Modern Geometry With Applications
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Author | : George A. Jennings |
Publisher | : Springer Science & Business Media |
Total Pages | : 193 |
Release | : 2012-12-06 |
Genre | : Mathematics |
ISBN | : 1461208556 |
Download Modern Geometry with Applications Book in PDF, Epub and Kindle
This introduction to modern geometry differs from other books in the field due to its emphasis on applications and its discussion of special relativity as a major example of a non-Euclidean geometry. Additionally, it covers the two important areas of non-Euclidean geometry, spherical geometry and projective geometry, as well as emphasising transformations, and conics and planetary orbits. Much emphasis is placed on applications throughout the book, which motivate the topics, and many additional applications are given in the exercises. It makes an excellent introduction for those who need to know how geometry is used in addition to its formal theory.
Author | : B.A. Dubrovin |
Publisher | : Springer Science & Business Media |
Total Pages | : 452 |
Release | : 1985-08-05 |
Genre | : Mathematics |
ISBN | : 0387961623 |
Download Modern Geometry— Methods and Applications Book in PDF, Epub and Kindle
Up until recently, Riemannian geometry and basic topology were not included, even by departments or faculties of mathematics, as compulsory subjects in a university-level mathematical education. The standard courses in the classical differential geometry of curves and surfaces which were given instead (and still are given in some places) have come gradually to be viewed as anachronisms. However, there has been hitherto no unanimous agreement as to exactly how such courses should be brought up to date, that is to say, which parts of modern geometry should be regarded as absolutely essential to a modern mathematical education, and what might be the appropriate level of abstractness of their exposition. The task of designing a modernized course in geometry was begun in 1971 in the mechanics division of the Faculty of Mechanics and Mathematics of Moscow State University. The subject-matter and level of abstractness of its exposition were dictated by the view that, in addition to the geometry of curves and surfaces, the following topics are certainly useful in the various areas of application of mathematics (especially in elasticity and relativity, to name but two), and are therefore essential: the theory of tensors (including covariant differentiation of them); Riemannian curvature; geodesics and the calculus of variations (including the conservation laws and Hamiltonian formalism); the particular case of skew-symmetric tensors (i. e.
Author | : George Jennings |
Publisher | : |
Total Pages | : 204 |
Release | : 1994 |
Genre | : Mathematics |
ISBN | : |
Download Modern Geometry with Applications Book in PDF, Epub and Kindle
This is an introduction to the theory and applications of modern geometry. It differs from other books in its field in its emphasis on applications and its discussion of Special Relativity as a major example of a non-Euclidean geometry. Besides Special Relativity, it covers two other important areas of non-Euclidean geometry: spherical geometry (used in navigation and astronomy) and projective geometry (used in art). In addition, it reviews many useful topics from Euclidean geometry, emphasizing transformations, and includes a chapter on conics and planetary orbits. Applications are stressed throughout the book. Every topic is motivated by an application and many additional applications are given in the exercises. The book would be an excellent introduction to higher geometry for those students, especially prospective mathematics and teachers, who need to know how geometry is used in addition to its formal theory.
Author | : B.A. Dubrovin |
Publisher | : Springer Science & Business Media |
Total Pages | : 447 |
Release | : 2012-12-06 |
Genre | : Mathematics |
ISBN | : 146121100X |
Download Modern Geometry— Methods and Applications Book in PDF, Epub and Kindle
Up until recently, Riemannian geometry and basic topology were not included, even by departments or faculties of mathematics, as compulsory subjects in a university-level mathematical education. The standard courses in the classical differential geometry of curves and surfaces which were given instead (and still are given in some places) have come gradually to be viewed as anachronisms. However, there has been hitherto no unanimous agreement as to exactly how such courses should be brought up to date, that is to say, which parts of modern geometry should be regarded as absolutely essential to a modern mathematical education, and what might be the appropriate level of abstractness of their exposition. The task of designing a modernized course in geometry was begun in 1971 in the mechanics division of the Faculty of Mechanics and Mathematics of Moscow State University. The subject-matter and level of abstractness of its exposition were dictated by the view that, in addition to the geometry of curves and surfaces, the following topics are certainly useful in the various areas of application of mathematics (especially in elasticity and relativity, to name but two), and are therefore essential: the theory of tensors (including covariant differentiation of them); Riemannian curvature; geodesics and the calculus of variations (including the conservation laws and Hamiltonian formalism); the particular case of skew-symmetric tensors (i. e.
