Differential Geometry with Applications to Mechanics and Physics

الغلاف الأمامي
CRC Press, ١٢‏/٠٩‏/٢٠٠٠ - 480 من الصفحات
0 مراجعات
An introduction to differential geometry with applications to mechanics and physics. It covers topology and differential calculus in banach spaces; differentiable manifold and mapping submanifolds; tangent vector space; tangent bundle, vector field on manifold, Lie algebra structure, and one-parameter group of diffeomorphisms; exterior differential forms; Lie derivative and Lie algebra; n-form integration on n-manifold; Riemann geometry; and more. It includes 133 solved exercises.
 

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المحتويات

TOPOLOGY AND DIFFERENTIAL CALCULUS REQUIREMENTS
1
Exercises
30
MANIFOLDS
37
Differentiable mappings
50
Submanifolds
59
Exercises
65
TANGENT VECTOR SPACE
71
Tangentspace
80
LIE DERIVATIVE LIE GROUP
185
Frobenius theorem
204
Exercises
224
Stokes Theorem Cohomology
235
An introduction to cohomology theory
243
Exercises
253
Affine connection
285
Geodesic and Euler equation
300

Exercises
87
Tangent bundle
93
Oneparameter group of diffeomorphisms
102
COTANGENT BUNDLE VECTOR BUNDLE OF TENSORS
125
Exercises
144
EXTERIOR DIFFERENTIAL FORMS
153
Pullback of a differential form
167
Orientable manifolds
174
Exercises
310
LAGRANGE AND HAMILTON MECHANICS
325
Canonical transformations and integral invariants
344
Exercises
381
Bibliography
443
Index
449
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