Differential Forms with Applications to the Physical Sciences (Google eBook)
A graduate-level text introducing the use of exterior differential forms as a powerful tool in the analysis of a variety of mathematical problems in the physical and engineering sciences. Directed primarily to graduate-level engineers and physical scientists, it has also been used successfully to introduce modern differential geometry to graduate students in mathematics. Includes 45 illustrations. Index.
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2-chain afﬁne affine connection apply boundary cijk coefﬁcients compute consider constants of structure contact transformation convex coordinate neighborhood coordinate system corresponding curvature curve deﬁned denote determinant differential equations differential forms differential geometry domain equations of motion Euclidean space example expressed exterior derivative exterior product ﬁnd ﬁnite ﬁt ﬁx ﬁxed follows formula frame e1 free of dt function f given hence hypersurface implies inner product integrability conditions integral-invariant Laplacian linear transformation linearly independent manifold matrix moves by parallel moving frame multiplication n-dimensional normal notation one-forms oriented orthogonal orthonormal basis p-form p-vectors parallel displacement proof prove real numbers relations result Rham’s Riemannian geometry right invariant satisﬁes satisfying Section Show skew-symmetric smooth functions solution spherical Suppose symmetric tangent space tangent vector tensor theorem trajectory two-form unique variables vector ﬁeld veriﬁed write