Author | : Michael Henle |
Publisher | : Pearson |
Total Pages | : 404 |
Release | : 2001 |
Genre | : Mathematics |
ISBN | : |
Download Modern Geometries Book in PDF, Epub and Kindle
Engaging, accessible, and extensively illustrated, this brief, but solid introduction to modern geometry describes geometry as it is understood and used by contemporary mathematicians and theoretical scientists. Basically non-Euclidean in approach, it relates geometry to familiar ideas from analytic geometry, staying firmly in the Cartesian plane. It uses the principle geometric concept of congruence or geometric transformation--introducing and using the Erlanger Program explicitly throughout. It features significant modern applications of geometry--e.g., the geometry of relativity, symmetry, art and crystallography, finite geometry and computation. Covers a full range of topics from plane geometry, projective geometry, solid geometry, discrete geometry, and axiom systems. For anyone interested in an introduction to geometry used by contemporary mathematicians and theoretical scientists.
Author | : Walter A. Meyer |
Publisher | : Elsevier |
Total Pages | : 560 |
Release | : 2006-02-21 |
Genre | : Mathematics |
ISBN | : 0080478034 |
Download Geometry and Its Applications Book in PDF, Epub and Kindle
Meyer's Geometry and Its Applications, Second Edition, combines traditional geometry with current ideas to present a modern approach that is grounded in real-world applications. It balances the deductive approach with discovery learning, and introduces axiomatic, Euclidean geometry, non-Euclidean geometry, and transformational geometry. The text integrates applications and examples throughout and includes historical notes in many chapters. The Second Edition of Geometry and Its Applications is a significant text for any college or university that focuses on geometry's usefulness in other disciplines. It is especially appropriate for engineering and science majors, as well as future mathematics teachers. Realistic applications integrated throughout the text, including (but not limited to): Symmetries of artistic patterns Physics Robotics Computer vision Computer graphics Stability of architectural structures Molecular biology Medicine Pattern recognition Historical notes included in many chapters
Author | : B. A. Dubrovin |
Publisher | : Springer Science & Business Media |
Total Pages | : 432 |
Release | : 1984 |
Genre | : Geometry |
ISBN | : 0387972714 |
Download Modern Geometry - Methods and Applications Book in PDF, Epub and Kindle
Part II. The geometry and topology of manifolds. This is the second volume of a three-volume introduction to modern geometry, with emphasis on applications to other areas of mathematics and theoretical physics. Topics covered include homotopy groups, fibre bundles, dynamical systems, and foliations. The exposition is simple and concrete, and in a terminology palatable to physicists.
Author | : Leonard M. Blumenthal |
Publisher | : Courier Dover Publications |
Total Pages | : 209 |
Release | : 2017-04-19 |
Genre | : Mathematics |
ISBN | : 0486821137 |
Download A Modern View of Geometry Book in PDF, Epub and Kindle
Elegant exposition of postulation geometry of planes offers rigorous, lucid treatment of coordination of affine and projective planes, set theory, propositional calculus, affine planes with Desargues and Pappus properties, more. 1961 edition.
Author | : Roger A. Johnson |
Publisher | : Courier Corporation |
Total Pages | : 338 |
Release | : 2013-01-08 |
Genre | : Mathematics |
ISBN | : 048615498X |
Download Advanced Euclidean Geometry Book in PDF, Epub and Kindle
This classic text explores the geometry of the triangle and the circle, concentrating on extensions of Euclidean theory, and examining in detail many relatively recent theorems. 1929 edition.
Author | : John Oprea |
Publisher | : MAA |
Total Pages | : 508 |
Release | : 2007-09-06 |
Genre | : Mathematics |
ISBN | : 9780883857489 |
Download Differential Geometry and Its Applications Book in PDF, Epub and Kindle
This book studies the differential geometry of surfaces and its relevance to engineering and the sciences.