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...Lectures on vector calculus paul renteln department of physics california state university san bernardino ca march revised c ii contents algebra and index notation orthonormality the kronecker delta components dummy indices i dot product einstein summation convention products lengths angles rotations matrices cross levi civita symbol epsilon symbols determinants iii tensor problems fields gradient lagrange multipliers divergence laplacian curl with other coordinate systems change variables from cartesian to spherical polar derivations derivatives unit vectors in a non basis operators coordinates integration line integrals surface volume integral theorems green s theorem stokes gauss generalized permutations b determinant as multilinear map cofactors adjugate multiplicative homomorphism cramer rule iv...