Continuum Mechanics: The Continuum Hypothesis

This lecture introduces the concept of Continuum Mechanics, which focuses on the study of forces and bodies' response without considering small scales explicitly. The Continuum Hypothesis is explained through the evaluation of gas density and mass, emphasizing the continuum body's treatment. By using asymptotics and scaling, the lecture demonstrates how the continuum hypothesis is a valuable mathematical modeling tool in solving mechanical problems. The discussion concludes by highlighting the significance of effectively ignoring the molecular nature of matter when evaluating appropriate scales.