Applied Differential Geometry

  • Filename: applied-differential-geometry.
  • ISBN: 0521269296
  • Release Date: 1985-05-31
  • Number of pages: 414
  • Author: William L. Burke
  • Publisher: Cambridge University Press

This is a self-contained introductory textbook on the calculus of differential forms and modern differential geometry. The intended audience is physicists, so the author emphasises applications and geometrical reasoning in order to give results and concepts a precise but intuitive meaning without getting bogged down in analysis. The large number of diagrams helps elucidate the fundamental ideas. Mathematical topics covered include differentiable manifolds, differential forms and twisted forms, the Hodge star operator, exterior differential systems and symplectic geometry. All of the mathematics is motivated and illustrated by useful physical examples.

Applied Differential Geometry

  • Filename: applied-differential-geometry.
  • ISBN: 9789812770721
  • Release Date: 2007
  • Number of pages: 1311
  • Author:
  • Publisher: World Scientific

This graduate-level monographic textbook treats applied differential geometry from a modern scientific perspective. Co-authored by the originator of the worldOCOs leading human motion simulator OCo OC Human Biodynamics EngineOCO, a complex, 264-DOF bio-mechanical system, modeled by differential-geometric tools OCo this is the first book that combines modern differential geometry with a wide spectrum of applications, from modern mechanics and physics, via nonlinear control, to biology and human sciences. The book is designed for a two-semester course, which gives mathematicians a variety of applications for their theory and physicists, as well as other scientists and engineers, a strong theory underlying their models."

Modern Differential Geometry for Physicists

  • Filename: modern-differential-geometry-for-physicists.
  • ISBN: 9810235623
  • Release Date: 1999
  • Number of pages: 289
  • Author: Chris J. Isham
  • Publisher: World Scientific

"The result is a book which provides a rapid initiation to the material in question with care and sufficient detail to allow the reader to emerge with a genuine familiarity with the foundations of these subjects".Mathematical Reviews"This book is carefully written, and attention is paid to rigor and relevant details The key notions are discussed with great care and from many points of view, which attenuates the shock of the formalism". Mathematical Reviews

Differential Geometry Applied to Dynamical Systems

  • Filename: differential-geometry-applied-to-dynamical-systems.
  • ISBN: 9789814277143
  • Release Date: 2009
  • Number of pages: 312
  • Author: Jean-Marc Ginoux
  • Publisher: World Scientific

This book aims to present a new approach called Flow Curvature Method that applies Differential Geometry to Dynamical Systems. Hence, for a trajectory curve, an integral of any n-dimensional dynamical system as a curve in Euclidean n-space, the curvature of the trajectory — or the flow — may be analytically computed. Then, the location of the points where the curvature of the flow vanishes defines a manifold called flow curvature manifold. Such a manifold being defined from the time derivatives of the velocity vector field, contains information about the dynamics of the system, hence identifying the main features of the system such as fixed points and their stability, local bifurcations of codimension one, center manifold equation, normal forms, linear invariant manifolds (straight lines, planes, hyperplanes).In the case of singularly perturbed systems or slow-fast dynamical systems, the flow curvature manifold directly provides the slow invariant manifold analytical equation associated with such systems. Also, starting from the flow curvature manifold, it will be demonstrated how to find again the corresponding dynamical system, thus solving the inverse problem.

Applicable Differential Geometry

  • Filename: applicable-differential-geometry.
  • ISBN: 0521231906
  • Release Date: 1986
  • Number of pages: 394
  • Author: M. Crampin
  • Publisher: Cambridge University Press

An introduction to geometrical topics used in applied mathematics and theoretical physics.

Differential Geometry

  • Filename: differential-geometry.
  • ISBN: 0821854070
  • Release Date: 1987-12-31
  • Number of pages: 273
  • Author: Mladen Luksic
  • Publisher: American Mathematical Soc.

