Differential Geometry with Applications to Mechanics and Physics
CRC Press, ١٢/٠٩/٢٠٠٠ - 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.
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TOPOLOGY AND DIFFERENTIAL CALCULUS REQUIREMENTS
TANGENT VECTOR SPACE
LIE DERIVATIVE LIE GROUP
Stokes Theorem Cohomology
An introduction to cohomology theory
Geodesic and Euler equation
Oneparameter group of diffeomorphisms
COTANGENT BUNDLE VECTOR BUNDLE OF TENSORS
EXTERIOR DIFFERENTIAL FORMS
Pullback of a differential form
absolute integral invariant Answer atlas basis bilinear form called canonical equations canonical transformation chart class C1 components configuration space constant coordinate system cotangent bundle covector D A mapping deduce defined definition denoted differentiable manifold differentiable mapping differential equation differential form differential system domain equivalent Example Exercise expression exterior differential finite form of degree formula function geometry group of diffeomorphisms Hamilton-Jacobi equation Hamiltonian homeomorphism implies integral curve introduce isomorphism Jacobian Lagrange equations Lagrangian lecture Lie algebra Lie derivative mapping of class matrix metric tensor neighborhood nonzero notion obtain one-form one-parameter group orbits orientable p-form particles phase space Poisson bracket Proof prove pull-back Remark respect submanifold symplectic tangent bundle tangent vector tensor field tensor of type theorem topological space trajectory vector bundle vector field vector space velocity zero