Applied Differential Geometry: A Modern Introduction

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World Scientific, 2007 - Geometry, Differential - 1311 pages
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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."
 

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Contents

Introductio
1
239
3
Lie Groups
30
Tensors Actions and Functors
51
Z in Rl
59
1
109
i
121
Applied Manifold Geometry
137
1
555
1
587
1
597
1
715
5 Applied Jet Geometry
797
j1
868
Geometrical Path Integrals and Their Applications
983
The Basic Form of a Path Integral
996

Manifolds
148
Motions
216
Manifoldl
222
Manoeuvresl
228
1
268
1
462
1
470
4 Applied Bundle Geometry
485
4
501
4 5
508
Hamiltonian Path Integral
1003
1
1032
1
1149
i
1188
String Theory
1232
i
1247
Bibliography
1253
Ifafel
1295
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