Continuum Mechanics: Mass Conservation

This lecture covers the development of the global principle of mass conservation in continuum mechanics, including the definition of a body, vector transformation laws, and the derivation of the local expression for mass conservation using the principle of locality. The slides progress from defining stress and dynamics to discussing constitutive laws and continuum mechanics theory. The lecture emphasizes the geometry of body motion, solid deformation, and the tools needed for expressing and solving problems in continuum mechanics, such as tensor calculus. It concludes with a detailed explanation of the density of flux in a continuum and the projection of mass flux density vectors. The instructor also explores the transformation of vectors and the local statement of mass conservation.