Differential Geometry and Its Applications

John Oprea

494 pages, parution le 06/01/2004 (2^eme édition)

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Résumé

For undergraduate courses in Differential Geometry.

Designed not just for the math major but for all students of science, this text provides an introduction to the basics of the calculus of variations and optimal control theory as well as differential geometry. It then applies these essential ideas to understand various phenomena, such as soap film formation and particle motion on surfaces.

Features

NEW - New section on industrial applications of differential geometry - Shows engineering and physics students the practical applications of what they are learning to industry.
NEW - New Maple projects for calculation and visualization - Provides students with another practical side to pure math.
NEW - New examples for Gauss-Bonnet.
Immediate focus on surfaces - Allows the text to be used for a one-semester course while still covering interesting material that prepares students for future geometry courses.
Explorations of concepts using the symbolic computational software, MAPLE - Including how geodesics may be plotted on surfaces; an illustration of the Clairaut relation; how particles move under the influence of gravity, but constrained to a surface; why Ennepers surface is minimal, but not area minimizing - Allows students to see (and therefore believe) the mathematics that has been described.
Duplication of results for surfaces and higher dimensional manifolds - Encourages students to make the transition from easily visualizable mathematics to more abstract kinds.
Spiral coverage of topics - Revisits the same topics from different viewpoints throughout the text (e.g. geodesics, least area surfaces of revolution, surfaces of Delaunay) - Shows students a unity in mathematics and its applications.
An honestly mathematical writing style that is easily understood by science majors - Allows majors and non-majors alike to read and understand the material.
An interdisciplinary approach - Highlights for students the interconnections among various kinds of mathematics and sciences.
An entire chapter devoted to an exposition of the calculus of variations from first principles.
Brief reviews of relevant ideas from linear algebra and complex variables - Helps students with weaker backgrounds.
Over 80 worked examples - Provides students with fundamental models and illustrations of important concepts.
Over 400 exercises - Including many that are computational, while others require proofs or characterizations of geometric phenomena - Gives students ample opportunity to practice the concepts learned.

Sommaire

The Geometry of Curves
Surfaces
Curvature(s)
Constant Mean Curvature Surfaces
Geodesics, Metrics and Isometries
Holonomy and the Gauss-Bonnet Theorem
Minimal Surfaces and Complex Variables
The Calculus of Variations and Geometry
A Glimpse at Higher Dimensions

List of Examples, Definitions and Remarks
Answers and Hints to Selected Exercises
References
Index

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Caractéristiques techniques

	PAPIER
Éditeur(s)	Prentice Hall
Auteur(s)	John Oprea
Parution	06/01/2004
Édition	2^eme édition
Nb. de pages	494
Couverture	Relié
Poids	760g
Intérieur	Noir et Blanc
EAN13	9780130652461