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Differential Forms

Author: Henri Cartan
Publisher: Courier Corporation
ISBN: 0486139115
Size: 29.49 MB
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The famous mathematician addresses both pure and applied branches of mathematics in a book equally essential as a text, reference, or a brilliant mathematical exercise. "Superb." — Mathematical Review. 1971 edition.

Tensors Differential Forms And Variational Principles

Author: David Lovelock
Publisher: Courier Corporation
ISBN: 048613198X
Size: 43.72 MB
Format: PDF
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Incisive, self-contained account of tensor analysis and the calculus of exterior differential forms, interaction between the concept of invariance and the calculus of variations. Emphasis is on analytical techniques. Includes problems.

Cohomology And Differential Forms

Author: Izu Vaisman
Publisher: Courier Dover Publications
ISBN: 0486815129
Size: 76.96 MB
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Self-contained development of cohomological theory of manifolds with various sheaves and its application to differential geometry covers categories and functions, sheaves and cohomology, fiber and vector bundles, and cohomology classes and differential forms. 1973 edition.

A Geometric Approach To Differential Forms

Author: David Bachman
Publisher: Springer Science & Business Media
ISBN: 0817683046
Size: 22.73 MB
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This text presents differential forms from a geometric perspective accessible at the undergraduate level. It begins with basic concepts such as partial differentiation and multiple integration and gently develops the entire machinery of differential forms. The subject is approached with the idea that complex concepts can be built up by analogy from simpler cases, which, being inherently geometric, often can be best understood visually. Each new concept is presented with a natural picture that students can easily grasp. Algebraic properties then follow. The book contains excellent motivation, numerous illustrations and solutions to selected problems.

Differential Geometry Of Curves And Surfaces

Author: Manfredo P. do Carmo
Publisher: Courier Dover Publications
ISBN: 0486806995
Size: 29.11 MB
Format: PDF, Mobi
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One of the most widely used texts in its field, this volume introduces the differential geometry of curves and surfaces in both local and global aspects. The presentation departs from the traditional approach with its more extensive use of elementary linear algebra and its emphasis on basic geometrical facts rather than machinery or random details. Many examples and exercises enhance the clear, well-written exposition, along with hints and answers to some of the problems. The treatment begins with a chapter on curves, followed by explorations of regular surfaces, the geometry of the Gauss map, the intrinsic geometry of surfaces, and global differential geometry. Suitable for advanced undergraduates and graduate students of mathematics, this text's prerequisites include an undergraduate course in linear algebra and some familiarity with the calculus of several variables. For this second edition, the author has corrected, revised, and updated the entire volume.

Thinking In Problems

Author: Alexander A. Roytvarf
Publisher: Springer Science & Business Media
ISBN: 0817684069
Size: 73.62 MB
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This concise, self-contained textbook gives an in-depth look at problem-solving from a mathematician’s point-of-view. Each chapter builds off the previous one, while introducing a variety of methods that could be used when approaching any given problem. Creative thinking is the key to solving mathematical problems, and this book outlines the tools necessary to improve the reader’s technique. The text is divided into twelve chapters, each providing corresponding hints, explanations, and finalization of solutions for the problems in the given chapter. For the reader’s convenience, each exercise is marked with the required background level. This book implements a variety of strategies that can be used to solve mathematical problems in fields such as analysis, calculus, linear and multilinear algebra and combinatorics. It includes applications to mathematical physics, geometry, and other branches of mathematics. Also provided within the text are real-life problems in engineering and technology. Thinking in Problems is intended for advanced undergraduate and graduate students in the classroom or as a self-study guide. Prerequisites include linear algebra and analysis.

Differential Geometry

Author: Erwin Kreyszig
Publisher: Courier Corporation
ISBN: 0486318621
Size: 59.66 MB
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An introductory textbook on the differential geometry of curves and surfaces in 3-dimensional Euclidean space, presented in its simplest, most essential form. With problems and solutions. Includes 99 illustrations.

Invariants Of Quadratic Differential Forms

Author: Joseph Edmund Wright
Publisher: Courier Corporation
ISBN: 0486497682
Size: 21.55 MB
Format: PDF
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"This classic monograph by a mathematician affiliated with Trinity College, Cambridge, offers a brief account of the invariant theory connected with a single quadratic differential form. A historical overview is followed by considerations of the methods of Christoffel and Lie as well as Maschke's symbolic method and explorations of geometrical and dynamical methods. 1960 edition"--