Differential Geometry with Applications to Mechanics and PhysicsCRC Press, 12/09/2000 - 480 من الصفحات 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. |
المحتوى
Preface | 1 |
2 | 8 |
Differentiation of R into Banach | 17 |
Exercises | 30 |
MANIFOLDS | 37 |
Differentiable mappings | 50 |
Submanifolds | 64 |
2 | 71 |
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 | 80 |
TANGENT BUNDLEVECTOR FIELDONEPARAMETER | 91 |
Lie algebra structure | 97 |
2 | 104 |
Exercises | 111 |
COTANGENT BUNDLE VECTOR BUNDLE OF TENSORS | 125 |
Exercises | 136 |
Exercises | 144 |
EXTERIOR DIFFERENTIAL FORMS | 153 |
Differential forms on a manifold | 162 |
Exterior differentiation | 170 |
Exercises | 178 |
Exercises | 310 |
LAGRANGE AND HAMILTON MECHANICS | 325 |
Canonical transformations and integral invariants | 344 |
Exercises | 381 |
Canonical transformations in mechanics | 404 |
HamiltonJacobi equation | 415 |
A variational principle of analytical mechanics | 422 |
Exercises | 429 |
| 443 | |
| 449 | |
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عبارات ومصطلحات مألوفة
Answer atlas ax¹ Banach basis bijection bracket chart class C¹ components coordinate system cose cotangent bundle covector deduce defined definition denoted differentiable manifold differentiable mapping differential equation differential form domain dx¹ dx² dx³ Example Exercise expression Əqi Əx¹ form of degree group of diffeomorphisms Hamiltonian homeomorphism implies integral curve isomorphism Jacobian Lie algebra Lie derivative mapping f mapping ƒ mapping of class matrix metric neighborhood notion one-form one-parameter group open set p-form P₁ P₂ phase space point xe Poisson bracket Proof prove pull-back Remark respect Riemannian submanifold symplectic tangent bundle tangent vector tensor field tensor of type theorem topological space U₁ vector bundle vector field vector space zero ән дн др ду дх