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Vector Algebra in Three Dimensions
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4-vector angle arbitrary atomic axis boundary conditions Cartesian coordinates collision components Consider constant continuum theory convective derivative coordinate system defined Derive Eq dimensions dipole Dirac delta function direction discussion displacement dp/dt dv/dt dyadic elastic electron element equal equation of motion Exercise expression flow force frequency function of position gradient gravitational Green's function Hamilton's identity incompressible invariant irrotational kinetic energy Lagrangian function Laplace's equation length linear Lorentz transformation mass material mathematical Maxwell-Boltzmann distribution membrane modulus momenta momentum space normal modes notation particle path phase space physical plane polar coordinates problem Prove quadrupole radius region relative represented result rotation satisfy scalar product shear solution of Laplace's speed sphere spherical strain stress matrix string surface integral symmetrical tensor theorem total energy unit area unit vectors unit volume vanishes variables variation principle vector function wave equation write zero