Differential geometry is used today in many disciplines. A final chapter is devoted to it. Download the book's table of contents, preface, and index at the book's web site: faculty.luther.edu/ macdonal/vagc. From a review of Linear and Geometric Algebra: Alan Macdonald's text is an excellent resource if you are just beginning the study of geometric algebra and would like to learn or review traditional linear algebra in the process. The clarity and evenness of the writing, as well as the originality of presentation that is evident throughout this text, suggest that the author has been successful as a mathematics teacher in the undergraduate classroom. This carefully crafted text is ideal for anyone learning geometric algebra in relative isolation, which I suspect will be the case for many readers. -- Jeffrey Dunham, William R. Kenan Jr. Professor of Natural Sciences, Middlebury College
| Author | : A. R. Vasishtha |
| Publisher | : Krishna Prakashan Media |
| Total Pages | : 581 |
| Release | : |
| Genre | : |
| ISBN | : 8182835372 |