Normally, mathematical research has been divided into ``pure'' and ``applied,'' and only within the past decade has this distinction become blurred. However, differential geometry is one area of mathematics that has not made this distinction and has consistently played a vital role in both general areas. The papers in this volume represent the proceedings of a conference entitled ``Differential Geometry: The Interface Between Pure and Applied Mathematics,'' which was held in San Antonio, Texas, in April 1986. The purpose of the conference was to explore recent exciting applications and challenging classical problems in differential geometry. The papers represent a tremendous range of applications and techniques in such diverse areas as ordinary differential equations, Lie groups, algebra, numerical analysis, and control theory.

Differential Geometry

  • Filename: differential-geometry.
  • ISBN: 9783319069203
  • Release Date: 2014-07-02
  • Number of pages: 139
  • Author: Marcelo Epstein
  • Publisher: Springer

Differential Geometry offers a concise introduction to some basic notions of modern differential geometry and their applications to solid mechanics and physics. Concepts such as manifolds, groups, fibre bundles and groupoids are first introduced within a purely topological framework. They are shown to be relevant to the description of space-time, configuration spaces of mechanical systems, symmetries in general, microstructure and local and distant symmetries of the constitutive response of continuous media. Once these ideas have been grasped at the topological level, the differential structure needed for the description of physical fields is introduced in terms of differentiable manifolds and principal frame bundles. These mathematical concepts are then illustrated with examples from continuum kinematics, Lagrangian and Hamiltonian mechanics, Cauchy fluxes and dislocation theory. This book will be useful for researchers and graduate students in science and engineering.

Differential Geometry and Lie Groups for Physicists

  • Filename: differential-geometry-and-lie-groups-for-physicists.
  • ISBN: 9781139458030
  • Release Date: 2006-10-12
  • Number of pages:
  • Author: Marián Fecko
  • Publisher: Cambridge University Press

Differential geometry plays an increasingly important role in modern theoretical physics and applied mathematics. This textbook gives an introduction to geometrical topics useful in theoretical physics and applied mathematics, covering: manifolds, tensor fields, differential forms, connections, symplectic geometry, actions of Lie groups, bundles, spinors, and so on. Written in an informal style, the author places a strong emphasis on developing the understanding of the general theory through more than 1000 simple exercises, with complete solutions or detailed hints. The book will prepare readers for studying modern treatments of Lagrangian and Hamiltonian mechanics, electromagnetism, gauge fields, relativity and gravitation. Differential Geometry and Lie Groups for Physicists is well suited for courses in physics, mathematics and engineering for advanced undergraduate or graduate students, and can also be used for active self-study. The required mathematical background knowledge does not go beyond the level of standard introductory undergraduate mathematics courses.

Tensor Analysis and Elementary Differential Geometry for Physicists and Engineers

  • Filename: tensor-analysis-and-elementary-differential-geometry-for-physicists-and-engineers.
  • ISBN: 9783662484975
  • Release Date: 2016-08-16
  • Number of pages: 376
  • Author: Hung Nguyen-Schäfer
  • Publisher: Springer

This book comprehensively presents topics, such as Dirac notation, tensor analysis, elementary differential geometry of moving surfaces, and k-differential forms. Additionally, two new chapters of Cartan differential forms and Dirac and tensor notations in quantum mechanics are added to this second edition. The reader is provided with hands-on calculations and worked-out examples at which he will learn how to handle the bra-ket notation, tensors, differential geometry, and differential forms; and to apply them to the physical and engineering world. Many methods and applications are given in CFD, continuum mechanics, electrodynamics in special relativity, cosmology in the Minkowski four-dimensional spacetime, and relativistic and non-relativistic quantum mechanics. Tensors, differential geometry, differential forms, and Dirac notation are very useful advanced mathematical tools in many fields of modern physics and computational engineering. They are involved in special and general relativity physics, quantum mechanics, cosmology, electrodynamics, computational fluid dynamics (CFD), and continuum mechanics. The target audience of this all-in-one book primarily comprises graduate students in mathematics, physics, engineering, research scientists, and engineers.

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